algebra.algebra.subalgebra.basic | Mathlib porting status

(last sync)

feat(ring_theory/subring): centralizer as a subring (#18861)

Co-authored-by: Eric Rodriguez <37984851+ericrbg@users.noreply.github.com>

Diff

@@ -1049,10 +1049,15 @@ lemma mem_centralizer_iff {s : set A} {z : A} :
   z ∈ centralizer R s ↔ ∀ g ∈ s, g * z = z * g :=
 iff.rfl
 
+lemma center_le_centralizer (s) : center R A ≤ centralizer R s := s.center_subset_centralizer
+
 lemma centralizer_le (s t : set A) (h : s ⊆ t) :
   centralizer R t ≤ centralizer R s :=
 set.centralizer_subset h
 
+@[simp] lemma centralizer_eq_top_iff_subset {s : set A} : centralizer R s = ⊤ ↔ s ⊆ center R A :=
+set_like.ext'_iff.trans set.centralizer_eq_top_iff_subset
+
 @[simp]
 lemma centralizer_univ : centralizer R set.univ = center R A :=
 set_like.ext' (set.centralizer_univ A)

fix(algebra/module/submodule/basic): remove submodule_class (#18902)

This is redundant in the face of smul_mem_class.

This also adds a missing instance.

Diff

@@ -98,6 +98,9 @@ S.range_subset
 theorem smul_mem {x : A} (hx : x ∈ S) (r : R) : r • x ∈ S :=
 (algebra.smul_def r x).symm ▸ mul_mem (S.algebra_map_mem r) hx
 
+instance : smul_mem_class (subalgebra R A) R A :=
+{ smul_mem := λ S r x hx, smul_mem S hx r }
+
 protected theorem one_mem : (1 : A) ∈ S := one_mem S
 protected theorem mul_mem {x y : A} (hx : x ∈ S) (hy : y ∈ S) : x * y ∈ S := mul_mem hx hy
 protected theorem pow_mem {x : A} (hx : x ∈ S) (n : ℕ) : x ^ n ∈ S := pow_mem hx n

(first ported)

Changes in mathlib3port

mathlib3

mathlib3port

bump to nightly-2024-04-09-08

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

659ec6f7

Diff

@@ -194,10 +194,10 @@ protected theorem nsmul_mem {x : A} (hx : x ∈ S) (n : ℕ) : n • x ∈ S :=
 #align subalgebra.nsmul_mem Subalgebra.nsmul_mem
 -/
 
-#print Subalgebra.coe_nat_mem /-
-protected theorem coe_nat_mem (n : ℕ) : (n : A) ∈ S :=
-  coe_nat_mem S n
-#align subalgebra.coe_nat_mem Subalgebra.coe_nat_mem
+#print Subalgebra.natCast_mem /-
+protected theorem natCast_mem (n : ℕ) : (n : A) ∈ S :=
+  natCast_mem S n
+#align subalgebra.coe_nat_mem Subalgebra.natCast_mem
 -/
 
 #print Subalgebra.list_prod_mem /-
@@ -264,11 +264,11 @@ protected theorem zsmul_mem {R : Type u} {A : Type v} [CommRing R] [Ring A] [Alg
 #align subalgebra.zsmul_mem Subalgebra.zsmul_mem
 -/
 
-#print Subalgebra.coe_int_mem /-
-protected theorem coe_int_mem {R : Type u} {A : Type v} [CommRing R] [Ring A] [Algebra R A]
+#print Subalgebra.intCast_mem /-
+protected theorem intCast_mem {R : Type u} {A : Type v} [CommRing R] [Ring A] [Algebra R A]
     (S : Subalgebra R A) (n : ℤ) : (n : A) ∈ S :=
-  coe_int_mem S n
-#align subalgebra.coe_int_mem Subalgebra.coe_int_mem
+  intCast_mem S n
+#align subalgebra.coe_int_mem Subalgebra.intCast_mem
 -/
 
 #print Subalgebra.toAddSubmonoid /-
@@ -1910,7 +1910,7 @@ variable {R : Type _} [Semiring R]
 #print subalgebraOfSubsemiring /-
 /-- A subsemiring is a `ℕ`-subalgebra. -/
 def subalgebraOfSubsemiring (S : Subsemiring R) : Subalgebra ℕ R :=
-  { S with algebraMap_mem' := fun i => coe_nat_mem S i }
+  { S with algebraMap_mem' := fun i => natCast_mem S i }
 #align subalgebra_of_subsemiring subalgebraOfSubsemiring
 -/

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -1180,7 +1180,7 @@ theorem coe_iInf {ι : Sort _} {S : ι → Subalgebra R A} : (↑(⨅ i, S i) :
 
 #print Algebra.mem_iInf /-
 theorem mem_iInf {ι : Sort _} {S : ι → Subalgebra R A} {x : A} : (x ∈ ⨅ i, S i) ↔ ∀ i, x ∈ S i := by
-  simp only [iInf, mem_Inf, Set.forall_range_iff]
+  simp only [iInf, mem_Inf, Set.forall_mem_range]
 #align algebra.mem_infi Algebra.mem_iInf
 -/

bump to nightly-2024-02-01-06

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

5433bded

Diff

@@ -1865,7 +1865,30 @@ end Centralizer
 theorem mem_of_finset_sum_eq_one_of_pow_smul_mem {S : Type _} [CommRing S] [Algebra R S]
     (S' : Subalgebra R S) {ι : Type _} (ι' : Finset ι) (s : ι → S) (l : ι → S)
     (e : ∑ i in ι', l i * s i = 1) (hs : ∀ i, s i ∈ S') (hl : ∀ i, l i ∈ S') (x : S)
-    (H : ∀ i, ∃ n : ℕ, (s i ^ n : S) • x ∈ S') : x ∈ S' := by classical
+    (H : ∀ i, ∃ n : ℕ, (s i ^ n : S) • x ∈ S') : x ∈ S' := by
+  classical
+  suffices x ∈ (Algebra.ofId S' S).range.toSubmodule by obtain ⟨x, rfl⟩ := this; exact x.2
+  choose n hn using H
+  let s' : ι → S' := fun x => ⟨s x, hs x⟩
+  have : Ideal.span (s' '' ι') = ⊤ :=
+    by
+    rw [Ideal.eq_top_iff_one, Ideal.span, Finsupp.mem_span_iff_total]
+    refine'
+      ⟨(Finsupp.ofSupportFinite (fun i : ι' => (⟨l i, hl i⟩ : S')) (Set.toFinite _)).mapDomain
+          fun i => ⟨s' i, i, i.2, rfl⟩,
+        S'.to_submodule.injective_subtype _⟩
+    rw [Finsupp.total_mapDomain, Finsupp.total_apply, Finsupp.sum_fintype, map_sum,
+      Submodule.subtype_apply, Subalgebra.coe_one]
+    · exact finset.sum_attach.trans e
+    · exact fun _ => zero_smul _ _
+  let N := ι'.sup n
+  have hs' := Ideal.span_pow_eq_top _ this N
+  apply (Algebra.ofId S' S).range.toSubmodule.mem_of_span_top_of_smul_mem _ hs'
+  rintro ⟨_, _, ⟨i, hi, rfl⟩, rfl⟩
+  change s i ^ N • x ∈ _
+  rw [← tsub_add_cancel_of_le (show n i ≤ N from Finset.le_sup hi), pow_add, mul_smul]
+  refine' Submodule.smul_mem _ (⟨_, pow_mem (hs i) _⟩ : S') _
+  exact ⟨⟨_, hn i⟩, rfl⟩
 #align subalgebra.mem_of_finset_sum_eq_one_of_pow_smul_mem Subalgebra.mem_of_finset_sum_eq_one_of_pow_smul_mem
 -/

bump to nightly-2024-01-31-06

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

61100fe9

Diff

@@ -1865,30 +1865,7 @@ end Centralizer
 theorem mem_of_finset_sum_eq_one_of_pow_smul_mem {S : Type _} [CommRing S] [Algebra R S]
     (S' : Subalgebra R S) {ι : Type _} (ι' : Finset ι) (s : ι → S) (l : ι → S)
     (e : ∑ i in ι', l i * s i = 1) (hs : ∀ i, s i ∈ S') (hl : ∀ i, l i ∈ S') (x : S)
-    (H : ∀ i, ∃ n : ℕ, (s i ^ n : S) • x ∈ S') : x ∈ S' := by
-  classical
-  suffices x ∈ (Algebra.ofId S' S).range.toSubmodule by obtain ⟨x, rfl⟩ := this; exact x.2
-  choose n hn using H
-  let s' : ι → S' := fun x => ⟨s x, hs x⟩
-  have : Ideal.span (s' '' ι') = ⊤ :=
-    by
-    rw [Ideal.eq_top_iff_one, Ideal.span, Finsupp.mem_span_iff_total]
-    refine'
-      ⟨(Finsupp.ofSupportFinite (fun i : ι' => (⟨l i, hl i⟩ : S')) (Set.toFinite _)).mapDomain
-          fun i => ⟨s' i, i, i.2, rfl⟩,
-        S'.to_submodule.injective_subtype _⟩
-    rw [Finsupp.total_mapDomain, Finsupp.total_apply, Finsupp.sum_fintype, map_sum,
-      Submodule.subtype_apply, Subalgebra.coe_one]
-    · exact finset.sum_attach.trans e
-    · exact fun _ => zero_smul _ _
-  let N := ι'.sup n
-  have hs' := Ideal.span_pow_eq_top _ this N
-  apply (Algebra.ofId S' S).range.toSubmodule.mem_of_span_top_of_smul_mem _ hs'
-  rintro ⟨_, _, ⟨i, hi, rfl⟩, rfl⟩
-  change s i ^ N • x ∈ _
-  rw [← tsub_add_cancel_of_le (show n i ≤ N from Finset.le_sup hi), pow_add, mul_smul]
-  refine' Submodule.smul_mem _ (⟨_, pow_mem (hs i) _⟩ : S') _
-  exact ⟨⟨_, hn i⟩, rfl⟩
+    (H : ∀ i, ∃ n : ℕ, (s i ^ n : S) • x ∈ S') : x ∈ S' := by classical
 #align subalgebra.mem_of_finset_sum_eq_one_of_pow_smul_mem Subalgebra.mem_of_finset_sum_eq_one_of_pow_smul_mem
 -/

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,10 +3,10 @@ Copyright (c) 2018 Kenny Lau. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau, Yury Kudryashov
 -/
-import Mathbin.Algebra.Algebra.Basic
-import Mathbin.Data.Set.UnionLift
-import Mathbin.LinearAlgebra.Finsupp
-import Mathbin.RingTheory.Ideal.Operations
+import Algebra.Algebra.Basic
+import Data.Set.UnionLift
+import LinearAlgebra.Finsupp
+import RingTheory.Ideal.Operations
 
 #align_import algebra.algebra.subalgebra.basic from "leanprover-community/mathlib"@"b915e9392ecb2a861e1e766f0e1df6ac481188ca"

bump to nightly-2023-08-17-09

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

60285dcc

Diff

@@ -55,7 +55,7 @@ instance : SetLike (Subalgebra R A) A
 instance : SubsemiringClass (Subalgebra R A) A
     where
   add_mem := add_mem'
-  mul_mem := mul_mem'
+  hMul_mem := hMul_mem'
   one_mem := one_mem'
   zero_mem := zero_mem'
 
@@ -107,7 +107,7 @@ protected def copy (S : Subalgebra R A) (s : Set A) (hs : s = ↑S) : Subalgebra
     where
   carrier := s
   add_mem' _ _ := hs.symm ▸ S.add_mem'
-  mul_mem' _ _ := hs.symm ▸ S.mul_mem'
+  hMul_mem' _ _ := hs.symm ▸ S.hMul_mem'
   algebraMap_mem' := hs.symm ▸ S.algebraMap_mem'
 #align subalgebra.copy Subalgebra.copy
 -/
@@ -152,7 +152,7 @@ theorem range_le : Set.range (algebraMap R A) ≤ S :=
 
 #print Subalgebra.smul_mem /-
 theorem smul_mem {x : A} (hx : x ∈ S) (r : R) : r • x ∈ S :=
-  (Algebra.smul_def r x).symm ▸ mul_mem (S.algebraMap_mem r) hx
+  (Algebra.smul_def r x).symm ▸ hMul_mem (S.algebraMap_mem r) hx
 #align subalgebra.smul_mem Subalgebra.smul_mem
 -/
 
@@ -166,7 +166,7 @@ protected theorem one_mem : (1 : A) ∈ S :=
 
 #print Subalgebra.mul_mem /-
 protected theorem mul_mem {x y : A} (hx : x ∈ S) (hy : y ∈ S) : x * y ∈ S :=
-  mul_mem hx hy
+  hMul_mem hx hy
 #align subalgebra.mul_mem Subalgebra.mul_mem
 -/
 
@@ -749,7 +749,7 @@ variable (p : Submodule R A)
 def toSubalgebra (p : Submodule R A) (h_one : (1 : A) ∈ p)
     (h_mul : ∀ x y, x ∈ p → y ∈ p → x * y ∈ p) : Subalgebra R A :=
   { p with
-    mul_mem' := h_mul
+    hMul_mem' := h_mul
     algebraMap_mem' := fun r => by
       rw [Algebra.algebraMap_eq_smul_one]
       exact p.smul_mem _ h_one }
@@ -793,7 +793,7 @@ theorem toSubalgebra_toSubmodule (p : Submodule R A) (h_one h_mul) :
 #print Subalgebra.toSubmodule_toSubalgebra /-
 @[simp]
 theorem Subalgebra.toSubmodule_toSubalgebra (S : Subalgebra R A) :
-    (S.toSubmodule.toSubalgebra S.one_mem fun _ _ => S.mul_mem) = S :=
+    (S.toSubmodule.toSubalgebra S.one_mem fun _ _ => S.hMul_mem) = S :=
   SetLike.coe_injective rfl
 #align subalgebra.to_submodule_to_subalgebra Subalgebra.toSubmodule_toSubalgebra
 -/
@@ -896,7 +896,7 @@ def equalizer (ϕ ψ : A →ₐ[R] B) : Subalgebra R A
   carrier := {a | ϕ a = ψ a}
   add_mem' x y (hx : ϕ x = ψ x) (hy : ϕ y = ψ y) := by
     rw [Set.mem_setOf_eq, ϕ.map_add, ψ.map_add, hx, hy]
-  mul_mem' x y (hx : ϕ x = ψ x) (hy : ϕ y = ψ y) := by
+  hMul_mem' x y (hx : ϕ x = ψ x) (hy : ϕ y = ψ y) := by
     rw [Set.mem_setOf_eq, ϕ.map_mul, ψ.map_mul, hx, hy]
   algebraMap_mem' x := by rw [Set.mem_setOf_eq, AlgHom.commutes, AlgHom.commutes]
 #align alg_hom.equalizer AlgHom.equalizer
@@ -1102,7 +1102,7 @@ theorem mem_sup_right {S T : Subalgebra R A} : ∀ {x : A}, x ∈ T → x ∈ S
 
 #print Algebra.mul_mem_sup /-
 theorem mul_mem_sup {S T : Subalgebra R A} {x y : A} (hx : x ∈ S) (hy : y ∈ T) : x * y ∈ S ⊔ T :=
-  (S ⊔ T).mul_mem (mem_sup_left hx) (mem_sup_right hy)
+  (S ⊔ T).hMul_mem (mem_sup_left hx) (mem_sup_right hy)
 #align algebra.mul_mem_sup Algebra.mul_mem_sup
 -/
 
@@ -1534,7 +1534,7 @@ theorem coe_iSup_of_directed [Nonempty ι] {S : ι → Subalgebra R A} (dir : Di
     ↑(iSup S) = ⋃ i, (S i : Set A) :=
   let K : Subalgebra R A :=
     { carrier := ⋃ i, S i
-      mul_mem' := fun x y hx hy =>
+      hMul_mem' := fun x y hx hy =>
         let ⟨i, hi⟩ := Set.mem_iUnion.1 hx
         let ⟨j, hj⟩ := Set.mem_iUnion.1 hy
         let ⟨k, hik, hjk⟩ := dir i j
@@ -1730,7 +1730,7 @@ theorem range_algebraMap {R A : Type _} [CommRing R] [CommRing A] [Algebra R A]
 #print Subalgebra.noZeroSMulDivisors_top /-
 instance noZeroSMulDivisors_top [NoZeroDivisors A] (S : Subalgebra R A) : NoZeroSMulDivisors S A :=
   ⟨fun c x h =>
-    have : (c : A) = 0 ∨ x = 0 := eq_zero_or_eq_zero_of_mul_eq_zero h
+    have : (c : A) = 0 ∨ x = 0 := eq_zero_or_eq_zero_of_hMul_eq_zero h
     this.imp_left (@Subtype.ext_iff _ _ c 0).mpr⟩
 #align subalgebra.no_zero_smul_divisors_top Subalgebra.noZeroSMulDivisors_top
 -/

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,17 +2,14 @@
 Copyright (c) 2018 Kenny Lau. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau, Yury Kudryashov
-
-! This file was ported from Lean 3 source module algebra.algebra.subalgebra.basic
-! leanprover-community/mathlib commit b915e9392ecb2a861e1e766f0e1df6ac481188ca
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.Algebra.Basic
 import Mathbin.Data.Set.UnionLift
 import Mathbin.LinearAlgebra.Finsupp
 import Mathbin.RingTheory.Ideal.Operations
 
+#align_import algebra.algebra.subalgebra.basic from "leanprover-community/mathlib"@"b915e9392ecb2a861e1e766f0e1df6ac481188ca"
+
 /-!
 # Subalgebras over Commutative Semiring

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -50,8 +50,6 @@ variable [CommSemiring R]
 
 variable [Semiring A] [Algebra R A] [Semiring B] [Algebra R B] [Semiring C] [Algebra R C]
 
-include R
-
 instance : SetLike (Subalgebra R A) A
     where
   coe := Subalgebra.carrier
@@ -64,25 +62,33 @@ instance : SubsemiringClass (Subalgebra R A) A
   one_mem := one_mem'
   zero_mem := zero_mem'
 
+#print Subalgebra.mem_carrier /-
 @[simp]
 theorem mem_carrier {s : Subalgebra R A} {x : A} : x ∈ s.carrier ↔ x ∈ s :=
   Iff.rfl
 #align subalgebra.mem_carrier Subalgebra.mem_carrier
+-/
 
+#print Subalgebra.ext /-
 @[ext]
 theorem ext {S T : Subalgebra R A} (h : ∀ x : A, x ∈ S ↔ x ∈ T) : S = T :=
   SetLike.ext h
 #align subalgebra.ext Subalgebra.ext
+-/
 
+#print Subalgebra.mem_toSubsemiring /-
 @[simp]
 theorem mem_toSubsemiring {S : Subalgebra R A} {x} : x ∈ S.toSubsemiring ↔ x ∈ S :=
   Iff.rfl
 #align subalgebra.mem_to_subsemiring Subalgebra.mem_toSubsemiring
+-/
 
+#print Subalgebra.coe_toSubsemiring /-
 @[simp]
 theorem coe_toSubsemiring (S : Subalgebra R A) : (↑S.toSubsemiring : Set A) = S :=
   rfl
 #align subalgebra.coe_to_subsemiring Subalgebra.coe_toSubsemiring
+-/
 
 #print Subalgebra.toSubsemiring_injective /-
 theorem toSubsemiring_injective :
@@ -97,6 +103,7 @@ theorem toSubsemiring_inj {S U : Subalgebra R A} : S.toSubsemiring = U.toSubsemi
 #align subalgebra.to_subsemiring_inj Subalgebra.toSubsemiring_inj
 -/
 
+#print Subalgebra.copy /-
 /-- Copy of a subalgebra with a new `carrier` equal to the old one. Useful to fix definitional
 equalities. -/
 protected def copy (S : Subalgebra R A) (s : Set A) (hs : s = ↑S) : Subalgebra R A
@@ -106,117 +113,166 @@ protected def copy (S : Subalgebra R A) (s : Set A) (hs : s = ↑S) : Subalgebra
   mul_mem' _ _ := hs.symm ▸ S.mul_mem'
   algebraMap_mem' := hs.symm ▸ S.algebraMap_mem'
 #align subalgebra.copy Subalgebra.copy
+-/
 
+#print Subalgebra.coe_copy /-
 @[simp]
 theorem coe_copy (S : Subalgebra R A) (s : Set A) (hs : s = ↑S) : (S.copy s hs : Set A) = s :=
   rfl
 #align subalgebra.coe_copy Subalgebra.coe_copy
+-/
 
+#print Subalgebra.copy_eq /-
 theorem copy_eq (S : Subalgebra R A) (s : Set A) (hs : s = ↑S) : S.copy s hs = S :=
   SetLike.coe_injective hs
 #align subalgebra.copy_eq Subalgebra.copy_eq
+-/
 
 variable (S : Subalgebra R A)
 
+#print Subalgebra.algebraMap_mem /-
 theorem algebraMap_mem (r : R) : algebraMap R A r ∈ S :=
   S.algebraMap_mem' r
 #align subalgebra.algebra_map_mem Subalgebra.algebraMap_mem
+-/
 
+#print Subalgebra.rangeS_le /-
 theorem rangeS_le : (algebraMap R A).srange ≤ S.toSubsemiring := fun x ⟨r, hr⟩ =>
   hr ▸ S.algebraMap_mem r
 #align subalgebra.srange_le Subalgebra.rangeS_le
+-/
 
+#print Subalgebra.range_subset /-
 theorem range_subset : Set.range (algebraMap R A) ⊆ S := fun x ⟨r, hr⟩ => hr ▸ S.algebraMap_mem r
 #align subalgebra.range_subset Subalgebra.range_subset
+-/
 
+#print Subalgebra.range_le /-
 theorem range_le : Set.range (algebraMap R A) ≤ S :=
   S.range_subset
 #align subalgebra.range_le Subalgebra.range_le
+-/
 
+#print Subalgebra.smul_mem /-
 theorem smul_mem {x : A} (hx : x ∈ S) (r : R) : r • x ∈ S :=
   (Algebra.smul_def r x).symm ▸ mul_mem (S.algebraMap_mem r) hx
 #align subalgebra.smul_mem Subalgebra.smul_mem
+-/
 
 instance : SMulMemClass (Subalgebra R A) R A where smul_mem S r x hx := smul_mem S hx r
 
+#print Subalgebra.one_mem /-
 protected theorem one_mem : (1 : A) ∈ S :=
   one_mem S
 #align subalgebra.one_mem Subalgebra.one_mem
+-/
 
+#print Subalgebra.mul_mem /-
 protected theorem mul_mem {x y : A} (hx : x ∈ S) (hy : y ∈ S) : x * y ∈ S :=
   mul_mem hx hy
 #align subalgebra.mul_mem Subalgebra.mul_mem
+-/
 
+#print Subalgebra.pow_mem /-
 protected theorem pow_mem {x : A} (hx : x ∈ S) (n : ℕ) : x ^ n ∈ S :=
   pow_mem hx n
 #align subalgebra.pow_mem Subalgebra.pow_mem
+-/
 
+#print Subalgebra.zero_mem /-
 protected theorem zero_mem : (0 : A) ∈ S :=
   zero_mem S
 #align subalgebra.zero_mem Subalgebra.zero_mem
+-/
 
+#print Subalgebra.add_mem /-
 protected theorem add_mem {x y : A} (hx : x ∈ S) (hy : y ∈ S) : x + y ∈ S :=
   add_mem hx hy
 #align subalgebra.add_mem Subalgebra.add_mem
+-/
 
+#print Subalgebra.nsmul_mem /-
 protected theorem nsmul_mem {x : A} (hx : x ∈ S) (n : ℕ) : n • x ∈ S :=
   nsmul_mem hx n
 #align subalgebra.nsmul_mem Subalgebra.nsmul_mem
+-/
 
+#print Subalgebra.coe_nat_mem /-
 protected theorem coe_nat_mem (n : ℕ) : (n : A) ∈ S :=
   coe_nat_mem S n
 #align subalgebra.coe_nat_mem Subalgebra.coe_nat_mem
+-/
 
+#print Subalgebra.list_prod_mem /-
 protected theorem list_prod_mem {L : List A} (h : ∀ x ∈ L, x ∈ S) : L.Prod ∈ S :=
   list_prod_mem h
 #align subalgebra.list_prod_mem Subalgebra.list_prod_mem
+-/
 
+#print Subalgebra.list_sum_mem /-
 protected theorem list_sum_mem {L : List A} (h : ∀ x ∈ L, x ∈ S) : L.Sum ∈ S :=
   list_sum_mem h
 #align subalgebra.list_sum_mem Subalgebra.list_sum_mem
+-/
 
+#print Subalgebra.multiset_sum_mem /-
 protected theorem multiset_sum_mem {m : Multiset A} (h : ∀ x ∈ m, x ∈ S) : m.Sum ∈ S :=
   multiset_sum_mem m h
 #align subalgebra.multiset_sum_mem Subalgebra.multiset_sum_mem
+-/
 
+#print Subalgebra.sum_mem /-
 protected theorem sum_mem {ι : Type w} {t : Finset ι} {f : ι → A} (h : ∀ x ∈ t, f x ∈ S) :
     ∑ x in t, f x ∈ S :=
   sum_mem h
 #align subalgebra.sum_mem Subalgebra.sum_mem
+-/
 
+#print Subalgebra.multiset_prod_mem /-
 protected theorem multiset_prod_mem {R : Type u} {A : Type v} [CommSemiring R] [CommSemiring A]
     [Algebra R A] (S : Subalgebra R A) {m : Multiset A} (h : ∀ x ∈ m, x ∈ S) : m.Prod ∈ S :=
   multiset_prod_mem m h
 #align subalgebra.multiset_prod_mem Subalgebra.multiset_prod_mem
+-/
 
+#print Subalgebra.prod_mem /-
 protected theorem prod_mem {R : Type u} {A : Type v} [CommSemiring R] [CommSemiring A] [Algebra R A]
     (S : Subalgebra R A) {ι : Type w} {t : Finset ι} {f : ι → A} (h : ∀ x ∈ t, f x ∈ S) :
     ∏ x in t, f x ∈ S :=
   prod_mem h
 #align subalgebra.prod_mem Subalgebra.prod_mem
+-/
 
 instance {R A : Type _} [CommRing R] [Ring A] [Algebra R A] : SubringClass (Subalgebra R A) A :=
   { Subalgebra.subsemiringClass with neg_mem := fun S x hx => neg_one_smul R x ▸ S.smul_mem hx _ }
 
+#print Subalgebra.neg_mem /-
 protected theorem neg_mem {R : Type u} {A : Type v} [CommRing R] [Ring A] [Algebra R A]
     (S : Subalgebra R A) {x : A} (hx : x ∈ S) : -x ∈ S :=
   neg_mem hx
 #align subalgebra.neg_mem Subalgebra.neg_mem
+-/
 
+#print Subalgebra.sub_mem /-
 protected theorem sub_mem {R : Type u} {A : Type v} [CommRing R] [Ring A] [Algebra R A]
     (S : Subalgebra R A) {x y : A} (hx : x ∈ S) (hy : y ∈ S) : x - y ∈ S :=
   sub_mem hx hy
 #align subalgebra.sub_mem Subalgebra.sub_mem
+-/
 
+#print Subalgebra.zsmul_mem /-
 protected theorem zsmul_mem {R : Type u} {A : Type v} [CommRing R] [Ring A] [Algebra R A]
     (S : Subalgebra R A) {x : A} (hx : x ∈ S) (n : ℤ) : n • x ∈ S :=
   zsmul_mem hx n
 #align subalgebra.zsmul_mem Subalgebra.zsmul_mem
+-/
 
+#print Subalgebra.coe_int_mem /-
 protected theorem coe_int_mem {R : Type u} {A : Type v} [CommRing R] [Ring A] [Algebra R A]
     (S : Subalgebra R A) (n : ℤ) : (n : A) ∈ S :=
   coe_int_mem S n
 #align subalgebra.coe_int_mem Subalgebra.coe_int_mem
+-/
 
 #print Subalgebra.toAddSubmonoid /-
 /-- The projection from a subalgebra of `A` to an additive submonoid of `A`. -/
@@ -240,17 +296,21 @@ def toSubring {R : Type u} {A : Type v} [CommRing R] [Ring A] [Algebra R A] (S :
 #align subalgebra.to_subring Subalgebra.toSubring
 -/
 
+#print Subalgebra.mem_toSubring /-
 @[simp]
 theorem mem_toSubring {R : Type u} {A : Type v} [CommRing R] [Ring A] [Algebra R A]
     {S : Subalgebra R A} {x} : x ∈ S.toSubring ↔ x ∈ S :=
   Iff.rfl
 #align subalgebra.mem_to_subring Subalgebra.mem_toSubring
+-/
 
+#print Subalgebra.coe_toSubring /-
 @[simp]
 theorem coe_toSubring {R : Type u} {A : Type v} [CommRing R] [Ring A] [Algebra R A]
     (S : Subalgebra R A) : (↑S.toSubring : Set A) = S :=
   rfl
 #align subalgebra.coe_to_subring Subalgebra.coe_toSubring
+-/
 
 #print Subalgebra.toSubring_injective /-
 theorem toSubring_injective {R : Type u} {A : Type v} [CommRing R] [Ring A] [Algebra R A] :
@@ -274,77 +334,106 @@ section
 /-! `subalgebra`s inherit structure from their `subsemiring` / `semiring` coercions. -/
 
 
+#print Subalgebra.toSemiring /-
 instance toSemiring {R A} [CommSemiring R] [Semiring A] [Algebra R A] (S : Subalgebra R A) :
     Semiring S :=
   S.toSubsemiring.toSemiring
 #align subalgebra.to_semiring Subalgebra.toSemiring
+-/
 
+#print Subalgebra.toCommSemiring /-
 instance toCommSemiring {R A} [CommSemiring R] [CommSemiring A] [Algebra R A] (S : Subalgebra R A) :
     CommSemiring S :=
   S.toSubsemiring.toCommSemiring
 #align subalgebra.to_comm_semiring Subalgebra.toCommSemiring
+-/
 
+#print Subalgebra.toRing /-
 instance toRing {R A} [CommRing R] [Ring A] [Algebra R A] (S : Subalgebra R A) : Ring S :=
   S.toSubring.toRing
 #align subalgebra.to_ring Subalgebra.toRing
+-/
 
+#print Subalgebra.toCommRing /-
 instance toCommRing {R A} [CommRing R] [CommRing A] [Algebra R A] (S : Subalgebra R A) :
     CommRing S :=
   S.toSubring.toCommRing
 #align subalgebra.to_comm_ring Subalgebra.toCommRing
+-/
 
+#print Subalgebra.toOrderedSemiring /-
 instance toOrderedSemiring {R A} [CommSemiring R] [OrderedSemiring A] [Algebra R A]
     (S : Subalgebra R A) : OrderedSemiring S :=
   S.toSubsemiring.toOrderedSemiring
 #align subalgebra.to_ordered_semiring Subalgebra.toOrderedSemiring
+-/
 
+#print Subalgebra.toStrictOrderedSemiring /-
 instance toStrictOrderedSemiring {R A} [CommSemiring R] [StrictOrderedSemiring A] [Algebra R A]
     (S : Subalgebra R A) : StrictOrderedSemiring S :=
   S.toSubsemiring.toStrictOrderedSemiring
 #align subalgebra.to_strict_ordered_semiring Subalgebra.toStrictOrderedSemiring
+-/
 
+#print Subalgebra.toOrderedCommSemiring /-
 instance toOrderedCommSemiring {R A} [CommSemiring R] [OrderedCommSemiring A] [Algebra R A]
     (S : Subalgebra R A) : OrderedCommSemiring S :=
   S.toSubsemiring.toOrderedCommSemiring
 #align subalgebra.to_ordered_comm_semiring Subalgebra.toOrderedCommSemiring
+-/
 
+#print Subalgebra.toStrictOrderedCommSemiring /-
 instance toStrictOrderedCommSemiring {R A} [CommSemiring R] [StrictOrderedCommSemiring A]
     [Algebra R A] (S : Subalgebra R A) : StrictOrderedCommSemiring S :=
   S.toSubsemiring.toStrictOrderedCommSemiring
 #align subalgebra.to_strict_ordered_comm_semiring Subalgebra.toStrictOrderedCommSemiring
+-/
 
+#print Subalgebra.toOrderedRing /-
 instance toOrderedRing {R A} [CommRing R] [OrderedRing A] [Algebra R A] (S : Subalgebra R A) :
     OrderedRing S :=
   S.toSubring.toOrderedRing
 #align subalgebra.to_ordered_ring Subalgebra.toOrderedRing
+-/
 
+#print Subalgebra.toOrderedCommRing /-
 instance toOrderedCommRing {R A} [CommRing R] [OrderedCommRing A] [Algebra R A]
     (S : Subalgebra R A) : OrderedCommRing S :=
   S.toSubring.toOrderedCommRing
 #align subalgebra.to_ordered_comm_ring Subalgebra.toOrderedCommRing
+-/
 
+#print Subalgebra.toLinearOrderedSemiring /-
 instance toLinearOrderedSemiring {R A} [CommSemiring R] [LinearOrderedSemiring A] [Algebra R A]
     (S : Subalgebra R A) : LinearOrderedSemiring S :=
   S.toSubsemiring.toLinearOrderedSemiring
 #align subalgebra.to_linear_ordered_semiring Subalgebra.toLinearOrderedSemiring
+-/
 
+#print Subalgebra.toLinearOrderedCommSemiring /-
 instance toLinearOrderedCommSemiring {R A} [CommSemiring R] [LinearOrderedCommSemiring A]
     [Algebra R A] (S : Subalgebra R A) : LinearOrderedCommSemiring S :=
   S.toSubsemiring.toLinearOrderedCommSemiring
 #align subalgebra.to_linear_ordered_comm_semiring Subalgebra.toLinearOrderedCommSemiring
+-/
 
+#print Subalgebra.toLinearOrderedRing /-
 instance toLinearOrderedRing {R A} [CommRing R] [LinearOrderedRing A] [Algebra R A]
     (S : Subalgebra R A) : LinearOrderedRing S :=
   S.toSubring.toLinearOrderedRing
 #align subalgebra.to_linear_ordered_ring Subalgebra.toLinearOrderedRing
+-/
 
+#print Subalgebra.toLinearOrderedCommRing /-
 instance toLinearOrderedCommRing {R A} [CommRing R] [LinearOrderedCommRing A] [Algebra R A]
     (S : Subalgebra R A) : LinearOrderedCommRing S :=
   S.toSubring.toLinearOrderedCommRing
 #align subalgebra.to_linear_ordered_comm_ring Subalgebra.toLinearOrderedCommRing
+-/
 
 end
 
+#print Subalgebra.toSubmodule /-
 /-- The forgetful map from `subalgebra` to `submodule` as an `order_embedding` -/
 def toSubmodule : Subalgebra R A ↪o Submodule R A
     where
@@ -359,27 +448,34 @@ def toSubmodule : Subalgebra R A ↪o Submodule R A
       inj' := fun S T h => ext <| by apply SetLike.ext_iff.1 h }
   map_rel_iff' S T := SetLike.coe_subset_coe.symm.trans SetLike.coe_subset_coe
 #align subalgebra.to_submodule Subalgebra.toSubmodule
+-/
 
+#print Subalgebra.mem_toSubmodule /-
 /- TODO: bundle other forgetful maps between algebraic substructures, e.g.
   `to_subsemiring` and `to_subring` in this file. -/
 @[simp]
 theorem mem_toSubmodule {x} : x ∈ S.toSubmodule ↔ x ∈ S :=
   Iff.rfl
 #align subalgebra.mem_to_submodule Subalgebra.mem_toSubmodule
+-/
 
+#print Subalgebra.coe_toSubmodule /-
 @[simp]
 theorem coe_toSubmodule (S : Subalgebra R A) : (↑S.toSubmodule : Set A) = S :=
   rfl
 #align subalgebra.coe_to_submodule Subalgebra.coe_toSubmodule
+-/
 
 section
 
 /-! `subalgebra`s inherit structure from their `submodule` coercions. -/
 
 
+#print Subalgebra.module' /-
 instance module' [Semiring R'] [SMul R' R] [Module R' A] [IsScalarTower R' R A] : Module R' S :=
   S.toSubmodule.module'
 #align subalgebra.module' Subalgebra.module'
+-/
 
 instance : Module R S :=
   S.module'
@@ -387,6 +483,7 @@ instance : Module R S :=
 instance [Semiring R'] [SMul R' R] [Module R' A] [IsScalarTower R' R A] : IsScalarTower R' R S :=
   S.toSubmodule.IsScalarTower
 
+#print Subalgebra.algebra' /-
 instance algebra' [CommSemiring R'] [SMul R' R] [Algebra R' A] [IsScalarTower R' R A] :
     Algebra R' S :=
   {
@@ -400,29 +497,38 @@ instance algebra' [CommSemiring R'] [SMul R' R] [Algebra R' A] [IsScalarTower R'
     commutes' := fun c x => Subtype.eq <| Algebra.commutes _ _
     smul_def' := fun c x => Subtype.eq <| Algebra.smul_def _ _ }
 #align subalgebra.algebra' Subalgebra.algebra'
+-/
 
 instance : Algebra R S :=
   S.algebra'
 
 end
 
+#print Subalgebra.noZeroSMulDivisors_bot /-
 instance noZeroSMulDivisors_bot [NoZeroSMulDivisors R A] : NoZeroSMulDivisors R S :=
   ⟨fun c x h =>
     have : c = 0 ∨ (x : A) = 0 := eq_zero_or_eq_zero_of_smul_eq_zero (congr_arg coe h)
     this.imp_right (@Subtype.ext_iff _ _ x 0).mpr⟩
 #align subalgebra.no_zero_smul_divisors_bot Subalgebra.noZeroSMulDivisors_bot
+-/
 
+#print Subalgebra.coe_add /-
 protected theorem coe_add (x y : S) : (↑(x + y) : A) = ↑x + ↑y :=
   rfl
 #align subalgebra.coe_add Subalgebra.coe_add
+-/
 
+#print Subalgebra.coe_mul /-
 protected theorem coe_mul (x y : S) : (↑(x * y) : A) = ↑x * ↑y :=
   rfl
 #align subalgebra.coe_mul Subalgebra.coe_mul
+-/
 
+#print Subalgebra.coe_zero /-
 protected theorem coe_zero : ((0 : S) : A) = 0 :=
   rfl
 #align subalgebra.coe_zero Subalgebra.coe_zero
+-/
 
 #print Subalgebra.coe_one /-
 protected theorem coe_one : ((1 : S) : A) = 1 :=
@@ -430,71 +536,97 @@ protected theorem coe_one : ((1 : S) : A) = 1 :=
 #align subalgebra.coe_one Subalgebra.coe_one
 -/
 
+#print Subalgebra.coe_neg /-
 protected theorem coe_neg {R : Type u} {A : Type v} [CommRing R] [Ring A] [Algebra R A]
     {S : Subalgebra R A} (x : S) : (↑(-x) : A) = -↑x :=
   rfl
 #align subalgebra.coe_neg Subalgebra.coe_neg
+-/
 
+#print Subalgebra.coe_sub /-
 protected theorem coe_sub {R : Type u} {A : Type v} [CommRing R] [Ring A] [Algebra R A]
     {S : Subalgebra R A} (x y : S) : (↑(x - y) : A) = ↑x - ↑y :=
   rfl
 #align subalgebra.coe_sub Subalgebra.coe_sub
+-/
 
+#print Subalgebra.coe_smul /-
 @[simp, norm_cast]
 theorem coe_smul [Semiring R'] [SMul R' R] [Module R' A] [IsScalarTower R' R A] (r : R') (x : S) :
     (↑(r • x) : A) = r • ↑x :=
   rfl
 #align subalgebra.coe_smul Subalgebra.coe_smul
+-/
 
+#print Subalgebra.coe_algebraMap /-
 @[simp, norm_cast]
 theorem coe_algebraMap [CommSemiring R'] [SMul R' R] [Algebra R' A] [IsScalarTower R' R A]
     (r : R') : ↑(algebraMap R' S r) = algebraMap R' A r :=
   rfl
 #align subalgebra.coe_algebra_map Subalgebra.coe_algebraMap
+-/
 
+#print Subalgebra.coe_pow /-
 protected theorem coe_pow (x : S) (n : ℕ) : (↑(x ^ n) : A) = ↑x ^ n :=
   SubmonoidClass.coe_pow x n
 #align subalgebra.coe_pow Subalgebra.coe_pow
+-/
 
+#print Subalgebra.coe_eq_zero /-
 protected theorem coe_eq_zero {x : S} : (x : A) = 0 ↔ x = 0 :=
   ZeroMemClass.coe_eq_zero
 #align subalgebra.coe_eq_zero Subalgebra.coe_eq_zero
+-/
 
+#print Subalgebra.coe_eq_one /-
 protected theorem coe_eq_one {x : S} : (x : A) = 1 ↔ x = 1 :=
   OneMemClass.coe_eq_one
 #align subalgebra.coe_eq_one Subalgebra.coe_eq_one
+-/
 
+#print Subalgebra.val /-
 -- todo: standardize on the names these morphisms
 -- compare with submodule.subtype
 /-- Embedding of a subalgebra into the algebra. -/
 def val : S →ₐ[R] A := by refine_struct { toFun := (coe : S → A) } <;> intros <;> rfl
 #align subalgebra.val Subalgebra.val
+-/
 
+#print Subalgebra.coe_val /-
 @[simp]
 theorem coe_val : (S.val : S → A) = coe :=
   rfl
 #align subalgebra.coe_val Subalgebra.coe_val
+-/
 
+#print Subalgebra.val_apply /-
 theorem val_apply (x : S) : S.val x = (x : A) :=
   rfl
 #align subalgebra.val_apply Subalgebra.val_apply
+-/
 
+#print Subalgebra.toSubsemiring_subtype /-
 @[simp]
 theorem toSubsemiring_subtype : S.toSubsemiring.Subtype = (S.val : S →+* A) :=
   rfl
 #align subalgebra.to_subsemiring_subtype Subalgebra.toSubsemiring_subtype
+-/
 
+#print Subalgebra.toSubring_subtype /-
 @[simp]
 theorem toSubring_subtype {R A : Type _} [CommRing R] [Ring A] [Algebra R A] (S : Subalgebra R A) :
     S.toSubring.Subtype = (S.val : S →+* A) :=
   rfl
 #align subalgebra.to_subring_subtype Subalgebra.toSubring_subtype
+-/
 
+#print Subalgebra.toSubmoduleEquiv /-
 /-- Linear equivalence between `S : submodule R A` and `S`. Though these types are equal,
 we define it as a `linear_equiv` to avoid type equalities. -/
 def toSubmoduleEquiv (S : Subalgebra R A) : S.toSubmodule ≃ₗ[R] S :=
   LinearEquiv.ofEq _ _ rfl
 #align subalgebra.to_submodule_equiv Subalgebra.toSubmoduleEquiv
+-/
 
 #print Subalgebra.map /-
 /-- Transport a subalgebra via an algebra homomorphism. -/
@@ -504,14 +636,18 @@ def map (f : A →ₐ[R] B) (S : Subalgebra R A) : Subalgebra R B :=
 #align subalgebra.map Subalgebra.map
 -/
 
+#print Subalgebra.map_mono /-
 theorem map_mono {S₁ S₂ : Subalgebra R A} {f : A →ₐ[R] B} : S₁ ≤ S₂ → S₁.map f ≤ S₂.map f :=
   Set.image_subset f
 #align subalgebra.map_mono Subalgebra.map_mono
+-/
 
+#print Subalgebra.map_injective /-
 theorem map_injective {f : A →ₐ[R] B} (hf : Function.Injective f) : Function.Injective (map f) :=
   fun S₁ S₂ ih =>
   ext <| Set.ext_iff.1 <| Set.image_injective.2 hf <| Set.ext <| SetLike.ext_iff.mp ih
 #align subalgebra.map_injective Subalgebra.map_injective
+-/
 
 #print Subalgebra.map_id /-
 @[simp]
@@ -527,14 +663,18 @@ theorem map_map (S : Subalgebra R A) (g : B →ₐ[R] C) (f : A →ₐ[R] B) :
 #align subalgebra.map_map Subalgebra.map_map
 -/
 
+#print Subalgebra.mem_map /-
 theorem mem_map {S : Subalgebra R A} {f : A →ₐ[R] B} {y : B} : y ∈ map f S ↔ ∃ x ∈ S, f x = y :=
   Subsemiring.mem_map
 #align subalgebra.mem_map Subalgebra.mem_map
+-/
 
+#print Subalgebra.map_toSubmodule /-
 theorem map_toSubmodule {S : Subalgebra R A} {f : A →ₐ[R] B} :
     (S.map f).toSubmodule = S.toSubmodule.map f.toLinearMap :=
   SetLike.coe_injective rfl
 #align subalgebra.map_to_submodule Subalgebra.map_toSubmodule
+-/
 
 #print Subalgebra.map_toSubsemiring /-
 theorem map_toSubsemiring {S : Subalgebra R A} {f : A →ₐ[R] B} :
@@ -543,10 +683,12 @@ theorem map_toSubsemiring {S : Subalgebra R A} {f : A →ₐ[R] B} :
 #align subalgebra.map_to_subsemiring Subalgebra.map_toSubsemiring
 -/
 
+#print Subalgebra.coe_map /-
 @[simp]
 theorem coe_map (S : Subalgebra R A) (f : A →ₐ[R] B) : (S.map f : Set B) = f '' S :=
   rfl
 #align subalgebra.coe_map Subalgebra.coe_map
+-/
 
 #print Subalgebra.comap /-
 /-- Preimage of a subalgebra under an algebra homomorphism. -/
@@ -557,33 +699,45 @@ def comap (f : A →ₐ[R] B) (S : Subalgebra R B) : Subalgebra R A :=
 #align subalgebra.comap Subalgebra.comap
 -/
 
+#print Subalgebra.map_le /-
 theorem map_le {S : Subalgebra R A} {f : A →ₐ[R] B} {U : Subalgebra R B} :
     map f S ≤ U ↔ S ≤ comap f U :=
   Set.image_subset_iff
 #align subalgebra.map_le Subalgebra.map_le
+-/
 
+#print Subalgebra.gc_map_comap /-
 theorem gc_map_comap (f : A →ₐ[R] B) : GaloisConnection (map f) (comap f) := fun S U => map_le
 #align subalgebra.gc_map_comap Subalgebra.gc_map_comap
+-/
 
+#print Subalgebra.mem_comap /-
 @[simp]
 theorem mem_comap (S : Subalgebra R B) (f : A →ₐ[R] B) (x : A) : x ∈ S.comap f ↔ f x ∈ S :=
   Iff.rfl
 #align subalgebra.mem_comap Subalgebra.mem_comap
+-/
 
+#print Subalgebra.coe_comap /-
 @[simp, norm_cast]
 theorem coe_comap (S : Subalgebra R B) (f : A →ₐ[R] B) : (S.comap f : Set A) = f ⁻¹' (S : Set B) :=
   rfl
 #align subalgebra.coe_comap Subalgebra.coe_comap
+-/
 
+#print Subalgebra.noZeroDivisors /-
 instance noZeroDivisors {R A : Type _} [CommSemiring R] [Semiring A] [NoZeroDivisors A]
     [Algebra R A] (S : Subalgebra R A) : NoZeroDivisors S :=
   S.toSubsemiring.NoZeroDivisors
 #align subalgebra.no_zero_divisors Subalgebra.noZeroDivisors
+-/
 
+#print Subalgebra.isDomain /-
 instance isDomain {R A : Type _} [CommRing R] [Ring A] [IsDomain A] [Algebra R A]
     (S : Subalgebra R A) : IsDomain S :=
   Subring.isDomain S.toSubring
 #align subalgebra.is_domain Subalgebra.isDomain
+-/
 
 end Subalgebra
 
@@ -593,6 +747,7 @@ variable {R A : Type _} [CommSemiring R] [Semiring A] [Algebra R A]
 
 variable (p : Submodule R A)
 
+#print Submodule.toSubalgebra /-
 /-- A submodule containing `1` and closed under multiplication is a subalgebra. -/
 def toSubalgebra (p : Submodule R A) (h_one : (1 : A) ∈ p)
     (h_mul : ∀ x y, x ∈ p → y ∈ p → x * y ∈ p) : Subalgebra R A :=
@@ -602,19 +757,25 @@ def toSubalgebra (p : Submodule R A) (h_one : (1 : A) ∈ p)
       rw [Algebra.algebraMap_eq_smul_one]
       exact p.smul_mem _ h_one }
 #align submodule.to_subalgebra Submodule.toSubalgebra
+-/
 
+#print Submodule.mem_toSubalgebra /-
 @[simp]
 theorem mem_toSubalgebra {p : Submodule R A} {h_one h_mul} {x} :
     x ∈ p.toSubalgebra h_one h_mul ↔ x ∈ p :=
   Iff.rfl
 #align submodule.mem_to_subalgebra Submodule.mem_toSubalgebra
+-/
 
+#print Submodule.coe_toSubalgebra /-
 @[simp]
 theorem coe_toSubalgebra (p : Submodule R A) (h_one h_mul) :
     (p.toSubalgebra h_one h_mul : Set A) = p :=
   rfl
 #align submodule.coe_to_subalgebra Submodule.coe_toSubalgebra
+-/
 
+#print Submodule.toSubalgebra_mk /-
 @[simp]
 theorem toSubalgebra_mk (s : Set A) (h0 hadd hsmul h1 hmul) :
     (Submodule.mk s hadd h0 hsmul : Submodule R A).toSubalgebra h1 hmul =
@@ -622,18 +783,23 @@ theorem toSubalgebra_mk (s : Set A) (h0 hadd hsmul h1 hmul) :
         exact hsmul r h1 :=
   rfl
 #align submodule.to_subalgebra_mk Submodule.toSubalgebra_mk
+-/
 
+#print Submodule.toSubalgebra_toSubmodule /-
 @[simp]
 theorem toSubalgebra_toSubmodule (p : Submodule R A) (h_one h_mul) :
     (p.toSubalgebra h_one h_mul).toSubmodule = p :=
   SetLike.coe_injective rfl
 #align submodule.to_subalgebra_to_submodule Submodule.toSubalgebra_toSubmodule
+-/
 
+#print Subalgebra.toSubmodule_toSubalgebra /-
 @[simp]
 theorem Subalgebra.toSubmodule_toSubalgebra (S : Subalgebra R A) :
     (S.toSubmodule.toSubalgebra S.one_mem fun _ _ => S.mul_mem) = S :=
   SetLike.coe_injective rfl
 #align subalgebra.to_submodule_to_subalgebra Subalgebra.toSubmodule_toSubalgebra
+-/
 
 end Submodule
 
@@ -654,19 +820,25 @@ protected def range (φ : A →ₐ[R] B) : Subalgebra R B :=
 #align alg_hom.range AlgHom.range
 -/
 
+#print AlgHom.mem_range /-
 @[simp]
 theorem mem_range (φ : A →ₐ[R] B) {y : B} : y ∈ φ.range ↔ ∃ x, φ x = y :=
   RingHom.mem_rangeS
 #align alg_hom.mem_range AlgHom.mem_range
+-/
 
+#print AlgHom.mem_range_self /-
 theorem mem_range_self (φ : A →ₐ[R] B) (x : A) : φ x ∈ φ.range :=
   φ.mem_range.2 ⟨x, rfl⟩
 #align alg_hom.mem_range_self AlgHom.mem_range_self
+-/
 
+#print AlgHom.coe_range /-
 @[simp]
 theorem coe_range (φ : A →ₐ[R] B) : (φ.range : Set B) = Set.range φ := by ext;
   rw [SetLike.mem_coe, mem_range]; rfl
 #align alg_hom.coe_range AlgHom.coe_range
+-/
 
 #print AlgHom.range_comp /-
 theorem range_comp (f : A →ₐ[R] B) (g : B →ₐ[R] C) : (g.comp f).range = f.range.map g :=
@@ -674,32 +846,43 @@ theorem range_comp (f : A →ₐ[R] B) (g : B →ₐ[R] C) : (g.comp f).range =
 #align alg_hom.range_comp AlgHom.range_comp
 -/
 
+#print AlgHom.range_comp_le_range /-
 theorem range_comp_le_range (f : A →ₐ[R] B) (g : B →ₐ[R] C) : (g.comp f).range ≤ g.range :=
   SetLike.coe_mono (Set.range_comp_subset_range f g)
 #align alg_hom.range_comp_le_range AlgHom.range_comp_le_range
+-/
 
+#print AlgHom.codRestrict /-
 /-- Restrict the codomain of an algebra homomorphism. -/
 def codRestrict (f : A →ₐ[R] B) (S : Subalgebra R B) (hf : ∀ x, f x ∈ S) : A →ₐ[R] S :=
   { RingHom.codRestrict (f : A →+* B) S hf with commutes' := fun r => Subtype.eq <| f.commutes r }
 #align alg_hom.cod_restrict AlgHom.codRestrict
+-/
 
+#print AlgHom.val_comp_codRestrict /-
 @[simp]
 theorem val_comp_codRestrict (f : A →ₐ[R] B) (S : Subalgebra R B) (hf : ∀ x, f x ∈ S) :
     S.val.comp (f.codRestrict S hf) = f :=
   AlgHom.ext fun _ => rfl
 #align alg_hom.val_comp_cod_restrict AlgHom.val_comp_codRestrict
+-/
 
+#print AlgHom.coe_codRestrict /-
 @[simp]
 theorem coe_codRestrict (f : A →ₐ[R] B) (S : Subalgebra R B) (hf : ∀ x, f x ∈ S) (x : A) :
     ↑(f.codRestrict S hf x) = f x :=
   rfl
 #align alg_hom.coe_cod_restrict AlgHom.coe_codRestrict
+-/
 
+#print AlgHom.injective_codRestrict /-
 theorem injective_codRestrict (f : A →ₐ[R] B) (S : Subalgebra R B) (hf : ∀ x, f x ∈ S) :
     Function.Injective (f.codRestrict S hf) ↔ Function.Injective f :=
   ⟨fun H x y hxy => H <| Subtype.eq hxy, fun H x y hxy => H (congr_arg Subtype.val hxy : _)⟩
 #align alg_hom.injective_cod_restrict AlgHom.injective_codRestrict
+-/
 
+#print AlgHom.rangeRestrict /-
 /-- Restrict the codomain of a alg_hom `f` to `f.range`.
 
 This is the bundled version of `set.range_factorization`. -/
@@ -707,6 +890,7 @@ This is the bundled version of `set.range_factorization`. -/
 def rangeRestrict (f : A →ₐ[R] B) : A →ₐ[R] f.range :=
   f.codRestrict f.range f.mem_range_self
 #align alg_hom.range_restrict AlgHom.rangeRestrict
+-/
 
 #print AlgHom.equalizer /-
 /-- The equalizer of two R-algebra homomorphisms -/
@@ -721,17 +905,21 @@ def equalizer (ϕ ψ : A →ₐ[R] B) : Subalgebra R A
 #align alg_hom.equalizer AlgHom.equalizer
 -/
 
+#print AlgHom.mem_equalizer /-
 @[simp]
 theorem mem_equalizer (ϕ ψ : A →ₐ[R] B) (x : A) : x ∈ ϕ.equalizer ψ ↔ ϕ x = ψ x :=
   Iff.rfl
 #align alg_hom.mem_equalizer AlgHom.mem_equalizer
+-/
 
+#print AlgHom.fintypeRange /-
 /-- The range of a morphism of algebras is a fintype, if the domain is a fintype.
 
 Note that this instance can cause a diamond with `subtype.fintype` if `B` is also a fintype. -/
 instance fintypeRange [Fintype A] [DecidableEq B] (φ : A →ₐ[R] B) : Fintype φ.range :=
   Set.fintypeRange φ
 #align alg_hom.fintype_range AlgHom.fintypeRange
+-/
 
 end AlgHom
 
@@ -741,6 +929,7 @@ variable {R : Type u} {A : Type v} {B : Type w}
 
 variable [CommSemiring R] [Semiring A] [Semiring B] [Algebra R A] [Algebra R B]
 
+#print AlgEquiv.ofLeftInverse /-
 /-- Restrict an algebra homomorphism with a left inverse to an algebra isomorphism to its range.
 
 This is a computable alternative to `alg_equiv.of_injective`. -/
@@ -754,42 +943,55 @@ def ofLeftInverse {g : B → A} {f : A →ₐ[R] B} (h : Function.LeftInverse g
         let ⟨x', hx'⟩ := f.mem_range.mp x.Prop
         show f (g x) = x by rw [← hx', h x'] }
 #align alg_equiv.of_left_inverse AlgEquiv.ofLeftInverse
+-/
 
+#print AlgEquiv.ofLeftInverse_apply /-
 @[simp]
 theorem ofLeftInverse_apply {g : B → A} {f : A →ₐ[R] B} (h : Function.LeftInverse g f) (x : A) :
     ↑(ofLeftInverse h x) = f x :=
   rfl
 #align alg_equiv.of_left_inverse_apply AlgEquiv.ofLeftInverse_apply
+-/
 
+#print AlgEquiv.ofLeftInverse_symm_apply /-
 @[simp]
 theorem ofLeftInverse_symm_apply {g : B → A} {f : A →ₐ[R] B} (h : Function.LeftInverse g f)
     (x : f.range) : (ofLeftInverse h).symm x = g x :=
   rfl
 #align alg_equiv.of_left_inverse_symm_apply AlgEquiv.ofLeftInverse_symm_apply
+-/
 
+#print AlgEquiv.ofInjective /-
 /-- Restrict an injective algebra homomorphism to an algebra isomorphism -/
 noncomputable def ofInjective (f : A →ₐ[R] B) (hf : Function.Injective f) : A ≃ₐ[R] f.range :=
   ofLeftInverse (Classical.choose_spec hf.HasLeftInverse)
 #align alg_equiv.of_injective AlgEquiv.ofInjective
+-/
 
+#print AlgEquiv.ofInjective_apply /-
 @[simp]
 theorem ofInjective_apply (f : A →ₐ[R] B) (hf : Function.Injective f) (x : A) :
     ↑(ofInjective f hf x) = f x :=
   rfl
 #align alg_equiv.of_injective_apply AlgEquiv.ofInjective_apply
+-/
 
+#print AlgEquiv.ofInjectiveField /-
 /-- Restrict an algebra homomorphism between fields to an algebra isomorphism -/
 noncomputable def ofInjectiveField {E F : Type _} [DivisionRing E] [Semiring F] [Nontrivial F]
     [Algebra R E] [Algebra R F] (f : E →ₐ[R] F) : E ≃ₐ[R] f.range :=
   ofInjective f f.toRingHom.Injective
 #align alg_equiv.of_injective_field AlgEquiv.ofInjectiveField
+-/
 
+#print AlgEquiv.subalgebraMap /-
 /-- Given an equivalence `e : A ≃ₐ[R] B` of `R`-algebras and a subalgebra `S` of `A`,
 `subalgebra_map` is the induced equivalence between `S` and `S.map e` -/
 @[simps]
 def subalgebraMap (e : A ≃ₐ[R] B) (S : Subalgebra R A) : S ≃ₐ[R] S.map e.toAlgHom :=
   { e.toRingEquiv.subsemiringMap S.toSubsemiring with commutes' := fun r => by ext; simp }
 #align alg_equiv.subalgebra_map AlgEquiv.subalgebraMap
+-/
 
 end AlgEquiv
 
@@ -809,12 +1011,15 @@ def adjoin (s : Set A) : Subalgebra R A :=
 
 variable {R}
 
+#print Algebra.gc /-
 protected theorem gc : GaloisConnection (adjoin R : Set A → Subalgebra R A) coe := fun s S =>
   ⟨fun H => le_trans (le_trans (Set.subset_union_right _ _) Subsemiring.subset_closure) H, fun H =>
     show Subsemiring.closure (Set.range (algebraMap R A) ∪ s) ≤ S.toSubsemiring from
       Subsemiring.closure_le.2 <| Set.union_subset S.range_subset H⟩
 #align algebra.gc Algebra.gc
+-/
 
+#print Algebra.gi /-
 /-- Galois insertion between `adjoin` and `coe`. -/
 protected def gi : GaloisInsertion (adjoin R : Set A → Subalgebra R A) coe
     where
@@ -823,180 +1028,248 @@ protected def gi : GaloisInsertion (adjoin R : Set A → Subalgebra R A) coe
   le_l_u S := (Algebra.gc (S : Set A) (adjoin R S)).1 <| le_rfl
   choice_eq _ _ := Subalgebra.copy_eq _ _ _
 #align algebra.gi Algebra.gi
+-/
 
 instance : CompleteLattice (Subalgebra R A) :=
   GaloisInsertion.liftCompleteLattice Algebra.gi
 
+#print Algebra.coe_top /-
 @[simp]
 theorem coe_top : (↑(⊤ : Subalgebra R A) : Set A) = Set.univ :=
   rfl
 #align algebra.coe_top Algebra.coe_top
+-/
 
+#print Algebra.mem_top /-
 @[simp]
 theorem mem_top {x : A} : x ∈ (⊤ : Subalgebra R A) :=
   Set.mem_univ x
 #align algebra.mem_top Algebra.mem_top
+-/
 
+#print Algebra.top_toSubmodule /-
 @[simp]
 theorem top_toSubmodule : (⊤ : Subalgebra R A).toSubmodule = ⊤ :=
   rfl
 #align algebra.top_to_submodule Algebra.top_toSubmodule
+-/
 
+#print Algebra.top_toSubsemiring /-
 @[simp]
 theorem top_toSubsemiring : (⊤ : Subalgebra R A).toSubsemiring = ⊤ :=
   rfl
 #align algebra.top_to_subsemiring Algebra.top_toSubsemiring
+-/
 
+#print Algebra.top_toSubring /-
 @[simp]
 theorem top_toSubring {R A : Type _} [CommRing R] [Ring A] [Algebra R A] :
     (⊤ : Subalgebra R A).toSubring = ⊤ :=
   rfl
 #align algebra.top_to_subring Algebra.top_toSubring
+-/
 
+#print Algebra.toSubmodule_eq_top /-
 @[simp]
 theorem toSubmodule_eq_top {S : Subalgebra R A} : S.toSubmodule = ⊤ ↔ S = ⊤ :=
   Subalgebra.toSubmodule.Injective.eq_iff' top_toSubmodule
 #align algebra.to_submodule_eq_top Algebra.toSubmodule_eq_top
+-/
 
+#print Algebra.toSubsemiring_eq_top /-
 @[simp]
 theorem toSubsemiring_eq_top {S : Subalgebra R A} : S.toSubsemiring = ⊤ ↔ S = ⊤ :=
   Subalgebra.toSubsemiring_injective.eq_iff' top_toSubsemiring
 #align algebra.to_subsemiring_eq_top Algebra.toSubsemiring_eq_top
+-/
 
+#print Algebra.toSubring_eq_top /-
 @[simp]
 theorem toSubring_eq_top {R A : Type _} [CommRing R] [Ring A] [Algebra R A] {S : Subalgebra R A} :
     S.toSubring = ⊤ ↔ S = ⊤ :=
   Subalgebra.toSubring_injective.eq_iff' top_toSubring
 #align algebra.to_subring_eq_top Algebra.toSubring_eq_top
+-/
 
+#print Algebra.mem_sup_left /-
 theorem mem_sup_left {S T : Subalgebra R A} : ∀ {x : A}, x ∈ S → x ∈ S ⊔ T :=
   show S ≤ S ⊔ T from le_sup_left
 #align algebra.mem_sup_left Algebra.mem_sup_left
+-/
 
+#print Algebra.mem_sup_right /-
 theorem mem_sup_right {S T : Subalgebra R A} : ∀ {x : A}, x ∈ T → x ∈ S ⊔ T :=
   show T ≤ S ⊔ T from le_sup_right
 #align algebra.mem_sup_right Algebra.mem_sup_right
+-/
 
+#print Algebra.mul_mem_sup /-
 theorem mul_mem_sup {S T : Subalgebra R A} {x y : A} (hx : x ∈ S) (hy : y ∈ T) : x * y ∈ S ⊔ T :=
   (S ⊔ T).mul_mem (mem_sup_left hx) (mem_sup_right hy)
 #align algebra.mul_mem_sup Algebra.mul_mem_sup
+-/
 
+#print Algebra.map_sup /-
 theorem map_sup (f : A →ₐ[R] B) (S T : Subalgebra R A) : (S ⊔ T).map f = S.map f ⊔ T.map f :=
   (Subalgebra.gc_map_comap f).l_sup
 #align algebra.map_sup Algebra.map_sup
+-/
 
+#print Algebra.coe_inf /-
 @[simp, norm_cast]
 theorem coe_inf (S T : Subalgebra R A) : (↑(S ⊓ T) : Set A) = S ∩ T :=
   rfl
 #align algebra.coe_inf Algebra.coe_inf
+-/
 
+#print Algebra.mem_inf /-
 @[simp]
 theorem mem_inf {S T : Subalgebra R A} {x : A} : x ∈ S ⊓ T ↔ x ∈ S ∧ x ∈ T :=
   Iff.rfl
 #align algebra.mem_inf Algebra.mem_inf
+-/
 
+#print Algebra.inf_toSubmodule /-
 @[simp]
 theorem inf_toSubmodule (S T : Subalgebra R A) :
     (S ⊓ T).toSubmodule = S.toSubmodule ⊓ T.toSubmodule :=
   rfl
 #align algebra.inf_to_submodule Algebra.inf_toSubmodule
+-/
 
+#print Algebra.inf_toSubsemiring /-
 @[simp]
 theorem inf_toSubsemiring (S T : Subalgebra R A) :
     (S ⊓ T).toSubsemiring = S.toSubsemiring ⊓ T.toSubsemiring :=
   rfl
 #align algebra.inf_to_subsemiring Algebra.inf_toSubsemiring
+-/
 
+#print Algebra.coe_sInf /-
 @[simp, norm_cast]
 theorem coe_sInf (S : Set (Subalgebra R A)) : (↑(sInf S) : Set A) = ⋂ s ∈ S, ↑s :=
   sInf_image
 #align algebra.coe_Inf Algebra.coe_sInf
+-/
 
+#print Algebra.mem_sInf /-
 theorem mem_sInf {S : Set (Subalgebra R A)} {x : A} : x ∈ sInf S ↔ ∀ p ∈ S, x ∈ p := by
   simp only [← SetLike.mem_coe, coe_Inf, Set.mem_iInter₂]
 #align algebra.mem_Inf Algebra.mem_sInf
+-/
 
+#print Algebra.sInf_toSubmodule /-
 @[simp]
 theorem sInf_toSubmodule (S : Set (Subalgebra R A)) :
     (sInf S).toSubmodule = sInf (Subalgebra.toSubmodule '' S) :=
   SetLike.coe_injective <| by simp
 #align algebra.Inf_to_submodule Algebra.sInf_toSubmodule
+-/
 
+#print Algebra.sInf_toSubsemiring /-
 @[simp]
 theorem sInf_toSubsemiring (S : Set (Subalgebra R A)) :
     (sInf S).toSubsemiring = sInf (Subalgebra.toSubsemiring '' S) :=
   SetLike.coe_injective <| by simp
 #align algebra.Inf_to_subsemiring Algebra.sInf_toSubsemiring
+-/
 
+#print Algebra.coe_iInf /-
 @[simp, norm_cast]
 theorem coe_iInf {ι : Sort _} {S : ι → Subalgebra R A} : (↑(⨅ i, S i) : Set A) = ⋂ i, S i := by
   simp [iInf]
 #align algebra.coe_infi Algebra.coe_iInf
+-/
 
+#print Algebra.mem_iInf /-
 theorem mem_iInf {ι : Sort _} {S : ι → Subalgebra R A} {x : A} : (x ∈ ⨅ i, S i) ↔ ∀ i, x ∈ S i := by
   simp only [iInf, mem_Inf, Set.forall_range_iff]
 #align algebra.mem_infi Algebra.mem_iInf
+-/
 
+#print Algebra.iInf_toSubmodule /-
 @[simp]
 theorem iInf_toSubmodule {ι : Sort _} (S : ι → Subalgebra R A) :
     (⨅ i, S i).toSubmodule = ⨅ i, (S i).toSubmodule :=
   SetLike.coe_injective <| by simp
 #align algebra.infi_to_submodule Algebra.iInf_toSubmodule
+-/
 
 instance : Inhabited (Subalgebra R A) :=
   ⟨⊥⟩
 
+#print Algebra.mem_bot /-
 theorem mem_bot {x : A} : x ∈ (⊥ : Subalgebra R A) ↔ x ∈ Set.range (algebraMap R A) :=
   suffices (ofId R A).range = (⊥ : Subalgebra R A) by
     rw [← this, ← SetLike.mem_coe, AlgHom.coe_range]; rfl
   le_bot_iff.mp fun x hx => Subalgebra.range_le _ ((ofId R A).coe_range ▸ hx)
 #align algebra.mem_bot Algebra.mem_bot
+-/
 
+#print Algebra.toSubmodule_bot /-
 theorem toSubmodule_bot : (⊥ : Subalgebra R A).toSubmodule = R ∙ 1 := by ext x;
   simp [mem_bot, -Set.singleton_one, Submodule.mem_span_singleton, Algebra.smul_def]
 #align algebra.to_submodule_bot Algebra.toSubmodule_bot
+-/
 
+#print Algebra.coe_bot /-
 @[simp]
 theorem coe_bot : ((⊥ : Subalgebra R A) : Set A) = Set.range (algebraMap R A) := by
   simp [Set.ext_iff, Algebra.mem_bot]
 #align algebra.coe_bot Algebra.coe_bot
+-/
 
+#print Algebra.eq_top_iff /-
 theorem eq_top_iff {S : Subalgebra R A} : S = ⊤ ↔ ∀ x : A, x ∈ S :=
   ⟨fun h x => by rw [h] <;> exact mem_top, fun h => by
     ext x <;> exact ⟨fun _ => mem_top, fun _ => h x⟩⟩
 #align algebra.eq_top_iff Algebra.eq_top_iff
+-/
 
+#print Algebra.range_top_iff_surjective /-
 theorem range_top_iff_surjective (f : A →ₐ[R] B) :
     f.range = (⊤ : Subalgebra R B) ↔ Function.Surjective f :=
   Algebra.eq_top_iff
 #align algebra.range_top_iff_surjective Algebra.range_top_iff_surjective
+-/
 
+#print Algebra.range_id /-
 @[simp]
 theorem range_id : (AlgHom.id R A).range = ⊤ :=
   SetLike.coe_injective Set.range_id
 #align algebra.range_id Algebra.range_id
+-/
 
+#print Algebra.map_top /-
 @[simp]
 theorem map_top (f : A →ₐ[R] B) : (⊤ : Subalgebra R A).map f = f.range :=
   SetLike.coe_injective Set.image_univ
 #align algebra.map_top Algebra.map_top
+-/
 
+#print Algebra.map_bot /-
 @[simp]
 theorem map_bot (f : A →ₐ[R] B) : (⊥ : Subalgebra R A).map f = ⊥ :=
   SetLike.coe_injective <| by
     simp only [← Set.range_comp, (· ∘ ·), Algebra.coe_bot, Subalgebra.coe_map, f.commutes]
 #align algebra.map_bot Algebra.map_bot
+-/
 
+#print Algebra.comap_top /-
 @[simp]
 theorem comap_top (f : A →ₐ[R] B) : (⊤ : Subalgebra R B).comap f = ⊤ :=
   eq_top_iff.2 fun x => mem_top
 #align algebra.comap_top Algebra.comap_top
+-/
 
+#print Algebra.toTop /-
 /-- `alg_hom` to `⊤ : subalgebra R A`. -/
 def toTop : A →ₐ[R] (⊤ : Subalgebra R A) :=
   (AlgHom.id R A).codRestrict ⊤ fun _ => mem_top
 #align algebra.to_top Algebra.toTop
+-/
 
+#print Algebra.surjective_algebraMap_iff /-
 theorem surjective_algebraMap_iff :
     Function.Surjective (algebraMap R A) ↔ (⊤ : Subalgebra R A) = ⊥ :=
   ⟨fun h =>
@@ -1005,13 +1278,17 @@ theorem surjective_algebraMap_iff :
       hx ▸ Subalgebra.algebraMap_mem _ _,
     fun h y => Algebra.mem_bot.1 <| eq_bot_iff.1 h (Algebra.mem_top : y ∈ _)⟩
 #align algebra.surjective_algebra_map_iff Algebra.surjective_algebraMap_iff
+-/
 
+#print Algebra.bijective_algebraMap_iff /-
 theorem bijective_algebraMap_iff {R A : Type _} [Field R] [Semiring A] [Nontrivial A]
     [Algebra R A] : Function.Bijective (algebraMap R A) ↔ (⊤ : Subalgebra R A) = ⊥ :=
   ⟨fun h => surjective_algebraMap_iff.1 h.2, fun h =>
     ⟨(algebraMap R A).Injective, surjective_algebraMap_iff.2 h⟩⟩
 #align algebra.bijective_algebra_map_iff Algebra.bijective_algebraMap_iff
+-/
 
+#print Algebra.botEquivOfInjective /-
 /-- The bottom subalgebra is isomorphic to the base ring. -/
 noncomputable def botEquivOfInjective (h : Function.Injective (algebraMap R A)) :
     (⊥ : Subalgebra R A) ≃ₐ[R] R :=
@@ -1021,13 +1298,16 @@ noncomputable def botEquivOfInjective (h : Function.Injective (algebraMap R A))
         let ⟨x, hx⟩ := Algebra.mem_bot.1 hy
         ⟨x, Subtype.eq hx⟩⟩
 #align algebra.bot_equiv_of_injective Algebra.botEquivOfInjective
+-/
 
+#print Algebra.botEquiv /-
 /-- The bottom subalgebra is isomorphic to the field. -/
 @[simps symm_apply]
 noncomputable def botEquiv (F R : Type _) [Field F] [Semiring R] [Nontrivial R] [Algebra F R] :
     (⊥ : Subalgebra F R) ≃ₐ[F] F :=
   botEquivOfInjective (RingHom.injective _)
 #align algebra.bot_equiv Algebra.botEquiv
+-/
 
 end Algebra
 
@@ -1041,6 +1321,7 @@ variable [CommSemiring R] [Semiring A] [Algebra R A] [Semiring B] [Algebra R B]
 
 variable (S : Subalgebra R A)
 
+#print Subalgebra.topEquiv /-
 /-- The top subalgebra is isomorphic to the algebra.
 
 This is the algebra version of `submodule.top_equiv`. -/
@@ -1048,6 +1329,7 @@ This is the algebra version of `submodule.top_equiv`. -/
 def topEquiv : (⊤ : Subalgebra R A) ≃ₐ[R] A :=
   AlgEquiv.ofAlgHom (Subalgebra.val ⊤) toTop rfl <| AlgHom.ext fun _ => Subtype.ext rfl
 #align subalgebra.top_equiv Subalgebra.topEquiv
+-/
 
 #print Subalgebra.subsingleton_of_subsingleton /-
 instance subsingleton_of_subsingleton [Subsingleton A] : Subsingleton (Subalgebra R A) :=
@@ -1077,9 +1359,11 @@ instance AlgEquiv.subsingleton_right [Subsingleton (Subalgebra R B)] : Subsingle
 #align alg_equiv.subsingleton_right AlgEquiv.subsingleton_right
 -/
 
+#print Subalgebra.range_val /-
 theorem range_val : S.val.range = S :=
   ext <| Set.ext_iff.1 <| S.val.coe_range.trans Subtype.range_val
 #align subalgebra.range_val Subalgebra.range_val
+-/
 
 instance : Unique (Subalgebra R R) :=
   { Algebra.Subalgebra.inhabited with
@@ -1088,6 +1372,7 @@ instance : Unique (Subalgebra R R) :=
       refine' le_antisymm (fun r hr => _) bot_le
       simp only [Set.mem_range, mem_bot, id.map_eq_self, exists_apply_eq_apply, default] }
 
+#print Subalgebra.inclusion /-
 /-- The map `S → T` when `S` is a subalgebra contained in the subalgebra `T`.
 
 This is the subalgebra version of `submodule.of_le`, or `subring.inclusion`  -/
@@ -1100,38 +1385,52 @@ def inclusion {S T : Subalgebra R A} (h : S ≤ T) : S →ₐ[R] T
   map_zero' := rfl
   commutes' _ := rfl
 #align subalgebra.inclusion Subalgebra.inclusion
+-/
 
+#print Subalgebra.inclusion_injective /-
 theorem inclusion_injective {S T : Subalgebra R A} (h : S ≤ T) : Function.Injective (inclusion h) :=
   fun _ _ => Subtype.ext ∘ Subtype.mk.inj
 #align subalgebra.inclusion_injective Subalgebra.inclusion_injective
+-/
 
+#print Subalgebra.inclusion_self /-
 @[simp]
 theorem inclusion_self {S : Subalgebra R A} : inclusion (le_refl S) = AlgHom.id R S :=
   AlgHom.ext fun x => Subtype.ext rfl
 #align subalgebra.inclusion_self Subalgebra.inclusion_self
+-/
 
+#print Subalgebra.inclusion_mk /-
 @[simp]
 theorem inclusion_mk {S T : Subalgebra R A} (h : S ≤ T) (x : A) (hx : x ∈ S) :
     inclusion h ⟨x, hx⟩ = ⟨x, h hx⟩ :=
   rfl
 #align subalgebra.inclusion_mk Subalgebra.inclusion_mk
+-/
 
+#print Subalgebra.inclusion_right /-
 theorem inclusion_right {S T : Subalgebra R A} (h : S ≤ T) (x : T) (m : (x : A) ∈ S) :
     inclusion h ⟨x, m⟩ = x :=
   Subtype.ext rfl
 #align subalgebra.inclusion_right Subalgebra.inclusion_right
+-/
 
+#print Subalgebra.inclusion_inclusion /-
 @[simp]
 theorem inclusion_inclusion {S T U : Subalgebra R A} (hst : S ≤ T) (htu : T ≤ U) (x : S) :
     inclusion htu (inclusion hst x) = inclusion (le_trans hst htu) x :=
   Subtype.ext rfl
 #align subalgebra.inclusion_inclusion Subalgebra.inclusion_inclusion
+-/
 
+#print Subalgebra.coe_inclusion /-
 @[simp]
 theorem coe_inclusion {S T : Subalgebra R A} (h : S ≤ T) (s : S) : (inclusion h s : A) = s :=
   rfl
 #align subalgebra.coe_inclusion Subalgebra.coe_inclusion
+-/
 
+#print Subalgebra.equivOfEq /-
 /-- Two subalgebras that are equal are also equivalent as algebras.
 
 This is the `subalgebra` version of `linear_equiv.of_eq` and `equiv.set.of_eq`. -/
@@ -1145,28 +1444,36 @@ def equivOfEq (S T : Subalgebra R A) (h : S = T) : S ≃ₐ[R] T :=
     map_mul' := fun _ _ => rfl
     commutes' := fun _ => rfl }
 #align subalgebra.equiv_of_eq Subalgebra.equivOfEq
+-/
 
+#print Subalgebra.equivOfEq_symm /-
 @[simp]
 theorem equivOfEq_symm (S T : Subalgebra R A) (h : S = T) :
     (equivOfEq S T h).symm = equivOfEq T S h.symm :=
   rfl
 #align subalgebra.equiv_of_eq_symm Subalgebra.equivOfEq_symm
+-/
 
+#print Subalgebra.equivOfEq_rfl /-
 @[simp]
 theorem equivOfEq_rfl (S : Subalgebra R A) : equivOfEq S S rfl = AlgEquiv.refl := by ext; rfl
 #align subalgebra.equiv_of_eq_rfl Subalgebra.equivOfEq_rfl
+-/
 
+#print Subalgebra.equivOfEq_trans /-
 @[simp]
 theorem equivOfEq_trans (S T U : Subalgebra R A) (hST : S = T) (hTU : T = U) :
     (equivOfEq S T hST).trans (equivOfEq T U hTU) = equivOfEq S U (trans hST hTU) :=
   rfl
 #align subalgebra.equiv_of_eq_trans Subalgebra.equivOfEq_trans
+-/
 
 section Prod
 
 variable (S₁ : Subalgebra R B)
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print Subalgebra.prod /-
 /-- The product of two subalgebras is a subalgebra. -/
 def prod : Subalgebra R (A × B) :=
   {
@@ -1174,37 +1481,50 @@ def prod : Subalgebra R (A × B) :=
     carrier := S ×ˢ S₁
     algebraMap_mem' := fun r => ⟨algebraMap_mem _ _, algebraMap_mem _ _⟩ }
 #align subalgebra.prod Subalgebra.prod
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print Subalgebra.coe_prod /-
 @[simp]
 theorem coe_prod : (prod S S₁ : Set (A × B)) = S ×ˢ S₁ :=
   rfl
 #align subalgebra.coe_prod Subalgebra.coe_prod
+-/
 
+#print Subalgebra.prod_toSubmodule /-
 theorem prod_toSubmodule : (S.Prod S₁).toSubmodule = S.toSubmodule.Prod S₁.toSubmodule :=
   rfl
 #align subalgebra.prod_to_submodule Subalgebra.prod_toSubmodule
+-/
 
+#print Subalgebra.mem_prod /-
 @[simp]
 theorem mem_prod {S : Subalgebra R A} {S₁ : Subalgebra R B} {x : A × B} :
     x ∈ prod S S₁ ↔ x.1 ∈ S ∧ x.2 ∈ S₁ :=
   Set.mem_prod
 #align subalgebra.mem_prod Subalgebra.mem_prod
+-/
 
+#print Subalgebra.prod_top /-
 @[simp]
 theorem prod_top : (prod ⊤ ⊤ : Subalgebra R (A × B)) = ⊤ := by ext <;> simp
 #align subalgebra.prod_top Subalgebra.prod_top
+-/
 
+#print Subalgebra.prod_mono /-
 theorem prod_mono {S T : Subalgebra R A} {S₁ T₁ : Subalgebra R B} :
     S ≤ T → S₁ ≤ T₁ → prod S S₁ ≤ prod T T₁ :=
   Set.prod_mono
 #align subalgebra.prod_mono Subalgebra.prod_mono
+-/
 
+#print Subalgebra.prod_inf_prod /-
 @[simp]
 theorem prod_inf_prod {S T : Subalgebra R A} {S₁ T₁ : Subalgebra R B} :
     S.Prod S₁ ⊓ T.Prod T₁ = (S ⊓ T).Prod (S₁ ⊓ T₁) :=
   SetLike.coe_injective Set.prod_inter_prod
 #align subalgebra.prod_inf_prod Subalgebra.prod_inf_prod
+-/
 
 end Prod
 
@@ -1212,6 +1532,7 @@ section SuprLift
 
 variable {ι : Type _}
 
+#print Subalgebra.coe_iSup_of_directed /-
 theorem coe_iSup_of_directed [Nonempty ι] {S : ι → Subalgebra R A} (dir : Directed (· ≤ ·) S) :
     ↑(iSup S) = ⋃ i, (S i : Set A) :=
   let K : Subalgebra R A :=
@@ -1234,7 +1555,9 @@ theorem coe_iSup_of_directed [Nonempty ι] {S : ι → Subalgebra R A} (dir : Di
       (SetLike.coe_subset_coe.1 (Set.iUnion_subset fun i => SetLike.coe_subset_coe.2 (le_iSup _ _)))
   this.symm ▸ rfl
 #align subalgebra.coe_supr_of_directed Subalgebra.coe_iSup_of_directed
+-/
 
+#print Subalgebra.iSupLift /-
 /-- Define an algebra homomorphism on a directed supremum of subalgebras by defining
 it on each subalgebra, and proving that it agrees on the intersection of subalgebras. -/
 noncomputable def iSupLift [Nonempty ι] (K : ι → Subalgebra R A) (dir : Directed (· ≤ ·) K)
@@ -1261,30 +1584,39 @@ noncomputable def iSupLift [Nonempty ι] (K : ι → Subalgebra R A) (dir : Dire
           Set.iUnionLift_const _ (fun _ => algebraMap _ _ r) (fun _ => rfl) _ fun i => by
             erw [AlgHom.commutes (f i)] }
 #align subalgebra.supr_lift Subalgebra.iSupLift
+-/
 
 variable [Nonempty ι] {K : ι → Subalgebra R A} {dir : Directed (· ≤ ·) K} {f : ∀ i, K i →ₐ[R] B}
   {hf : ∀ (i j : ι) (h : K i ≤ K j), f i = (f j).comp (inclusion h)} {T : Subalgebra R A}
   {hT : T = iSup K}
 
+#print Subalgebra.iSupLift_inclusion /-
 @[simp]
 theorem iSupLift_inclusion {i : ι} (x : K i) (h : K i ≤ T) :
     iSupLift K dir f hf T hT (inclusion h x) = f i x := by
   subst T <;> exact Set.iUnionLift_inclusion _ _
 #align subalgebra.supr_lift_inclusion Subalgebra.iSupLift_inclusion
+-/
 
+#print Subalgebra.iSupLift_comp_inclusion /-
 @[simp]
 theorem iSupLift_comp_inclusion {i : ι} (h : K i ≤ T) :
     (iSupLift K dir f hf T hT).comp (inclusion h) = f i := by ext <;> simp
 #align subalgebra.supr_lift_comp_inclusion Subalgebra.iSupLift_comp_inclusion
+-/
 
+#print Subalgebra.iSupLift_mk /-
 @[simp]
 theorem iSupLift_mk {i : ι} (x : K i) (hx : (x : A) ∈ T) :
     iSupLift K dir f hf T hT ⟨x, hx⟩ = f i x := by subst hT <;> exact Set.iUnionLift_mk x hx
 #align subalgebra.supr_lift_mk Subalgebra.iSupLift_mk
+-/
 
+#print Subalgebra.iSupLift_of_mem /-
 theorem iSupLift_of_mem {i : ι} (x : T) (hx : (x : A) ∈ K i) :
     iSupLift K dir f hf T hT x = f i ⟨x, hx⟩ := by subst hT <;> exact Set.iUnionLift_of_mem x hx
 #align subalgebra.supr_lift_of_mem Subalgebra.iSupLift_of_mem
+-/
 
 end SuprLift
 
@@ -1303,31 +1635,41 @@ variable {α β : Type _}
 instance [SMul A α] (S : Subalgebra R A) : SMul S α :=
   S.toSubsemiring.SMul
 
+#print Subalgebra.smul_def /-
 theorem smul_def [SMul A α] {S : Subalgebra R A} (g : S) (m : α) : g • m = (g : A) • m :=
   rfl
 #align subalgebra.smul_def Subalgebra.smul_def
+-/
 
+#print Subalgebra.smulCommClass_left /-
 instance smulCommClass_left [SMul A β] [SMul α β] [SMulCommClass A α β] (S : Subalgebra R A) :
     SMulCommClass S α β :=
   S.toSubsemiring.smulCommClass_left
 #align subalgebra.smul_comm_class_left Subalgebra.smulCommClass_left
+-/
 
+#print Subalgebra.smulCommClass_right /-
 instance smulCommClass_right [SMul α β] [SMul A β] [SMulCommClass α A β] (S : Subalgebra R A) :
     SMulCommClass α S β :=
   S.toSubsemiring.smulCommClass_right
 #align subalgebra.smul_comm_class_right Subalgebra.smulCommClass_right
+-/
 
+#print Subalgebra.isScalarTower_left /-
 /-- Note that this provides `is_scalar_tower S R R` which is needed by `smul_mul_assoc`. -/
 instance isScalarTower_left [SMul α β] [SMul A α] [SMul A β] [IsScalarTower A α β]
     (S : Subalgebra R A) : IsScalarTower S α β :=
   S.toSubsemiring.IsScalarTower
 #align subalgebra.is_scalar_tower_left Subalgebra.isScalarTower_left
+-/
 
+#print Subalgebra.isScalarTower_mid /-
 instance isScalarTower_mid {R S T : Type _} [CommSemiring R] [Semiring S] [AddCommMonoid T]
     [Algebra R S] [Module R T] [Module S T] [IsScalarTower R S T] (S' : Subalgebra R S) :
     IsScalarTower R S' T :=
   ⟨fun x y z => (smul_assoc _ (y : S) _ : _)⟩
 #align subalgebra.is_scalar_tower_mid Subalgebra.isScalarTower_mid
+-/
 
 instance [SMul A α] [FaithfulSMul A α] (S : Subalgebra R A) : FaithfulSMul S α :=
   S.toSubsemiring.FaithfulSMul
@@ -1348,49 +1690,63 @@ instance [Zero α] [SMulWithZero A α] (S : Subalgebra R A) : SMulWithZero S α
 instance [Zero α] [MulActionWithZero A α] (S : Subalgebra R A) : MulActionWithZero S α :=
   S.toSubsemiring.MulActionWithZero
 
+#print Subalgebra.moduleLeft /-
 /-- The action by a subalgebra is the action by the underlying algebra. -/
 instance moduleLeft [AddCommMonoid α] [Module A α] (S : Subalgebra R A) : Module S α :=
   S.toSubsemiring.Module
 #align subalgebra.module_left Subalgebra.moduleLeft
+-/
 
+#print Subalgebra.toAlgebra /-
 /-- The action by a subalgebra is the action by the underlying algebra. -/
 instance toAlgebra {R A : Type _} [CommSemiring R] [CommSemiring A] [Semiring α] [Algebra R A]
     [Algebra A α] (S : Subalgebra R A) : Algebra S α :=
   Algebra.ofSubsemiring S.toSubsemiring
 #align subalgebra.to_algebra Subalgebra.toAlgebra
+-/
 
+#print Subalgebra.algebraMap_eq /-
 theorem algebraMap_eq {R A : Type _} [CommSemiring R] [CommSemiring A] [Semiring α] [Algebra R A]
     [Algebra A α] (S : Subalgebra R A) : algebraMap S α = (algebraMap A α).comp S.val :=
   rfl
 #align subalgebra.algebra_map_eq Subalgebra.algebraMap_eq
+-/
 
+#print Subalgebra.rangeS_algebraMap /-
 @[simp]
 theorem rangeS_algebraMap {R A : Type _} [CommSemiring R] [CommSemiring A] [Algebra R A]
     (S : Subalgebra R A) : (algebraMap S A).srange = S.toSubsemiring := by
   rw [algebra_map_eq, Algebra.id.map_eq_id, RingHom.id_comp, ← to_subsemiring_subtype,
     Subsemiring.rangeS_subtype]
 #align subalgebra.srange_algebra_map Subalgebra.rangeS_algebraMap
+-/
 
+#print Subalgebra.range_algebraMap /-
 @[simp]
 theorem range_algebraMap {R A : Type _} [CommRing R] [CommRing A] [Algebra R A]
     (S : Subalgebra R A) : (algebraMap S A).range = S.toSubring := by
   rw [algebra_map_eq, Algebra.id.map_eq_id, RingHom.id_comp, ← to_subring_subtype,
     Subring.range_subtype]
 #align subalgebra.range_algebra_map Subalgebra.range_algebraMap
+-/
 
+#print Subalgebra.noZeroSMulDivisors_top /-
 instance noZeroSMulDivisors_top [NoZeroDivisors A] (S : Subalgebra R A) : NoZeroSMulDivisors S A :=
   ⟨fun c x h =>
     have : (c : A) = 0 ∨ x = 0 := eq_zero_or_eq_zero_of_mul_eq_zero h
     this.imp_left (@Subtype.ext_iff _ _ c 0).mpr⟩
 #align subalgebra.no_zero_smul_divisors_top Subalgebra.noZeroSMulDivisors_top
+-/
 
 end Actions
 
 section Center
 
+#print Set.algebraMap_mem_center /-
 theorem Set.algebraMap_mem_center (r : R) : algebraMap R A r ∈ Set.center A := by
   simp [Algebra.commutes, Set.mem_center_iff]
 #align set.algebra_map_mem_center Set.algebraMap_mem_center
+-/
 
 variable (R A)
 
@@ -1402,9 +1758,11 @@ def center : Subalgebra R A :=
 #align subalgebra.center Subalgebra.center
 -/
 
+#print Subalgebra.coe_center /-
 theorem coe_center : (center R A : Set A) = Set.center A :=
   rfl
 #align subalgebra.coe_center Subalgebra.coe_center
+-/
 
 #print Subalgebra.center_toSubsemiring /-
 @[simp]
@@ -1413,16 +1771,20 @@ theorem center_toSubsemiring : (center R A).toSubsemiring = Subsemiring.center A
 #align subalgebra.center_to_subsemiring Subalgebra.center_toSubsemiring
 -/
 
+#print Subalgebra.center_toSubring /-
 @[simp]
 theorem center_toSubring (R A : Type _) [CommRing R] [Ring A] [Algebra R A] :
     (center R A).toSubring = Subring.center A :=
   rfl
 #align subalgebra.center_to_subring Subalgebra.center_toSubring
+-/
 
+#print Subalgebra.center_eq_top /-
 @[simp]
 theorem center_eq_top (A : Type _) [CommSemiring A] [Algebra R A] : center R A = ⊤ :=
   SetLike.coe_injective (Set.center_eq_univ A)
 #align subalgebra.center_eq_top Subalgebra.center_eq_top
+-/
 
 variable {R A}
 
@@ -1432,18 +1794,22 @@ instance : CommSemiring (center R A) :=
 instance {A : Type _} [Ring A] [Algebra R A] : CommRing (center R A) :=
   Subring.center.commRing
 
+#print Subalgebra.mem_center_iff /-
 theorem mem_center_iff {a : A} : a ∈ center R A ↔ ∀ b : A, b * a = a * b :=
   Iff.rfl
 #align subalgebra.mem_center_iff Subalgebra.mem_center_iff
+-/
 
 end Center
 
 section Centralizer
 
+#print Set.algebraMap_mem_centralizer /-
 @[simp]
 theorem Set.algebraMap_mem_centralizer {s : Set A} (r : R) : algebraMap R A r ∈ s.centralizer :=
   fun a h => (Algebra.commutes _ _).symm
 #align set.algebra_map_mem_centralizer Set.algebraMap_mem_centralizer
+-/
 
 variable (R)
 
@@ -1454,27 +1820,37 @@ def centralizer (s : Set A) : Subalgebra R A :=
 #align subalgebra.centralizer Subalgebra.centralizer
 -/
 
+#print Subalgebra.coe_centralizer /-
 @[simp, norm_cast]
 theorem coe_centralizer (s : Set A) : (centralizer R s : Set A) = s.centralizer :=
   rfl
 #align subalgebra.coe_centralizer Subalgebra.coe_centralizer
+-/
 
+#print Subalgebra.mem_centralizer_iff /-
 theorem mem_centralizer_iff {s : Set A} {z : A} : z ∈ centralizer R s ↔ ∀ g ∈ s, g * z = z * g :=
   Iff.rfl
 #align subalgebra.mem_centralizer_iff Subalgebra.mem_centralizer_iff
+-/
 
+#print Subalgebra.center_le_centralizer /-
 theorem center_le_centralizer (s) : center R A ≤ centralizer R s :=
   s.center_subset_centralizer
 #align subalgebra.center_le_centralizer Subalgebra.center_le_centralizer
+-/
 
+#print Subalgebra.centralizer_le /-
 theorem centralizer_le (s t : Set A) (h : s ⊆ t) : centralizer R t ≤ centralizer R s :=
   Set.centralizer_subset h
 #align subalgebra.centralizer_le Subalgebra.centralizer_le
+-/
 
+#print Subalgebra.centralizer_eq_top_iff_subset /-
 @[simp]
 theorem centralizer_eq_top_iff_subset {s : Set A} : centralizer R s = ⊤ ↔ s ⊆ center R A :=
   SetLike.ext'_iff.trans Set.centralizer_eq_top_iff_subset
 #align subalgebra.centralizer_eq_top_iff_subset Subalgebra.centralizer_eq_top_iff_subset
+-/
 
 #print Subalgebra.centralizer_univ /-
 @[simp]
@@ -1485,6 +1861,7 @@ theorem centralizer_univ : centralizer R Set.univ = center R A :=
 
 end Centralizer
 
+#print Subalgebra.mem_of_finset_sum_eq_one_of_pow_smul_mem /-
 /-- Suppose we are given `∑ i, lᵢ * sᵢ = 1` in `S`, and `S'` a subalgebra of `S` that contains
 `lᵢ` and `sᵢ`. To check that an `x : S` falls in `S'`, we only need to show that
 `r ^ n • x ∈ M'` for some `n` for each `r : s`. -/
@@ -1516,13 +1893,16 @@ theorem mem_of_finset_sum_eq_one_of_pow_smul_mem {S : Type _} [CommRing S] [Alge
   refine' Submodule.smul_mem _ (⟨_, pow_mem (hs i) _⟩ : S') _
   exact ⟨⟨_, hn i⟩, rfl⟩
 #align subalgebra.mem_of_finset_sum_eq_one_of_pow_smul_mem Subalgebra.mem_of_finset_sum_eq_one_of_pow_smul_mem
+-/
 
+#print Subalgebra.mem_of_span_eq_top_of_smul_pow_mem /-
 theorem mem_of_span_eq_top_of_smul_pow_mem {S : Type _} [CommRing S] [Algebra R S]
     (S' : Subalgebra R S) (s : Set S) (l : s →₀ S) (hs : Finsupp.total s S S coe l = 1)
     (hs' : s ⊆ S') (hl : ∀ i, l i ∈ S') (x : S) (H : ∀ r : s, ∃ n : ℕ, (r ^ n : S) • x ∈ S') :
     x ∈ S' :=
   mem_of_finset_sum_eq_one_of_pow_smul_mem S' l.support coe l hs (fun x => hs' x.2) hl x H
 #align subalgebra.mem_of_span_eq_top_of_smul_pow_mem Subalgebra.mem_of_span_eq_top_of_smul_pow_mem
+-/
 
 end Subalgebra
 
@@ -1537,11 +1917,13 @@ def subalgebraOfSubsemiring (S : Subsemiring R) : Subalgebra ℕ R :=
 #align subalgebra_of_subsemiring subalgebraOfSubsemiring
 -/
 
+#print mem_subalgebraOfSubsemiring /-
 @[simp]
 theorem mem_subalgebraOfSubsemiring {x : R} {S : Subsemiring R} :
     x ∈ subalgebraOfSubsemiring S ↔ x ∈ S :=
   Iff.rfl
 #align mem_subalgebra_of_subsemiring mem_subalgebraOfSubsemiring
+-/
 
 end Nat
 
@@ -1549,6 +1931,7 @@ section Int
 
 variable {R : Type _} [Ring R]
 
+#print subalgebraOfSubring /-
 /-- A subring is a `ℤ`-subalgebra. -/
 def subalgebraOfSubring (S : Subring R) : Subalgebra ℤ R :=
   { S with
@@ -1559,13 +1942,16 @@ def subalgebraOfSubring (S : Subring R) : Subalgebra ℤ R :=
           rw [Int.cast_sub, Int.cast_one]
           exact S.sub_mem ih S.one_mem }
 #align subalgebra_of_subring subalgebraOfSubring
+-/
 
 variable {S : Type _} [Semiring S]
 
+#print mem_subalgebraOfSubring /-
 @[simp]
 theorem mem_subalgebraOfSubring {x : R} {S : Subring R} : x ∈ subalgebraOfSubring S ↔ x ∈ S :=
   Iff.rfl
 #align mem_subalgebra_of_subring mem_subalgebraOfSubring
+-/
 
 end Int

bump to nightly-2023-06-10-07

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

3fdc57bc

Diff

@@ -180,7 +180,7 @@ protected theorem multiset_sum_mem {m : Multiset A} (h : ∀ x ∈ m, x ∈ S) :
 #align subalgebra.multiset_sum_mem Subalgebra.multiset_sum_mem
 
 protected theorem sum_mem {ι : Type w} {t : Finset ι} {f : ι → A} (h : ∀ x ∈ t, f x ∈ S) :
-    (∑ x in t, f x) ∈ S :=
+    ∑ x in t, f x ∈ S :=
   sum_mem h
 #align subalgebra.sum_mem Subalgebra.sum_mem
 
@@ -191,7 +191,7 @@ protected theorem multiset_prod_mem {R : Type u} {A : Type v} [CommSemiring R] [
 
 protected theorem prod_mem {R : Type u} {A : Type v} [CommSemiring R] [CommSemiring A] [Algebra R A]
     (S : Subalgebra R A) {ι : Type w} {t : Finset ι} {f : ι → A} (h : ∀ x ∈ t, f x ∈ S) :
-    (∏ x in t, f x) ∈ S :=
+    ∏ x in t, f x ∈ S :=
   prod_mem h
 #align subalgebra.prod_mem Subalgebra.prod_mem
 
@@ -1490,7 +1490,7 @@ end Centralizer
 `r ^ n • x ∈ M'` for some `n` for each `r : s`. -/
 theorem mem_of_finset_sum_eq_one_of_pow_smul_mem {S : Type _} [CommRing S] [Algebra R S]
     (S' : Subalgebra R S) {ι : Type _} (ι' : Finset ι) (s : ι → S) (l : ι → S)
-    (e : (∑ i in ι', l i * s i) = 1) (hs : ∀ i, s i ∈ S') (hl : ∀ i, l i ∈ S') (x : S)
+    (e : ∑ i in ι', l i * s i = 1) (hs : ∀ i, s i ∈ S') (hl : ∀ i, l i ∈ S') (x : S)
     (H : ∀ i, ∃ n : ℕ, (s i ^ n : S) • x ∈ S') : x ∈ S' := by
   classical
   suffices x ∈ (Algebra.ofId S' S).range.toSubmodule by obtain ⟨x, rfl⟩ := this; exact x.2

bump to nightly-2023-06-09-03

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

fe176e9b

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau, Yury Kudryashov
 
 ! This file was ported from Lean 3 source module algebra.algebra.subalgebra.basic
-! leanprover-community/mathlib commit 8130e5155d637db35907c272de9aec9dc851c03a
+! leanprover-community/mathlib commit b915e9392ecb2a861e1e766f0e1df6ac481188ca
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -1463,10 +1463,19 @@ theorem mem_centralizer_iff {s : Set A} {z : A} : z ∈ centralizer R s ↔ ∀
   Iff.rfl
 #align subalgebra.mem_centralizer_iff Subalgebra.mem_centralizer_iff
 
+theorem center_le_centralizer (s) : center R A ≤ centralizer R s :=
+  s.center_subset_centralizer
+#align subalgebra.center_le_centralizer Subalgebra.center_le_centralizer
+
 theorem centralizer_le (s t : Set A) (h : s ⊆ t) : centralizer R t ≤ centralizer R s :=
   Set.centralizer_subset h
 #align subalgebra.centralizer_le Subalgebra.centralizer_le
 
+@[simp]
+theorem centralizer_eq_top_iff_subset {s : Set A} : centralizer R s = ⊤ ↔ s ⊆ center R A :=
+  SetLike.ext'_iff.trans Set.centralizer_eq_top_iff_subset
+#align subalgebra.centralizer_eq_top_iff_subset Subalgebra.centralizer_eq_top_iff_subset
+
 #print Subalgebra.centralizer_univ /-
 @[simp]
 theorem centralizer_univ : centralizer R Set.univ = center R A :=

bump to nightly-2023-06-04-18

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

3fb4268b

Diff

@@ -712,7 +712,7 @@ def rangeRestrict (f : A →ₐ[R] B) : A →ₐ[R] f.range :=
 /-- The equalizer of two R-algebra homomorphisms -/
 def equalizer (ϕ ψ : A →ₐ[R] B) : Subalgebra R A
     where
-  carrier := { a | ϕ a = ψ a }
+  carrier := {a | ϕ a = ψ a}
   add_mem' x y (hx : ϕ x = ψ x) (hy : ϕ y = ψ y) := by
     rw [Set.mem_setOf_eq, ϕ.map_add, ψ.map_add, hx, hy]
   mul_mem' x y (hx : ϕ x = ψ x) (hy : ϕ y = ψ y) := by
@@ -1484,28 +1484,28 @@ theorem mem_of_finset_sum_eq_one_of_pow_smul_mem {S : Type _} [CommRing S] [Alge
     (e : (∑ i in ι', l i * s i) = 1) (hs : ∀ i, s i ∈ S') (hl : ∀ i, l i ∈ S') (x : S)
     (H : ∀ i, ∃ n : ℕ, (s i ^ n : S) • x ∈ S') : x ∈ S' := by
   classical
-    suffices x ∈ (Algebra.ofId S' S).range.toSubmodule by obtain ⟨x, rfl⟩ := this; exact x.2
-    choose n hn using H
-    let s' : ι → S' := fun x => ⟨s x, hs x⟩
-    have : Ideal.span (s' '' ι') = ⊤ :=
-      by
-      rw [Ideal.eq_top_iff_one, Ideal.span, Finsupp.mem_span_iff_total]
-      refine'
-        ⟨(Finsupp.ofSupportFinite (fun i : ι' => (⟨l i, hl i⟩ : S')) (Set.toFinite _)).mapDomain
-            fun i => ⟨s' i, i, i.2, rfl⟩,
-          S'.to_submodule.injective_subtype _⟩
-      rw [Finsupp.total_mapDomain, Finsupp.total_apply, Finsupp.sum_fintype, map_sum,
-        Submodule.subtype_apply, Subalgebra.coe_one]
-      · exact finset.sum_attach.trans e
-      · exact fun _ => zero_smul _ _
-    let N := ι'.sup n
-    have hs' := Ideal.span_pow_eq_top _ this N
-    apply (Algebra.ofId S' S).range.toSubmodule.mem_of_span_top_of_smul_mem _ hs'
-    rintro ⟨_, _, ⟨i, hi, rfl⟩, rfl⟩
-    change s i ^ N • x ∈ _
-    rw [← tsub_add_cancel_of_le (show n i ≤ N from Finset.le_sup hi), pow_add, mul_smul]
-    refine' Submodule.smul_mem _ (⟨_, pow_mem (hs i) _⟩ : S') _
-    exact ⟨⟨_, hn i⟩, rfl⟩
+  suffices x ∈ (Algebra.ofId S' S).range.toSubmodule by obtain ⟨x, rfl⟩ := this; exact x.2
+  choose n hn using H
+  let s' : ι → S' := fun x => ⟨s x, hs x⟩
+  have : Ideal.span (s' '' ι') = ⊤ :=
+    by
+    rw [Ideal.eq_top_iff_one, Ideal.span, Finsupp.mem_span_iff_total]
+    refine'
+      ⟨(Finsupp.ofSupportFinite (fun i : ι' => (⟨l i, hl i⟩ : S')) (Set.toFinite _)).mapDomain
+          fun i => ⟨s' i, i, i.2, rfl⟩,
+        S'.to_submodule.injective_subtype _⟩
+    rw [Finsupp.total_mapDomain, Finsupp.total_apply, Finsupp.sum_fintype, map_sum,
+      Submodule.subtype_apply, Subalgebra.coe_one]
+    · exact finset.sum_attach.trans e
+    · exact fun _ => zero_smul _ _
+  let N := ι'.sup n
+  have hs' := Ideal.span_pow_eq_top _ this N
+  apply (Algebra.ofId S' S).range.toSubmodule.mem_of_span_top_of_smul_mem _ hs'
+  rintro ⟨_, _, ⟨i, hi, rfl⟩, rfl⟩
+  change s i ^ N • x ∈ _
+  rw [← tsub_add_cancel_of_le (show n i ≤ N from Finset.le_sup hi), pow_add, mul_smul]
+  refine' Submodule.smul_mem _ (⟨_, pow_mem (hs i) _⟩ : S') _
+  exact ⟨⟨_, hn i⟩, rfl⟩
 #align subalgebra.mem_of_finset_sum_eq_one_of_pow_smul_mem Subalgebra.mem_of_finset_sum_eq_one_of_pow_smul_mem
 
 theorem mem_of_span_eq_top_of_smul_pow_mem {S : Type _} [CommRing S] [Algebra R S]

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -32,7 +32,7 @@ open scoped BigOperators
 #print Subalgebra /-
 /-- A subalgebra is a sub(semi)ring that includes the range of `algebra_map`. -/
 structure Subalgebra (R : Type u) (A : Type v) [CommSemiring R] [Semiring A] [Algebra R A] extends
-  Subsemiring A : Type v where
+    Subsemiring A : Type v where
   algebraMap_mem' : ∀ r, algebraMap R A r ∈ carrier
   zero_mem' := (algebraMap R A).map_zero ▸ algebra_map_mem' 0
   one_mem' := (algebraMap R A).map_one ▸ algebra_map_mem' 1

bump to nightly-2023-06-01-04

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

4d9eaa85

Diff

@@ -508,12 +508,10 @@ theorem map_mono {S₁ S₂ : Subalgebra R A} {f : A →ₐ[R] B} : S₁ ≤ S
   Set.image_subset f
 #align subalgebra.map_mono Subalgebra.map_mono
 
-#print Subalgebra.map_injective /-
 theorem map_injective {f : A →ₐ[R] B} (hf : Function.Injective f) : Function.Injective (map f) :=
   fun S₁ S₂ ih =>
   ext <| Set.ext_iff.1 <| Set.image_injective.2 hf <| Set.ext <| SetLike.ext_iff.mp ih
 #align subalgebra.map_injective Subalgebra.map_injective
--/
 
 #print Subalgebra.map_id /-
 @[simp]
@@ -743,7 +741,6 @@ variable {R : Type u} {A : Type v} {B : Type w}
 
 variable [CommSemiring R] [Semiring A] [Semiring B] [Algebra R A] [Algebra R B]
 
-#print AlgEquiv.ofLeftInverse /-
 /-- Restrict an algebra homomorphism with a left inverse to an algebra isomorphism to its range.
 
 This is a computable alternative to `alg_equiv.of_injective`. -/
@@ -757,38 +754,29 @@ def ofLeftInverse {g : B → A} {f : A →ₐ[R] B} (h : Function.LeftInverse g
         let ⟨x', hx'⟩ := f.mem_range.mp x.Prop
         show f (g x) = x by rw [← hx', h x'] }
 #align alg_equiv.of_left_inverse AlgEquiv.ofLeftInverse
--/
 
-#print AlgEquiv.ofLeftInverse_apply /-
 @[simp]
 theorem ofLeftInverse_apply {g : B → A} {f : A →ₐ[R] B} (h : Function.LeftInverse g f) (x : A) :
     ↑(ofLeftInverse h x) = f x :=
   rfl
 #align alg_equiv.of_left_inverse_apply AlgEquiv.ofLeftInverse_apply
--/
 
-#print AlgEquiv.ofLeftInverse_symm_apply /-
 @[simp]
 theorem ofLeftInverse_symm_apply {g : B → A} {f : A →ₐ[R] B} (h : Function.LeftInverse g f)
     (x : f.range) : (ofLeftInverse h).symm x = g x :=
   rfl
 #align alg_equiv.of_left_inverse_symm_apply AlgEquiv.ofLeftInverse_symm_apply
--/
 
-#print AlgEquiv.ofInjective /-
 /-- Restrict an injective algebra homomorphism to an algebra isomorphism -/
 noncomputable def ofInjective (f : A →ₐ[R] B) (hf : Function.Injective f) : A ≃ₐ[R] f.range :=
   ofLeftInverse (Classical.choose_spec hf.HasLeftInverse)
 #align alg_equiv.of_injective AlgEquiv.ofInjective
--/
 
-#print AlgEquiv.ofInjective_apply /-
 @[simp]
 theorem ofInjective_apply (f : A →ₐ[R] B) (hf : Function.Injective f) (x : A) :
     ↑(ofInjective f hf x) = f x :=
   rfl
 #align alg_equiv.of_injective_apply AlgEquiv.ofInjective_apply
--/
 
 /-- Restrict an algebra homomorphism between fields to an algebra isomorphism -/
 noncomputable def ofInjectiveField {E F : Type _} [DivisionRing E] [Semiring F] [Nontrivial F]

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -27,7 +27,7 @@ More lemmas about `adjoin` can be found in `ring_theory.adjoin`.
 
 universe u u' v w w'
 
-open BigOperators
+open scoped BigOperators
 
 #print Subalgebra /-
 /-- A subalgebra is a sub(semi)ring that includes the range of `algebra_map`. -/

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -64,45 +64,21 @@ instance : SubsemiringClass (Subalgebra R A) A
   one_mem := one_mem'
   zero_mem := zero_mem'
 
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-Case conversion may be inaccurate. Consider using '#align subalgebra.mem_carrier Subalgebra.mem_carrierₓ'. -/
 @[simp]
 theorem mem_carrier {s : Subalgebra R A} {x : A} : x ∈ s.carrier ↔ x ∈ s :=
   Iff.rfl
 #align subalgebra.mem_carrier Subalgebra.mem_carrier
 
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-Case conversion may be inaccurate. Consider using '#align subalgebra.ext Subalgebra.extₓ'. -/
 @[ext]
 theorem ext {S T : Subalgebra R A} (h : ∀ x : A, x ∈ S ↔ x ∈ T) : S = T :=
   SetLike.ext h
 #align subalgebra.ext Subalgebra.ext
 
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-Case conversion may be inaccurate. Consider using '#align subalgebra.mem_to_subsemiring Subalgebra.mem_toSubsemiringₓ'. -/
 @[simp]
 theorem mem_toSubsemiring {S : Subalgebra R A} {x} : x ∈ S.toSubsemiring ↔ x ∈ S :=
   Iff.rfl
 #align subalgebra.mem_to_subsemiring Subalgebra.mem_toSubsemiring
 
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-Case conversion may be inaccurate. Consider using '#align subalgebra.coe_to_subsemiring Subalgebra.coe_toSubsemiringₓ'. -/
 @[simp]
 theorem coe_toSubsemiring (S : Subalgebra R A) : (↑S.toSubsemiring : Set A) = S :=
   rfl
@@ -121,12 +97,6 @@ theorem toSubsemiring_inj {S U : Subalgebra R A} : S.toSubsemiring = U.toSubsemi
 #align subalgebra.to_subsemiring_inj Subalgebra.toSubsemiring_inj
 -/
 
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-Case conversion may be inaccurate. Consider using '#align subalgebra.copy Subalgebra.copyₓ'. -/
 /-- Copy of a subalgebra with a new `carrier` equal to the old one. Useful to fix definitional
 equalities. -/
 protected def copy (S : Subalgebra R A) (s : Set A) (hs : s = ↑S) : Subalgebra R A
@@ -137,208 +107,88 @@ protected def copy (S : Subalgebra R A) (s : Set A) (hs : s = ↑S) : Subalgebra
   algebraMap_mem' := hs.symm ▸ S.algebraMap_mem'
 #align subalgebra.copy Subalgebra.copy
 
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 @[simp]
 theorem coe_copy (S : Subalgebra R A) (s : Set A) (hs : s = ↑S) : (S.copy s hs : Set A) = s :=
   rfl
 #align subalgebra.coe_copy Subalgebra.coe_copy
 
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 theorem copy_eq (S : Subalgebra R A) (s : Set A) (hs : s = ↑S) : S.copy s hs = S :=
   SetLike.coe_injective hs
 #align subalgebra.copy_eq Subalgebra.copy_eq
 
 variable (S : Subalgebra R A)
 
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 theorem algebraMap_mem (r : R) : algebraMap R A r ∈ S :=
   S.algebraMap_mem' r
 #align subalgebra.algebra_map_mem Subalgebra.algebraMap_mem
 
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 theorem rangeS_le : (algebraMap R A).srange ≤ S.toSubsemiring := fun x ⟨r, hr⟩ =>
   hr ▸ S.algebraMap_mem r
 #align subalgebra.srange_le Subalgebra.rangeS_le
 
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 theorem range_subset : Set.range (algebraMap R A) ⊆ S := fun x ⟨r, hr⟩ => hr ▸ S.algebraMap_mem r
 #align subalgebra.range_subset Subalgebra.range_subset
 
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 theorem range_le : Set.range (algebraMap R A) ≤ S :=
   S.range_subset
 #align subalgebra.range_le Subalgebra.range_le
 
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 theorem smul_mem {x : A} (hx : x ∈ S) (r : R) : r • x ∈ S :=
   (Algebra.smul_def r x).symm ▸ mul_mem (S.algebraMap_mem r) hx
 #align subalgebra.smul_mem Subalgebra.smul_mem
 
 instance : SMulMemClass (Subalgebra R A) R A where smul_mem S r x hx := smul_mem S hx r
 
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 protected theorem one_mem : (1 : A) ∈ S :=
   one_mem S
 #align subalgebra.one_mem Subalgebra.one_mem
 
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 protected theorem mul_mem {x y : A} (hx : x ∈ S) (hy : y ∈ S) : x * y ∈ S :=
   mul_mem hx hy
 #align subalgebra.mul_mem Subalgebra.mul_mem
 
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 protected theorem pow_mem {x : A} (hx : x ∈ S) (n : ℕ) : x ^ n ∈ S :=
   pow_mem hx n
 #align subalgebra.pow_mem Subalgebra.pow_mem
 
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 protected theorem zero_mem : (0 : A) ∈ S :=
   zero_mem S
 #align subalgebra.zero_mem Subalgebra.zero_mem
 
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 protected theorem add_mem {x y : A} (hx : x ∈ S) (hy : y ∈ S) : x + y ∈ S :=
   add_mem hx hy
 #align subalgebra.add_mem Subalgebra.add_mem
 
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 protected theorem nsmul_mem {x : A} (hx : x ∈ S) (n : ℕ) : n • x ∈ S :=
   nsmul_mem hx n
 #align subalgebra.nsmul_mem Subalgebra.nsmul_mem
 
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 protected theorem coe_nat_mem (n : ℕ) : (n : A) ∈ S :=
   coe_nat_mem S n
 #align subalgebra.coe_nat_mem Subalgebra.coe_nat_mem
 
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 protected theorem list_prod_mem {L : List A} (h : ∀ x ∈ L, x ∈ S) : L.Prod ∈ S :=
   list_prod_mem h
 #align subalgebra.list_prod_mem Subalgebra.list_prod_mem
 
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 protected theorem list_sum_mem {L : List A} (h : ∀ x ∈ L, x ∈ S) : L.Sum ∈ S :=
   list_sum_mem h
 #align subalgebra.list_sum_mem Subalgebra.list_sum_mem
 
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 protected theorem multiset_sum_mem {m : Multiset A} (h : ∀ x ∈ m, x ∈ S) : m.Sum ∈ S :=
   multiset_sum_mem m h
 #align subalgebra.multiset_sum_mem Subalgebra.multiset_sum_mem
 
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 protected theorem sum_mem {ι : Type w} {t : Finset ι} {f : ι → A} (h : ∀ x ∈ t, f x ∈ S) :
     (∑ x in t, f x) ∈ S :=
   sum_mem h
 #align subalgebra.sum_mem Subalgebra.sum_mem
 
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 protected theorem multiset_prod_mem {R : Type u} {A : Type v} [CommSemiring R] [CommSemiring A]
     [Algebra R A] (S : Subalgebra R A) {m : Multiset A} (h : ∀ x ∈ m, x ∈ S) : m.Prod ∈ S :=
   multiset_prod_mem m h
 #align subalgebra.multiset_prod_mem Subalgebra.multiset_prod_mem
 
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 protected theorem prod_mem {R : Type u} {A : Type v} [CommSemiring R] [CommSemiring A] [Algebra R A]
     (S : Subalgebra R A) {ι : Type w} {t : Finset ι} {f : ι → A} (h : ∀ x ∈ t, f x ∈ S) :
     (∏ x in t, f x) ∈ S :=
@@ -348,45 +198,21 @@ protected theorem prod_mem {R : Type u} {A : Type v} [CommSemiring R] [CommSemir
 instance {R A : Type _} [CommRing R] [Ring A] [Algebra R A] : SubringClass (Subalgebra R A) A :=
   { Subalgebra.subsemiringClass with neg_mem := fun S x hx => neg_one_smul R x ▸ S.smul_mem hx _ }
 
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 protected theorem neg_mem {R : Type u} {A : Type v} [CommRing R] [Ring A] [Algebra R A]
     (S : Subalgebra R A) {x : A} (hx : x ∈ S) : -x ∈ S :=
   neg_mem hx
 #align subalgebra.neg_mem Subalgebra.neg_mem
 
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 protected theorem sub_mem {R : Type u} {A : Type v} [CommRing R] [Ring A] [Algebra R A]
     (S : Subalgebra R A) {x y : A} (hx : x ∈ S) (hy : y ∈ S) : x - y ∈ S :=
   sub_mem hx hy
 #align subalgebra.sub_mem Subalgebra.sub_mem
 
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 protected theorem zsmul_mem {R : Type u} {A : Type v} [CommRing R] [Ring A] [Algebra R A]
     (S : Subalgebra R A) {x : A} (hx : x ∈ S) (n : ℤ) : n • x ∈ S :=
   zsmul_mem hx n
 #align subalgebra.zsmul_mem Subalgebra.zsmul_mem
 
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 protected theorem coe_int_mem {R : Type u} {A : Type v} [CommRing R] [Ring A] [Algebra R A]
     (S : Subalgebra R A) (n : ℤ) : (n : A) ∈ S :=
   coe_int_mem S n
@@ -414,24 +240,12 @@ def toSubring {R : Type u} {A : Type v} [CommRing R] [Ring A] [Algebra R A] (S :
 #align subalgebra.to_subring Subalgebra.toSubring
 -/
 
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 @[simp]
 theorem mem_toSubring {R : Type u} {A : Type v} [CommRing R] [Ring A] [Algebra R A]
     {S : Subalgebra R A} {x} : x ∈ S.toSubring ↔ x ∈ S :=
   Iff.rfl
 #align subalgebra.mem_to_subring Subalgebra.mem_toSubring
 
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 @[simp]
 theorem coe_toSubring {R : Type u} {A : Type v} [CommRing R] [Ring A] [Algebra R A]
     (S : Subalgebra R A) : (↑S.toSubring : Set A) = S :=
@@ -460,154 +274,70 @@ section
 /-! `subalgebra`s inherit structure from their `subsemiring` / `semiring` coercions. -/
 
 
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 instance toSemiring {R A} [CommSemiring R] [Semiring A] [Algebra R A] (S : Subalgebra R A) :
     Semiring S :=
   S.toSubsemiring.toSemiring
 #align subalgebra.to_semiring Subalgebra.toSemiring
 
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 instance toCommSemiring {R A} [CommSemiring R] [CommSemiring A] [Algebra R A] (S : Subalgebra R A) :
     CommSemiring S :=
   S.toSubsemiring.toCommSemiring
 #align subalgebra.to_comm_semiring Subalgebra.toCommSemiring
 
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 instance toRing {R A} [CommRing R] [Ring A] [Algebra R A] (S : Subalgebra R A) : Ring S :=
   S.toSubring.toRing
 #align subalgebra.to_ring Subalgebra.toRing
 
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 instance toCommRing {R A} [CommRing R] [CommRing A] [Algebra R A] (S : Subalgebra R A) :
     CommRing S :=
   S.toSubring.toCommRing
 #align subalgebra.to_comm_ring Subalgebra.toCommRing
 
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 instance toOrderedSemiring {R A} [CommSemiring R] [OrderedSemiring A] [Algebra R A]
     (S : Subalgebra R A) : OrderedSemiring S :=
   S.toSubsemiring.toOrderedSemiring
 #align subalgebra.to_ordered_semiring Subalgebra.toOrderedSemiring
 
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 instance toStrictOrderedSemiring {R A} [CommSemiring R] [StrictOrderedSemiring A] [Algebra R A]
     (S : Subalgebra R A) : StrictOrderedSemiring S :=
   S.toSubsemiring.toStrictOrderedSemiring
 #align subalgebra.to_strict_ordered_semiring Subalgebra.toStrictOrderedSemiring
 
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 instance toOrderedCommSemiring {R A} [CommSemiring R] [OrderedCommSemiring A] [Algebra R A]
     (S : Subalgebra R A) : OrderedCommSemiring S :=
   S.toSubsemiring.toOrderedCommSemiring
 #align subalgebra.to_ordered_comm_semiring Subalgebra.toOrderedCommSemiring
 
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 instance toStrictOrderedCommSemiring {R A} [CommSemiring R] [StrictOrderedCommSemiring A]
     [Algebra R A] (S : Subalgebra R A) : StrictOrderedCommSemiring S :=
   S.toSubsemiring.toStrictOrderedCommSemiring
 #align subalgebra.to_strict_ordered_comm_semiring Subalgebra.toStrictOrderedCommSemiring
 
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 instance toOrderedRing {R A} [CommRing R] [OrderedRing A] [Algebra R A] (S : Subalgebra R A) :
     OrderedRing S :=
   S.toSubring.toOrderedRing
 #align subalgebra.to_ordered_ring Subalgebra.toOrderedRing
 
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 instance toOrderedCommRing {R A} [CommRing R] [OrderedCommRing A] [Algebra R A]
     (S : Subalgebra R A) : OrderedCommRing S :=
   S.toSubring.toOrderedCommRing
 #align subalgebra.to_ordered_comm_ring Subalgebra.toOrderedCommRing
 
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 instance toLinearOrderedSemiring {R A} [CommSemiring R] [LinearOrderedSemiring A] [Algebra R A]
     (S : Subalgebra R A) : LinearOrderedSemiring S :=
   S.toSubsemiring.toLinearOrderedSemiring
 #align subalgebra.to_linear_ordered_semiring Subalgebra.toLinearOrderedSemiring
 
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 instance toLinearOrderedCommSemiring {R A} [CommSemiring R] [LinearOrderedCommSemiring A]
     [Algebra R A] (S : Subalgebra R A) : LinearOrderedCommSemiring S :=
   S.toSubsemiring.toLinearOrderedCommSemiring
 #align subalgebra.to_linear_ordered_comm_semiring Subalgebra.toLinearOrderedCommSemiring
 
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 instance toLinearOrderedRing {R A} [CommRing R] [LinearOrderedRing A] [Algebra R A]
     (S : Subalgebra R A) : LinearOrderedRing S :=
   S.toSubring.toLinearOrderedRing
 #align subalgebra.to_linear_ordered_ring Subalgebra.toLinearOrderedRing
 
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 instance toLinearOrderedCommRing {R A} [CommRing R] [LinearOrderedCommRing A] [Algebra R A]
     (S : Subalgebra R A) : LinearOrderedCommRing S :=
   S.toSubring.toLinearOrderedCommRing
@@ -615,12 +345,6 @@ instance toLinearOrderedCommRing {R A} [CommRing R] [LinearOrderedCommRing A] [A
 
 end
 
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 /-- The forgetful map from `subalgebra` to `submodule` as an `order_embedding` -/
 def toSubmodule : Subalgebra R A ↪o Submodule R A
     where
@@ -636,9 +360,6 @@ def toSubmodule : Subalgebra R A ↪o Submodule R A
   map_rel_iff' S T := SetLike.coe_subset_coe.symm.trans SetLike.coe_subset_coe
 #align subalgebra.to_submodule Subalgebra.toSubmodule
 
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 /- TODO: bundle other forgetful maps between algebraic substructures, e.g.
   `to_subsemiring` and `to_subring` in this file. -/
 @[simp]
@@ -646,9 +367,6 @@ theorem mem_toSubmodule {x} : x ∈ S.toSubmodule ↔ x ∈ S :=
   Iff.rfl
 #align subalgebra.mem_to_submodule Subalgebra.mem_toSubmodule
 
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 @[simp]
 theorem coe_toSubmodule (S : Subalgebra R A) : (↑S.toSubmodule : Set A) = S :=
   rfl
@@ -659,12 +377,6 @@ section
 /-! `subalgebra`s inherit structure from their `submodule` coercions. -/
 
 
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-Case conversion may be inaccurate. Consider using '#align subalgebra.module' Subalgebra.module'ₓ'. -/
 instance module' [Semiring R'] [SMul R' R] [Module R' A] [IsScalarTower R' R A] : Module R' S :=
   S.toSubmodule.module'
 #align subalgebra.module' Subalgebra.module'
@@ -675,12 +387,6 @@ instance : Module R S :=
 instance [Semiring R'] [SMul R' R] [Module R' A] [IsScalarTower R' R A] : IsScalarTower R' R S :=
   S.toSubmodule.IsScalarTower
 
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 instance algebra' [CommSemiring R'] [SMul R' R] [Algebra R' A] [IsScalarTower R' R A] :
     Algebra R' S :=
   {
@@ -700,38 +406,20 @@ instance : Algebra R S :=
 
 end
 
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 instance noZeroSMulDivisors_bot [NoZeroSMulDivisors R A] : NoZeroSMulDivisors R S :=
   ⟨fun c x h =>
     have : c = 0 ∨ (x : A) = 0 := eq_zero_or_eq_zero_of_smul_eq_zero (congr_arg coe h)
     this.imp_right (@Subtype.ext_iff _ _ x 0).mpr⟩
 #align subalgebra.no_zero_smul_divisors_bot Subalgebra.noZeroSMulDivisors_bot
 
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 protected theorem coe_add (x y : S) : (↑(x + y) : A) = ↑x + ↑y :=
   rfl
 #align subalgebra.coe_add Subalgebra.coe_add
 
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 protected theorem coe_mul (x y : S) : (↑(x * y) : A) = ↑x * ↑y :=
   rfl
 #align subalgebra.coe_mul Subalgebra.coe_mul
 
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 protected theorem coe_zero : ((0 : S) : A) = 0 :=
   rfl
 #align subalgebra.coe_zero Subalgebra.coe_zero
@@ -742,120 +430,66 @@ protected theorem coe_one : ((1 : S) : A) = 1 :=
 #align subalgebra.coe_one Subalgebra.coe_one
 -/
 
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 protected theorem coe_neg {R : Type u} {A : Type v} [CommRing R] [Ring A] [Algebra R A]
     {S : Subalgebra R A} (x : S) : (↑(-x) : A) = -↑x :=
   rfl
 #align subalgebra.coe_neg Subalgebra.coe_neg
 
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 protected theorem coe_sub {R : Type u} {A : Type v} [CommRing R] [Ring A] [Algebra R A]
     {S : Subalgebra R A} (x y : S) : (↑(x - y) : A) = ↑x - ↑y :=
   rfl
 #align subalgebra.coe_sub Subalgebra.coe_sub
 
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 @[simp, norm_cast]
 theorem coe_smul [Semiring R'] [SMul R' R] [Module R' A] [IsScalarTower R' R A] (r : R') (x : S) :
     (↑(r • x) : A) = r • ↑x :=
   rfl
 #align subalgebra.coe_smul Subalgebra.coe_smul
 
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 @[simp, norm_cast]
 theorem coe_algebraMap [CommSemiring R'] [SMul R' R] [Algebra R' A] [IsScalarTower R' R A]
     (r : R') : ↑(algebraMap R' S r) = algebraMap R' A r :=
   rfl
 #align subalgebra.coe_algebra_map Subalgebra.coe_algebraMap
 
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 protected theorem coe_pow (x : S) (n : ℕ) : (↑(x ^ n) : A) = ↑x ^ n :=
   SubmonoidClass.coe_pow x n
 #align subalgebra.coe_pow Subalgebra.coe_pow
 
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 protected theorem coe_eq_zero {x : S} : (x : A) = 0 ↔ x = 0 :=
   ZeroMemClass.coe_eq_zero
 #align subalgebra.coe_eq_zero Subalgebra.coe_eq_zero
 
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 protected theorem coe_eq_one {x : S} : (x : A) = 1 ↔ x = 1 :=
   OneMemClass.coe_eq_one
 #align subalgebra.coe_eq_one Subalgebra.coe_eq_one
 
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 -- todo: standardize on the names these morphisms
 -- compare with submodule.subtype
 /-- Embedding of a subalgebra into the algebra. -/
 def val : S →ₐ[R] A := by refine_struct { toFun := (coe : S → A) } <;> intros <;> rfl
 #align subalgebra.val Subalgebra.val
 
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 @[simp]
 theorem coe_val : (S.val : S → A) = coe :=
   rfl
 #align subalgebra.coe_val Subalgebra.coe_val
 
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 theorem val_apply (x : S) : S.val x = (x : A) :=
   rfl
 #align subalgebra.val_apply Subalgebra.val_apply
 
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 @[simp]
 theorem toSubsemiring_subtype : S.toSubsemiring.Subtype = (S.val : S →+* A) :=
   rfl
 #align subalgebra.to_subsemiring_subtype Subalgebra.toSubsemiring_subtype
 
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 @[simp]
 theorem toSubring_subtype {R A : Type _} [CommRing R] [Ring A] [Algebra R A] (S : Subalgebra R A) :
     S.toSubring.Subtype = (S.val : S →+* A) :=
   rfl
 #align subalgebra.to_subring_subtype Subalgebra.toSubring_subtype
 
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 /-- Linear equivalence between `S : submodule R A` and `S`. Though these types are equal,
 we define it as a `linear_equiv` to avoid type equalities. -/
 def toSubmoduleEquiv (S : Subalgebra R A) : S.toSubmodule ≃ₗ[R] S :=
@@ -870,12 +504,6 @@ def map (f : A →ₐ[R] B) (S : Subalgebra R A) : Subalgebra R B :=
 #align subalgebra.map Subalgebra.map
 -/
 
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 theorem map_mono {S₁ S₂ : Subalgebra R A} {f : A →ₐ[R] B} : S₁ ≤ S₂ → S₁.map f ≤ S₂.map f :=
   Set.image_subset f
 #align subalgebra.map_mono Subalgebra.map_mono
@@ -901,16 +529,10 @@ theorem map_map (S : Subalgebra R A) (g : B →ₐ[R] C) (f : A →ₐ[R] B) :
 #align subalgebra.map_map Subalgebra.map_map
 -/
 
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 theorem mem_map {S : Subalgebra R A} {f : A →ₐ[R] B} {y : B} : y ∈ map f S ↔ ∃ x ∈ S, f x = y :=
   Subsemiring.mem_map
 #align subalgebra.mem_map Subalgebra.mem_map
 
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 theorem map_toSubmodule {S : Subalgebra R A} {f : A →ₐ[R] B} :
     (S.map f).toSubmodule = S.toSubmodule.map f.toLinearMap :=
   SetLike.coe_injective rfl
@@ -923,9 +545,6 @@ theorem map_toSubsemiring {S : Subalgebra R A} {f : A →ₐ[R] B} :
 #align subalgebra.map_to_subsemiring Subalgebra.map_toSubsemiring
 -/
 
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 @[simp]
 theorem coe_map (S : Subalgebra R A) (f : A →ₐ[R] B) : (S.map f : Set B) = f '' S :=
   rfl
@@ -940,59 +559,29 @@ def comap (f : A →ₐ[R] B) (S : Subalgebra R B) : Subalgebra R A :=
 #align subalgebra.comap Subalgebra.comap
 -/
 
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 theorem map_le {S : Subalgebra R A} {f : A →ₐ[R] B} {U : Subalgebra R B} :
     map f S ≤ U ↔ S ≤ comap f U :=
   Set.image_subset_iff
 #align subalgebra.map_le Subalgebra.map_le
 
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 theorem gc_map_comap (f : A →ₐ[R] B) : GaloisConnection (map f) (comap f) := fun S U => map_le
 #align subalgebra.gc_map_comap Subalgebra.gc_map_comap
 
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 @[simp]
 theorem mem_comap (S : Subalgebra R B) (f : A →ₐ[R] B) (x : A) : x ∈ S.comap f ↔ f x ∈ S :=
   Iff.rfl
 #align subalgebra.mem_comap Subalgebra.mem_comap
 
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 @[simp, norm_cast]
 theorem coe_comap (S : Subalgebra R B) (f : A →ₐ[R] B) : (S.comap f : Set A) = f ⁻¹' (S : Set B) :=
   rfl
 #align subalgebra.coe_comap Subalgebra.coe_comap
 
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 instance noZeroDivisors {R A : Type _} [CommSemiring R] [Semiring A] [NoZeroDivisors A]
     [Algebra R A] (S : Subalgebra R A) : NoZeroDivisors S :=
   S.toSubsemiring.NoZeroDivisors
 #align subalgebra.no_zero_divisors Subalgebra.noZeroDivisors
 
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 instance isDomain {R A : Type _} [CommRing R] [Ring A] [IsDomain A] [Algebra R A]
     (S : Subalgebra R A) : IsDomain S :=
   Subring.isDomain S.toSubring
@@ -1006,12 +595,6 @@ variable {R A : Type _} [CommSemiring R] [Semiring A] [Algebra R A]
 
 variable (p : Submodule R A)
 
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 /-- A submodule containing `1` and closed under multiplication is a subalgebra. -/
 def toSubalgebra (p : Submodule R A) (h_one : (1 : A) ∈ p)
     (h_mul : ∀ x y, x ∈ p → y ∈ p → x * y ∈ p) : Subalgebra R A :=
@@ -1022,27 +605,18 @@ def toSubalgebra (p : Submodule R A) (h_one : (1 : A) ∈ p)
       exact p.smul_mem _ h_one }
 #align submodule.to_subalgebra Submodule.toSubalgebra
 
-/- warning: submodule.mem_to_subalgebra -> Submodule.mem_toSubalgebra is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.mem_to_subalgebra Submodule.mem_toSubalgebraₓ'. -/
 @[simp]
 theorem mem_toSubalgebra {p : Submodule R A} {h_one h_mul} {x} :
     x ∈ p.toSubalgebra h_one h_mul ↔ x ∈ p :=
   Iff.rfl
 #align submodule.mem_to_subalgebra Submodule.mem_toSubalgebra
 
-/- warning: submodule.coe_to_subalgebra -> Submodule.coe_toSubalgebra is a dubious translation:
-<too large>
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 @[simp]
 theorem coe_toSubalgebra (p : Submodule R A) (h_one h_mul) :
     (p.toSubalgebra h_one h_mul : Set A) = p :=
   rfl
 #align submodule.coe_to_subalgebra Submodule.coe_toSubalgebra
 
-/- warning: submodule.to_subalgebra_mk -> Submodule.toSubalgebra_mk is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.to_subalgebra_mk Submodule.toSubalgebra_mkₓ'. -/
 @[simp]
 theorem toSubalgebra_mk (s : Set A) (h0 hadd hsmul h1 hmul) :
     (Submodule.mk s hadd h0 hsmul : Submodule R A).toSubalgebra h1 hmul =
@@ -1051,18 +625,12 @@ theorem toSubalgebra_mk (s : Set A) (h0 hadd hsmul h1 hmul) :
   rfl
 #align submodule.to_subalgebra_mk Submodule.toSubalgebra_mk
 
-/- warning: submodule.to_subalgebra_to_submodule -> Submodule.toSubalgebra_toSubmodule is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.to_subalgebra_to_submodule Submodule.toSubalgebra_toSubmoduleₓ'. -/
 @[simp]
 theorem toSubalgebra_toSubmodule (p : Submodule R A) (h_one h_mul) :
     (p.toSubalgebra h_one h_mul).toSubmodule = p :=
   SetLike.coe_injective rfl
 #align submodule.to_subalgebra_to_submodule Submodule.toSubalgebra_toSubmodule
 
-/- warning: subalgebra.to_submodule_to_subalgebra -> Subalgebra.toSubmodule_toSubalgebra is a dubious translation:
-<too large>
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 @[simp]
 theorem Subalgebra.toSubmodule_toSubalgebra (S : Subalgebra R A) :
     (S.toSubmodule.toSubalgebra S.one_mem fun _ _ => S.mul_mem) = S :=
@@ -1088,24 +656,15 @@ protected def range (φ : A →ₐ[R] B) : Subalgebra R B :=
 #align alg_hom.range AlgHom.range
 -/
 
-/- warning: alg_hom.mem_range -> AlgHom.mem_range is a dubious translation:
-<too large>
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 @[simp]
 theorem mem_range (φ : A →ₐ[R] B) {y : B} : y ∈ φ.range ↔ ∃ x, φ x = y :=
   RingHom.mem_rangeS
 #align alg_hom.mem_range AlgHom.mem_range
 
-/- warning: alg_hom.mem_range_self -> AlgHom.mem_range_self is a dubious translation:
-<too large>
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 theorem mem_range_self (φ : A →ₐ[R] B) (x : A) : φ x ∈ φ.range :=
   φ.mem_range.2 ⟨x, rfl⟩
 #align alg_hom.mem_range_self AlgHom.mem_range_self
 
-/- warning: alg_hom.coe_range -> AlgHom.coe_range is a dubious translation:
-<too large>
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 @[simp]
 theorem coe_range (φ : A →ₐ[R] B) : (φ.range : Set B) = Set.range φ := by ext;
   rw [SetLike.mem_coe, mem_range]; rfl
@@ -1117,56 +676,32 @@ theorem range_comp (f : A →ₐ[R] B) (g : B →ₐ[R] C) : (g.comp f).range =
 #align alg_hom.range_comp AlgHom.range_comp
 -/
 
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-Case conversion may be inaccurate. Consider using '#align alg_hom.range_comp_le_range AlgHom.range_comp_le_rangeₓ'. -/
 theorem range_comp_le_range (f : A →ₐ[R] B) (g : B →ₐ[R] C) : (g.comp f).range ≤ g.range :=
   SetLike.coe_mono (Set.range_comp_subset_range f g)
 #align alg_hom.range_comp_le_range AlgHom.range_comp_le_range
 
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 /-- Restrict the codomain of an algebra homomorphism. -/
 def codRestrict (f : A →ₐ[R] B) (S : Subalgebra R B) (hf : ∀ x, f x ∈ S) : A →ₐ[R] S :=
   { RingHom.codRestrict (f : A →+* B) S hf with commutes' := fun r => Subtype.eq <| f.commutes r }
 #align alg_hom.cod_restrict AlgHom.codRestrict
 
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 @[simp]
 theorem val_comp_codRestrict (f : A →ₐ[R] B) (S : Subalgebra R B) (hf : ∀ x, f x ∈ S) :
     S.val.comp (f.codRestrict S hf) = f :=
   AlgHom.ext fun _ => rfl
 #align alg_hom.val_comp_cod_restrict AlgHom.val_comp_codRestrict
 
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 @[simp]
 theorem coe_codRestrict (f : A →ₐ[R] B) (S : Subalgebra R B) (hf : ∀ x, f x ∈ S) (x : A) :
     ↑(f.codRestrict S hf x) = f x :=
   rfl
 #align alg_hom.coe_cod_restrict AlgHom.coe_codRestrict
 
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 theorem injective_codRestrict (f : A →ₐ[R] B) (S : Subalgebra R B) (hf : ∀ x, f x ∈ S) :
     Function.Injective (f.codRestrict S hf) ↔ Function.Injective f :=
   ⟨fun H x y hxy => H <| Subtype.eq hxy, fun H x y hxy => H (congr_arg Subtype.val hxy : _)⟩
 #align alg_hom.injective_cod_restrict AlgHom.injective_codRestrict
 
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 /-- Restrict the codomain of a alg_hom `f` to `f.range`.
 
 This is the bundled version of `set.range_factorization`. -/
@@ -1188,20 +723,11 @@ def equalizer (ϕ ψ : A →ₐ[R] B) : Subalgebra R A
 #align alg_hom.equalizer AlgHom.equalizer
 -/
 
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 @[simp]
 theorem mem_equalizer (ϕ ψ : A →ₐ[R] B) (x : A) : x ∈ ϕ.equalizer ψ ↔ ϕ x = ψ x :=
   Iff.rfl
 #align alg_hom.mem_equalizer AlgHom.mem_equalizer
 
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 /-- The range of a morphism of algebras is a fintype, if the domain is a fintype.
 
 Note that this instance can cause a diamond with `subtype.fintype` if `B` is also a fintype. -/
@@ -1264,24 +790,12 @@ theorem ofInjective_apply (f : A →ₐ[R] B) (hf : Function.Injective f) (x : A
 #align alg_equiv.of_injective_apply AlgEquiv.ofInjective_apply
 -/
 
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 /-- Restrict an algebra homomorphism between fields to an algebra isomorphism -/
 noncomputable def ofInjectiveField {E F : Type _} [DivisionRing E] [Semiring F] [Nontrivial F]
     [Algebra R E] [Algebra R F] (f : E →ₐ[R] F) : E ≃ₐ[R] f.range :=
   ofInjective f f.toRingHom.Injective
 #align alg_equiv.of_injective_field AlgEquiv.ofInjectiveField
 
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 /-- Given an equivalence `e : A ≃ₐ[R] B` of `R`-algebras and a subalgebra `S` of `A`,
 `subalgebra_map` is the induced equivalence between `S` and `S.map e` -/
 @[simps]
@@ -1307,24 +821,12 @@ def adjoin (s : Set A) : Subalgebra R A :=
 
 variable {R}
 
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 protected theorem gc : GaloisConnection (adjoin R : Set A → Subalgebra R A) coe := fun s S =>
   ⟨fun H => le_trans (le_trans (Set.subset_union_right _ _) Subsemiring.subset_closure) H, fun H =>
     show Subsemiring.closure (Set.range (algebraMap R A) ∪ s) ≤ S.toSubsemiring from
       Subsemiring.closure_le.2 <| Set.union_subset S.range_subset H⟩
 #align algebra.gc Algebra.gc
 
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 /-- Galois insertion between `adjoin` and `coe`. -/
 protected def gi : GaloisInsertion (adjoin R : Set A → Subalgebra R A) coe
     where
@@ -1337,239 +839,116 @@ protected def gi : GaloisInsertion (adjoin R : Set A → Subalgebra R A) coe
 instance : CompleteLattice (Subalgebra R A) :=
   GaloisInsertion.liftCompleteLattice Algebra.gi
 
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 @[simp]
 theorem coe_top : (↑(⊤ : Subalgebra R A) : Set A) = Set.univ :=
   rfl
 #align algebra.coe_top Algebra.coe_top
 
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 @[simp]
 theorem mem_top {x : A} : x ∈ (⊤ : Subalgebra R A) :=
   Set.mem_univ x
 #align algebra.mem_top Algebra.mem_top
 
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 @[simp]
 theorem top_toSubmodule : (⊤ : Subalgebra R A).toSubmodule = ⊤ :=
   rfl
 #align algebra.top_to_submodule Algebra.top_toSubmodule
 
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 @[simp]
 theorem top_toSubsemiring : (⊤ : Subalgebra R A).toSubsemiring = ⊤ :=
   rfl
 #align algebra.top_to_subsemiring Algebra.top_toSubsemiring
 
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 @[simp]
 theorem top_toSubring {R A : Type _} [CommRing R] [Ring A] [Algebra R A] :
     (⊤ : Subalgebra R A).toSubring = ⊤ :=
   rfl
 #align algebra.top_to_subring Algebra.top_toSubring
 
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 @[simp]
 theorem toSubmodule_eq_top {S : Subalgebra R A} : S.toSubmodule = ⊤ ↔ S = ⊤ :=
   Subalgebra.toSubmodule.Injective.eq_iff' top_toSubmodule
 #align algebra.to_submodule_eq_top Algebra.toSubmodule_eq_top
 
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 @[simp]
 theorem toSubsemiring_eq_top {S : Subalgebra R A} : S.toSubsemiring = ⊤ ↔ S = ⊤ :=
   Subalgebra.toSubsemiring_injective.eq_iff' top_toSubsemiring
 #align algebra.to_subsemiring_eq_top Algebra.toSubsemiring_eq_top
 
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 @[simp]
 theorem toSubring_eq_top {R A : Type _} [CommRing R] [Ring A] [Algebra R A] {S : Subalgebra R A} :
     S.toSubring = ⊤ ↔ S = ⊤ :=
   Subalgebra.toSubring_injective.eq_iff' top_toSubring
 #align algebra.to_subring_eq_top Algebra.toSubring_eq_top
 
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 theorem mem_sup_left {S T : Subalgebra R A} : ∀ {x : A}, x ∈ S → x ∈ S ⊔ T :=
   show S ≤ S ⊔ T from le_sup_left
 #align algebra.mem_sup_left Algebra.mem_sup_left
 
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 theorem mem_sup_right {S T : Subalgebra R A} : ∀ {x : A}, x ∈ T → x ∈ S ⊔ T :=
   show T ≤ S ⊔ T from le_sup_right
 #align algebra.mem_sup_right Algebra.mem_sup_right
 
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 theorem mul_mem_sup {S T : Subalgebra R A} {x y : A} (hx : x ∈ S) (hy : y ∈ T) : x * y ∈ S ⊔ T :=
   (S ⊔ T).mul_mem (mem_sup_left hx) (mem_sup_right hy)
 #align algebra.mul_mem_sup Algebra.mul_mem_sup
 
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 theorem map_sup (f : A →ₐ[R] B) (S T : Subalgebra R A) : (S ⊔ T).map f = S.map f ⊔ T.map f :=
   (Subalgebra.gc_map_comap f).l_sup
 #align algebra.map_sup Algebra.map_sup
 
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 @[simp, norm_cast]
 theorem coe_inf (S T : Subalgebra R A) : (↑(S ⊓ T) : Set A) = S ∩ T :=
   rfl
 #align algebra.coe_inf Algebra.coe_inf
 
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 @[simp]
 theorem mem_inf {S T : Subalgebra R A} {x : A} : x ∈ S ⊓ T ↔ x ∈ S ∧ x ∈ T :=
   Iff.rfl
 #align algebra.mem_inf Algebra.mem_inf
 
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 @[simp]
 theorem inf_toSubmodule (S T : Subalgebra R A) :
     (S ⊓ T).toSubmodule = S.toSubmodule ⊓ T.toSubmodule :=
   rfl
 #align algebra.inf_to_submodule Algebra.inf_toSubmodule
 
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 @[simp]
 theorem inf_toSubsemiring (S T : Subalgebra R A) :
     (S ⊓ T).toSubsemiring = S.toSubsemiring ⊓ T.toSubsemiring :=
   rfl
 #align algebra.inf_to_subsemiring Algebra.inf_toSubsemiring
 
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 @[simp, norm_cast]
 theorem coe_sInf (S : Set (Subalgebra R A)) : (↑(sInf S) : Set A) = ⋂ s ∈ S, ↑s :=
   sInf_image
 #align algebra.coe_Inf Algebra.coe_sInf
 
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 theorem mem_sInf {S : Set (Subalgebra R A)} {x : A} : x ∈ sInf S ↔ ∀ p ∈ S, x ∈ p := by
   simp only [← SetLike.mem_coe, coe_Inf, Set.mem_iInter₂]
 #align algebra.mem_Inf Algebra.mem_sInf
 
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 @[simp]
 theorem sInf_toSubmodule (S : Set (Subalgebra R A)) :
     (sInf S).toSubmodule = sInf (Subalgebra.toSubmodule '' S) :=
   SetLike.coe_injective <| by simp
 #align algebra.Inf_to_submodule Algebra.sInf_toSubmodule
 
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 @[simp]
 theorem sInf_toSubsemiring (S : Set (Subalgebra R A)) :
     (sInf S).toSubsemiring = sInf (Subalgebra.toSubsemiring '' S) :=
   SetLike.coe_injective <| by simp
 #align algebra.Inf_to_subsemiring Algebra.sInf_toSubsemiring
 
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 @[simp, norm_cast]
 theorem coe_iInf {ι : Sort _} {S : ι → Subalgebra R A} : (↑(⨅ i, S i) : Set A) = ⋂ i, S i := by
   simp [iInf]
 #align algebra.coe_infi Algebra.coe_iInf
 
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 theorem mem_iInf {ι : Sort _} {S : ι → Subalgebra R A} {x : A} : (x ∈ ⨅ i, S i) ↔ ∀ i, x ∈ S i := by
   simp only [iInf, mem_Inf, Set.forall_range_iff]
 #align algebra.mem_infi Algebra.mem_iInf
 
-/- warning: algebra.infi_to_submodule -> Algebra.iInf_toSubmodule is a dubious translation:
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 @[simp]
 theorem iInf_toSubmodule {ι : Sort _} (S : ι → Subalgebra R A) :
     (⨅ i, S i).toSubmodule = ⨅ i, (S i).toSubmodule :=
@@ -1579,117 +958,57 @@ theorem iInf_toSubmodule {ι : Sort _} (S : ι → Subalgebra R A) :
 instance : Inhabited (Subalgebra R A) :=
   ⟨⊥⟩
 
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 theorem mem_bot {x : A} : x ∈ (⊥ : Subalgebra R A) ↔ x ∈ Set.range (algebraMap R A) :=
   suffices (ofId R A).range = (⊥ : Subalgebra R A) by
     rw [← this, ← SetLike.mem_coe, AlgHom.coe_range]; rfl
   le_bot_iff.mp fun x hx => Subalgebra.range_le _ ((ofId R A).coe_range ▸ hx)
 #align algebra.mem_bot Algebra.mem_bot
 
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 theorem toSubmodule_bot : (⊥ : Subalgebra R A).toSubmodule = R ∙ 1 := by ext x;
   simp [mem_bot, -Set.singleton_one, Submodule.mem_span_singleton, Algebra.smul_def]
 #align algebra.to_submodule_bot Algebra.toSubmodule_bot
 
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 @[simp]
 theorem coe_bot : ((⊥ : Subalgebra R A) : Set A) = Set.range (algebraMap R A) := by
   simp [Set.ext_iff, Algebra.mem_bot]
 #align algebra.coe_bot Algebra.coe_bot
 
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 theorem eq_top_iff {S : Subalgebra R A} : S = ⊤ ↔ ∀ x : A, x ∈ S :=
   ⟨fun h x => by rw [h] <;> exact mem_top, fun h => by
     ext x <;> exact ⟨fun _ => mem_top, fun _ => h x⟩⟩
 #align algebra.eq_top_iff Algebra.eq_top_iff
 
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 theorem range_top_iff_surjective (f : A →ₐ[R] B) :
     f.range = (⊤ : Subalgebra R B) ↔ Function.Surjective f :=
   Algebra.eq_top_iff
 #align algebra.range_top_iff_surjective Algebra.range_top_iff_surjective
 
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 @[simp]
 theorem range_id : (AlgHom.id R A).range = ⊤ :=
   SetLike.coe_injective Set.range_id
 #align algebra.range_id Algebra.range_id
 
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 @[simp]
 theorem map_top (f : A →ₐ[R] B) : (⊤ : Subalgebra R A).map f = f.range :=
   SetLike.coe_injective Set.image_univ
 #align algebra.map_top Algebra.map_top
 
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 @[simp]
 theorem map_bot (f : A →ₐ[R] B) : (⊥ : Subalgebra R A).map f = ⊥ :=
   SetLike.coe_injective <| by
     simp only [← Set.range_comp, (· ∘ ·), Algebra.coe_bot, Subalgebra.coe_map, f.commutes]
 #align algebra.map_bot Algebra.map_bot
 
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 @[simp]
 theorem comap_top (f : A →ₐ[R] B) : (⊤ : Subalgebra R B).comap f = ⊤ :=
   eq_top_iff.2 fun x => mem_top
 #align algebra.comap_top Algebra.comap_top
 
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 /-- `alg_hom` to `⊤ : subalgebra R A`. -/
 def toTop : A →ₐ[R] (⊤ : Subalgebra R A) :=
   (AlgHom.id R A).codRestrict ⊤ fun _ => mem_top
 #align algebra.to_top Algebra.toTop
 
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 theorem surjective_algebraMap_iff :
     Function.Surjective (algebraMap R A) ↔ (⊤ : Subalgebra R A) = ⊥ :=
   ⟨fun h =>
@@ -1699,24 +1018,12 @@ theorem surjective_algebraMap_iff :
     fun h y => Algebra.mem_bot.1 <| eq_bot_iff.1 h (Algebra.mem_top : y ∈ _)⟩
 #align algebra.surjective_algebra_map_iff Algebra.surjective_algebraMap_iff
 
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 theorem bijective_algebraMap_iff {R A : Type _} [Field R] [Semiring A] [Nontrivial A]
     [Algebra R A] : Function.Bijective (algebraMap R A) ↔ (⊤ : Subalgebra R A) = ⊥ :=
   ⟨fun h => surjective_algebraMap_iff.1 h.2, fun h =>
     ⟨(algebraMap R A).Injective, surjective_algebraMap_iff.2 h⟩⟩
 #align algebra.bijective_algebra_map_iff Algebra.bijective_algebraMap_iff
 
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 /-- The bottom subalgebra is isomorphic to the base ring. -/
 noncomputable def botEquivOfInjective (h : Function.Injective (algebraMap R A)) :
     (⊥ : Subalgebra R A) ≃ₐ[R] R :=
@@ -1727,12 +1034,6 @@ noncomputable def botEquivOfInjective (h : Function.Injective (algebraMap R A))
         ⟨x, Subtype.eq hx⟩⟩
 #align algebra.bot_equiv_of_injective Algebra.botEquivOfInjective
 
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 /-- The bottom subalgebra is isomorphic to the field. -/
 @[simps symm_apply]
 noncomputable def botEquiv (F R : Type _) [Field F] [Semiring R] [Nontrivial R] [Algebra F R] :
@@ -1752,12 +1053,6 @@ variable [CommSemiring R] [Semiring A] [Algebra R A] [Semiring B] [Algebra R B]
 
 variable (S : Subalgebra R A)
 
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 /-- The top subalgebra is isomorphic to the algebra.
 
 This is the algebra version of `submodule.top_equiv`. -/
@@ -1794,12 +1089,6 @@ instance AlgEquiv.subsingleton_right [Subsingleton (Subalgebra R B)] : Subsingle
 #align alg_equiv.subsingleton_right AlgEquiv.subsingleton_right
 -/
 
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 theorem range_val : S.val.range = S :=
   ext <| Set.ext_iff.1 <| S.val.coe_range.trans Subtype.range_val
 #align subalgebra.range_val Subalgebra.range_val
@@ -1811,12 +1100,6 @@ instance : Unique (Subalgebra R R) :=
       refine' le_antisymm (fun r hr => _) bot_le
       simp only [Set.mem_range, mem_bot, id.map_eq_self, exists_apply_eq_apply, default] }
 
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 /-- The map `S → T` when `S` is a subalgebra contained in the subalgebra `T`.
 
 This is the subalgebra version of `submodule.of_le`, or `subring.inclusion`  -/
@@ -1830,64 +1113,37 @@ def inclusion {S T : Subalgebra R A} (h : S ≤ T) : S →ₐ[R] T
   commutes' _ := rfl
 #align subalgebra.inclusion Subalgebra.inclusion
 
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 theorem inclusion_injective {S T : Subalgebra R A} (h : S ≤ T) : Function.Injective (inclusion h) :=
   fun _ _ => Subtype.ext ∘ Subtype.mk.inj
 #align subalgebra.inclusion_injective Subalgebra.inclusion_injective
 
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 @[simp]
 theorem inclusion_self {S : Subalgebra R A} : inclusion (le_refl S) = AlgHom.id R S :=
   AlgHom.ext fun x => Subtype.ext rfl
 #align subalgebra.inclusion_self Subalgebra.inclusion_self
 
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 @[simp]
 theorem inclusion_mk {S T : Subalgebra R A} (h : S ≤ T) (x : A) (hx : x ∈ S) :
     inclusion h ⟨x, hx⟩ = ⟨x, h hx⟩ :=
   rfl
 #align subalgebra.inclusion_mk Subalgebra.inclusion_mk
 
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 theorem inclusion_right {S T : Subalgebra R A} (h : S ≤ T) (x : T) (m : (x : A) ∈ S) :
     inclusion h ⟨x, m⟩ = x :=
   Subtype.ext rfl
 #align subalgebra.inclusion_right Subalgebra.inclusion_right
 
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 @[simp]
 theorem inclusion_inclusion {S T U : Subalgebra R A} (hst : S ≤ T) (htu : T ≤ U) (x : S) :
     inclusion htu (inclusion hst x) = inclusion (le_trans hst htu) x :=
   Subtype.ext rfl
 #align subalgebra.inclusion_inclusion Subalgebra.inclusion_inclusion
 
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 @[simp]
 theorem coe_inclusion {S T : Subalgebra R A} (h : S ≤ T) (s : S) : (inclusion h s : A) = s :=
   rfl
 #align subalgebra.coe_inclusion Subalgebra.coe_inclusion
 
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 /-- Two subalgebras that are equal are also equivalent as algebras.
 
 This is the `subalgebra` version of `linear_equiv.of_eq` and `equiv.set.of_eq`. -/
@@ -1902,28 +1158,16 @@ def equivOfEq (S T : Subalgebra R A) (h : S = T) : S ≃ₐ[R] T :=
     commutes' := fun _ => rfl }
 #align subalgebra.equiv_of_eq Subalgebra.equivOfEq
 
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 @[simp]
 theorem equivOfEq_symm (S T : Subalgebra R A) (h : S = T) :
     (equivOfEq S T h).symm = equivOfEq T S h.symm :=
   rfl
 #align subalgebra.equiv_of_eq_symm Subalgebra.equivOfEq_symm
 
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 @[simp]
 theorem equivOfEq_rfl (S : Subalgebra R A) : equivOfEq S S rfl = AlgEquiv.refl := by ext; rfl
 #align subalgebra.equiv_of_eq_rfl Subalgebra.equivOfEq_rfl
 
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 @[simp]
 theorem equivOfEq_trans (S T U : Subalgebra R A) (hST : S = T) (hTU : T = U) :
     (equivOfEq S T hST).trans (equivOfEq T U hTU) = equivOfEq S U (trans hST hTU) :=
@@ -1934,12 +1178,6 @@ section Prod
 
 variable (S₁ : Subalgebra R B)
 
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 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /-- The product of two subalgebras is a subalgebra. -/
 def prod : Subalgebra R (A × B) :=
@@ -1949,58 +1187,31 @@ def prod : Subalgebra R (A × B) :=
     algebraMap_mem' := fun r => ⟨algebraMap_mem _ _, algebraMap_mem _ _⟩ }
 #align subalgebra.prod Subalgebra.prod
 
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 @[simp]
 theorem coe_prod : (prod S S₁ : Set (A × B)) = S ×ˢ S₁ :=
   rfl
 #align subalgebra.coe_prod Subalgebra.coe_prod
 
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 theorem prod_toSubmodule : (S.Prod S₁).toSubmodule = S.toSubmodule.Prod S₁.toSubmodule :=
   rfl
 #align subalgebra.prod_to_submodule Subalgebra.prod_toSubmodule
 
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 @[simp]
 theorem mem_prod {S : Subalgebra R A} {S₁ : Subalgebra R B} {x : A × B} :
     x ∈ prod S S₁ ↔ x.1 ∈ S ∧ x.2 ∈ S₁ :=
   Set.mem_prod
 #align subalgebra.mem_prod Subalgebra.mem_prod
 
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 @[simp]
 theorem prod_top : (prod ⊤ ⊤ : Subalgebra R (A × B)) = ⊤ := by ext <;> simp
 #align subalgebra.prod_top Subalgebra.prod_top
 
-/- warning: subalgebra.prod_mono -> Subalgebra.prod_mono is a dubious translation:
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 theorem prod_mono {S T : Subalgebra R A} {S₁ T₁ : Subalgebra R B} :
     S ≤ T → S₁ ≤ T₁ → prod S S₁ ≤ prod T T₁ :=
   Set.prod_mono
 #align subalgebra.prod_mono Subalgebra.prod_mono
 
-/- warning: subalgebra.prod_inf_prod -> Subalgebra.prod_inf_prod is a dubious translation:
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 @[simp]
 theorem prod_inf_prod {S T : Subalgebra R A} {S₁ T₁ : Subalgebra R B} :
     S.Prod S₁ ⊓ T.Prod T₁ = (S ⊓ T).Prod (S₁ ⊓ T₁) :=
@@ -2013,12 +1224,6 @@ section SuprLift
 
 variable {ι : Type _}
 
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 theorem coe_iSup_of_directed [Nonempty ι] {S : ι → Subalgebra R A} (dir : Directed (· ≤ ·) S) :
     ↑(iSup S) = ⋃ i, (S i : Set A) :=
   let K : Subalgebra R A :=
@@ -2042,9 +1247,6 @@ theorem coe_iSup_of_directed [Nonempty ι] {S : ι → Subalgebra R A} (dir : Di
   this.symm ▸ rfl
 #align subalgebra.coe_supr_of_directed Subalgebra.coe_iSup_of_directed
 
-/- warning: subalgebra.supr_lift -> Subalgebra.iSupLift is a dubious translation:
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 /-- Define an algebra homomorphism on a directed supremum of subalgebras by defining
 it on each subalgebra, and proving that it agrees on the intersection of subalgebras. -/
 noncomputable def iSupLift [Nonempty ι] (K : ι → Subalgebra R A) (dir : Directed (· ≤ ·) K)
@@ -2076,34 +1278,22 @@ variable [Nonempty ι] {K : ι → Subalgebra R A} {dir : Directed (· ≤ ·) K
   {hf : ∀ (i j : ι) (h : K i ≤ K j), f i = (f j).comp (inclusion h)} {T : Subalgebra R A}
   {hT : T = iSup K}
 
-/- warning: subalgebra.supr_lift_inclusion -> Subalgebra.iSupLift_inclusion is a dubious translation:
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 @[simp]
 theorem iSupLift_inclusion {i : ι} (x : K i) (h : K i ≤ T) :
     iSupLift K dir f hf T hT (inclusion h x) = f i x := by
   subst T <;> exact Set.iUnionLift_inclusion _ _
 #align subalgebra.supr_lift_inclusion Subalgebra.iSupLift_inclusion
 
-/- warning: subalgebra.supr_lift_comp_inclusion -> Subalgebra.iSupLift_comp_inclusion is a dubious translation:
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 @[simp]
 theorem iSupLift_comp_inclusion {i : ι} (h : K i ≤ T) :
     (iSupLift K dir f hf T hT).comp (inclusion h) = f i := by ext <;> simp
 #align subalgebra.supr_lift_comp_inclusion Subalgebra.iSupLift_comp_inclusion
 
-/- warning: subalgebra.supr_lift_mk -> Subalgebra.iSupLift_mk is a dubious translation:
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 @[simp]
 theorem iSupLift_mk {i : ι} (x : K i) (hx : (x : A) ∈ T) :
     iSupLift K dir f hf T hT ⟨x, hx⟩ = f i x := by subst hT <;> exact Set.iUnionLift_mk x hx
 #align subalgebra.supr_lift_mk Subalgebra.iSupLift_mk
 
-/- warning: subalgebra.supr_lift_of_mem -> Subalgebra.iSupLift_of_mem is a dubious translation:
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 theorem iSupLift_of_mem {i : ι} (x : T) (hx : (x : A) ∈ K i) :
     iSupLift K dir f hf T hT x = f i ⟨x, hx⟩ := by subst hT <;> exact Set.iUnionLift_of_mem x hx
 #align subalgebra.supr_lift_of_mem Subalgebra.iSupLift_of_mem
@@ -2125,47 +1315,26 @@ variable {α β : Type _}
 instance [SMul A α] (S : Subalgebra R A) : SMul S α :=
   S.toSubsemiring.SMul
 
-/- warning: subalgebra.smul_def -> Subalgebra.smul_def is a dubious translation:
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 theorem smul_def [SMul A α] {S : Subalgebra R A} (g : S) (m : α) : g • m = (g : A) • m :=
   rfl
 #align subalgebra.smul_def Subalgebra.smul_def
 
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 instance smulCommClass_left [SMul A β] [SMul α β] [SMulCommClass A α β] (S : Subalgebra R A) :
     SMulCommClass S α β :=
   S.toSubsemiring.smulCommClass_left
 #align subalgebra.smul_comm_class_left Subalgebra.smulCommClass_left
 
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 instance smulCommClass_right [SMul α β] [SMul A β] [SMulCommClass α A β] (S : Subalgebra R A) :
     SMulCommClass α S β :=
   S.toSubsemiring.smulCommClass_right
 #align subalgebra.smul_comm_class_right Subalgebra.smulCommClass_right
 
-/- warning: subalgebra.is_scalar_tower_left -> Subalgebra.isScalarTower_left is a dubious translation:
-<too large>
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 /-- Note that this provides `is_scalar_tower S R R` which is needed by `smul_mul_assoc`. -/
 instance isScalarTower_left [SMul α β] [SMul A α] [SMul A β] [IsScalarTower A α β]
     (S : Subalgebra R A) : IsScalarTower S α β :=
   S.toSubsemiring.IsScalarTower
 #align subalgebra.is_scalar_tower_left Subalgebra.isScalarTower_left
 
-/- warning: subalgebra.is_scalar_tower_mid -> Subalgebra.isScalarTower_mid is a dubious translation:
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 instance isScalarTower_mid {R S T : Type _} [CommSemiring R] [Semiring S] [AddCommMonoid T]
     [Algebra R S] [Module R T] [Module S T] [IsScalarTower R S T] (S' : Subalgebra R S) :
     IsScalarTower R S' T :=
@@ -2191,43 +1360,22 @@ instance [Zero α] [SMulWithZero A α] (S : Subalgebra R A) : SMulWithZero S α
 instance [Zero α] [MulActionWithZero A α] (S : Subalgebra R A) : MulActionWithZero S α :=
   S.toSubsemiring.MulActionWithZero
 
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 /-- The action by a subalgebra is the action by the underlying algebra. -/
 instance moduleLeft [AddCommMonoid α] [Module A α] (S : Subalgebra R A) : Module S α :=
   S.toSubsemiring.Module
 #align subalgebra.module_left Subalgebra.moduleLeft
 
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 /-- The action by a subalgebra is the action by the underlying algebra. -/
 instance toAlgebra {R A : Type _} [CommSemiring R] [CommSemiring A] [Semiring α] [Algebra R A]
     [Algebra A α] (S : Subalgebra R A) : Algebra S α :=
   Algebra.ofSubsemiring S.toSubsemiring
 #align subalgebra.to_algebra Subalgebra.toAlgebra
 
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 theorem algebraMap_eq {R A : Type _} [CommSemiring R] [CommSemiring A] [Semiring α] [Algebra R A]
     [Algebra A α] (S : Subalgebra R A) : algebraMap S α = (algebraMap A α).comp S.val :=
   rfl
 #align subalgebra.algebra_map_eq Subalgebra.algebraMap_eq
 
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 @[simp]
 theorem rangeS_algebraMap {R A : Type _} [CommSemiring R] [CommSemiring A] [Algebra R A]
     (S : Subalgebra R A) : (algebraMap S A).srange = S.toSubsemiring := by
@@ -2235,12 +1383,6 @@ theorem rangeS_algebraMap {R A : Type _} [CommSemiring R] [CommSemiring A] [Alge
     Subsemiring.rangeS_subtype]
 #align subalgebra.srange_algebra_map Subalgebra.rangeS_algebraMap
 
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 @[simp]
 theorem range_algebraMap {R A : Type _} [CommRing R] [CommRing A] [Algebra R A]
     (S : Subalgebra R A) : (algebraMap S A).range = S.toSubring := by
@@ -2248,12 +1390,6 @@ theorem range_algebraMap {R A : Type _} [CommRing R] [CommRing A] [Algebra R A]
     Subring.range_subtype]
 #align subalgebra.range_algebra_map Subalgebra.range_algebraMap
 
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 instance noZeroSMulDivisors_top [NoZeroDivisors A] (S : Subalgebra R A) : NoZeroSMulDivisors S A :=
   ⟨fun c x h =>
     have : (c : A) = 0 ∨ x = 0 := eq_zero_or_eq_zero_of_mul_eq_zero h
@@ -2264,12 +1400,6 @@ end Actions
 
 section Center
 
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 theorem Set.algebraMap_mem_center (r : R) : algebraMap R A r ∈ Set.center A := by
   simp [Algebra.commutes, Set.mem_center_iff]
 #align set.algebra_map_mem_center Set.algebraMap_mem_center
@@ -2284,12 +1414,6 @@ def center : Subalgebra R A :=
 #align subalgebra.center Subalgebra.center
 -/
 
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 theorem coe_center : (center R A : Set A) = Set.center A :=
   rfl
 #align subalgebra.coe_center Subalgebra.coe_center
@@ -2301,24 +1425,12 @@ theorem center_toSubsemiring : (center R A).toSubsemiring = Subsemiring.center A
 #align subalgebra.center_to_subsemiring Subalgebra.center_toSubsemiring
 -/
 
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 @[simp]
 theorem center_toSubring (R A : Type _) [CommRing R] [Ring A] [Algebra R A] :
     (center R A).toSubring = Subring.center A :=
   rfl
 #align subalgebra.center_to_subring Subalgebra.center_toSubring
 
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 @[simp]
 theorem center_eq_top (A : Type _) [CommSemiring A] [Algebra R A] : center R A = ⊤ :=
   SetLike.coe_injective (Set.center_eq_univ A)
@@ -2332,12 +1444,6 @@ instance : CommSemiring (center R A) :=
 instance {A : Type _} [Ring A] [Algebra R A] : CommRing (center R A) :=
   Subring.center.commRing
 
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 theorem mem_center_iff {a : A} : a ∈ center R A ↔ ∀ b : A, b * a = a * b :=
   Iff.rfl
 #align subalgebra.mem_center_iff Subalgebra.mem_center_iff
@@ -2346,12 +1452,6 @@ end Center
 
 section Centralizer
 
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 @[simp]
 theorem Set.algebraMap_mem_centralizer {s : Set A} (r : R) : algebraMap R A r ∈ s.centralizer :=
   fun a h => (Algebra.commutes _ _).symm
@@ -2366,33 +1466,15 @@ def centralizer (s : Set A) : Subalgebra R A :=
 #align subalgebra.centralizer Subalgebra.centralizer
 -/
 
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 @[simp, norm_cast]
 theorem coe_centralizer (s : Set A) : (centralizer R s : Set A) = s.centralizer :=
   rfl
 #align subalgebra.coe_centralizer Subalgebra.coe_centralizer
 
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 theorem mem_centralizer_iff {s : Set A} {z : A} : z ∈ centralizer R s ↔ ∀ g ∈ s, g * z = z * g :=
   Iff.rfl
 #align subalgebra.mem_centralizer_iff Subalgebra.mem_centralizer_iff
 
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 theorem centralizer_le (s t : Set A) (h : s ⊆ t) : centralizer R t ≤ centralizer R s :=
   Set.centralizer_subset h
 #align subalgebra.centralizer_le Subalgebra.centralizer_le
@@ -2406,9 +1488,6 @@ theorem centralizer_univ : centralizer R Set.univ = center R A :=
 
 end Centralizer
 
-/- warning: subalgebra.mem_of_finset_sum_eq_one_of_pow_smul_mem -> Subalgebra.mem_of_finset_sum_eq_one_of_pow_smul_mem is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align subalgebra.mem_of_finset_sum_eq_one_of_pow_smul_mem Subalgebra.mem_of_finset_sum_eq_one_of_pow_smul_memₓ'. -/
 /-- Suppose we are given `∑ i, lᵢ * sᵢ = 1` in `S`, and `S'` a subalgebra of `S` that contains
 `lᵢ` and `sᵢ`. To check that an `x : S` falls in `S'`, we only need to show that
 `r ^ n • x ∈ M'` for some `n` for each `r : s`. -/
@@ -2441,9 +1520,6 @@ theorem mem_of_finset_sum_eq_one_of_pow_smul_mem {S : Type _} [CommRing S] [Alge
     exact ⟨⟨_, hn i⟩, rfl⟩
 #align subalgebra.mem_of_finset_sum_eq_one_of_pow_smul_mem Subalgebra.mem_of_finset_sum_eq_one_of_pow_smul_mem
 
-/- warning: subalgebra.mem_of_span_eq_top_of_smul_pow_mem -> Subalgebra.mem_of_span_eq_top_of_smul_pow_mem is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align subalgebra.mem_of_span_eq_top_of_smul_pow_mem Subalgebra.mem_of_span_eq_top_of_smul_pow_memₓ'. -/
 theorem mem_of_span_eq_top_of_smul_pow_mem {S : Type _} [CommRing S] [Algebra R S]
     (S' : Subalgebra R S) (s : Set S) (l : s →₀ S) (hs : Finsupp.total s S S coe l = 1)
     (hs' : s ⊆ S') (hl : ∀ i, l i ∈ S') (x : S) (H : ∀ r : s, ∃ n : ℕ, (r ^ n : S) • x ∈ S') :
@@ -2464,12 +1540,6 @@ def subalgebraOfSubsemiring (S : Subsemiring R) : Subalgebra ℕ R :=
 #align subalgebra_of_subsemiring subalgebraOfSubsemiring
 -/
 
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 @[simp]
 theorem mem_subalgebraOfSubsemiring {x : R} {S : Subsemiring R} :
     x ∈ subalgebraOfSubsemiring S ↔ x ∈ S :=
@@ -2482,12 +1552,6 @@ section Int
 
 variable {R : Type _} [Ring R]
 
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 /-- A subring is a `ℤ`-subalgebra. -/
 def subalgebraOfSubring (S : Subring R) : Subalgebra ℤ R :=
   { S with
@@ -2501,12 +1565,6 @@ def subalgebraOfSubring (S : Subring R) : Subalgebra ℤ R :=
 
 variable {S : Type _} [Semiring S]
 
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 @[simp]
 theorem mem_subalgebraOfSubring {x : R} {S : Subring R} : x ∈ subalgebraOfSubring S ↔ x ∈ S :=
   Iff.rfl

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -1046,9 +1046,7 @@ Case conversion may be inaccurate. Consider using '#align submodule.to_subalgebr
 @[simp]
 theorem toSubalgebra_mk (s : Set A) (h0 hadd hsmul h1 hmul) :
     (Submodule.mk s hadd h0 hsmul : Submodule R A).toSubalgebra h1 hmul =
-      Subalgebra.mk s (@hmul) h1 (@hadd) h0 fun r =>
-        by
-        rw [Algebra.algebraMap_eq_smul_one]
+      Subalgebra.mk s (@hmul) h1 (@hadd) h0 fun r => by rw [Algebra.algebraMap_eq_smul_one];
         exact hsmul r h1 :=
   rfl
 #align submodule.to_subalgebra_mk Submodule.toSubalgebra_mk
@@ -1109,11 +1107,8 @@ theorem mem_range_self (φ : A →ₐ[R] B) (x : A) : φ x ∈ φ.range :=
 <too large>
 Case conversion may be inaccurate. Consider using '#align alg_hom.coe_range AlgHom.coe_rangeₓ'. -/
 @[simp]
-theorem coe_range (φ : A →ₐ[R] B) : (φ.range : Set B) = Set.range φ :=
-  by
-  ext
-  rw [SetLike.mem_coe, mem_range]
-  rfl
+theorem coe_range (φ : A →ₐ[R] B) : (φ.range : Set B) = Set.range φ := by ext;
+  rw [SetLike.mem_coe, mem_range]; rfl
 #align alg_hom.coe_range AlgHom.coe_range
 
 #print AlgHom.range_comp /-
@@ -1291,10 +1286,7 @@ Case conversion may be inaccurate. Consider using '#align alg_equiv.subalgebra_m
 `subalgebra_map` is the induced equivalence between `S` and `S.map e` -/
 @[simps]
 def subalgebraMap (e : A ≃ₐ[R] B) (S : Subalgebra R A) : S ≃ₐ[R] S.map e.toAlgHom :=
-  { e.toRingEquiv.subsemiringMap S.toSubsemiring with
-    commutes' := fun r => by
-      ext
-      simp }
+  { e.toRingEquiv.subsemiringMap S.toSubsemiring with commutes' := fun r => by ext; simp }
 #align alg_equiv.subalgebra_map AlgEquiv.subalgebraMap
 
 end AlgEquiv
@@ -1594,19 +1586,15 @@ but is expected to have type
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {x : A}, Iff (Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x (Bot.bot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toBot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) x (Set.range.{u2, succ u1} A R (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3))))
 Case conversion may be inaccurate. Consider using '#align algebra.mem_bot Algebra.mem_botₓ'. -/
 theorem mem_bot {x : A} : x ∈ (⊥ : Subalgebra R A) ↔ x ∈ Set.range (algebraMap R A) :=
-  suffices (ofId R A).range = (⊥ : Subalgebra R A)
-    by
-    rw [← this, ← SetLike.mem_coe, AlgHom.coe_range]
-    rfl
+  suffices (ofId R A).range = (⊥ : Subalgebra R A) by
+    rw [← this, ← SetLike.mem_coe, AlgHom.coe_range]; rfl
   le_bot_iff.mp fun x hx => Subalgebra.range_le _ ((ofId R A).coe_range ▸ hx)
 #align algebra.mem_bot Algebra.mem_bot
 
 /- warning: algebra.to_submodule_bot -> Algebra.toSubmodule_bot is a dubious translation:
 <too large>
 Case conversion may be inaccurate. Consider using '#align algebra.to_submodule_bot Algebra.toSubmodule_botₓ'. -/
-theorem toSubmodule_bot : (⊥ : Subalgebra R A).toSubmodule = R ∙ 1 :=
-  by
-  ext x
+theorem toSubmodule_bot : (⊥ : Subalgebra R A).toSubmodule = R ∙ 1 := by ext x;
   simp [mem_bot, -Set.singleton_one, Submodule.mem_span_singleton, Algebra.smul_def]
 #align algebra.to_submodule_bot Algebra.toSubmodule_bot
 
@@ -1930,10 +1918,7 @@ but is expected to have type
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), Eq.{succ u2} (AlgEquiv.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S)) (Subalgebra.equivOfEq.{u1, u2} R A _inst_1 _inst_2 _inst_3 S S (rfl.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) S)) (AlgEquiv.refl.{u1, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S))
 Case conversion may be inaccurate. Consider using '#align subalgebra.equiv_of_eq_rfl Subalgebra.equivOfEq_rflₓ'. -/
 @[simp]
-theorem equivOfEq_rfl (S : Subalgebra R A) : equivOfEq S S rfl = AlgEquiv.refl :=
-  by
-  ext
-  rfl
+theorem equivOfEq_rfl (S : Subalgebra R A) : equivOfEq S S rfl = AlgEquiv.refl := by ext; rfl
 #align subalgebra.equiv_of_eq_rfl Subalgebra.equivOfEq_rfl
 
 /- warning: subalgebra.equiv_of_eq_trans -> Subalgebra.equivOfEq_trans is a dubious translation:
@@ -2432,10 +2417,7 @@ theorem mem_of_finset_sum_eq_one_of_pow_smul_mem {S : Type _} [CommRing S] [Alge
     (e : (∑ i in ι', l i * s i) = 1) (hs : ∀ i, s i ∈ S') (hl : ∀ i, l i ∈ S') (x : S)
     (H : ∀ i, ∃ n : ℕ, (s i ^ n : S) • x ∈ S') : x ∈ S' := by
   classical
-    suffices x ∈ (Algebra.ofId S' S).range.toSubmodule
-      by
-      obtain ⟨x, rfl⟩ := this
-      exact x.2
+    suffices x ∈ (Algebra.ofId S' S).range.toSubmodule by obtain ⟨x, rfl⟩ := this; exact x.2
     choose n hn using H
     let s' : ι → S' := fun x => ⟨s x, hs x⟩
     have : Ideal.span (s' '' ι') = ⊤ :=

bump to nightly-2023-05-28-03

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

6c6011cf

Diff

@@ -637,10 +637,7 @@ def toSubmodule : Subalgebra R A ↪o Submodule R A
 #align subalgebra.to_submodule Subalgebra.toSubmodule
 
 /- warning: subalgebra.mem_to_submodule -> Subalgebra.mem_toSubmodule is a dubious translation:
-lean 3 declaration is
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+<too large>
 Case conversion may be inaccurate. Consider using '#align subalgebra.mem_to_submodule Subalgebra.mem_toSubmoduleₓ'. -/
 /- TODO: bundle other forgetful maps between algebraic substructures, e.g.
   `to_subsemiring` and `to_subring` in this file. -/
@@ -650,10 +647,7 @@ theorem mem_toSubmodule {x} : x ∈ S.toSubmodule ↔ x ∈ S :=
 #align subalgebra.mem_to_submodule Subalgebra.mem_toSubmodule
 
 /- warning: subalgebra.coe_to_submodule -> Subalgebra.coe_toSubmodule is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align subalgebra.coe_to_submodule Subalgebra.coe_toSubmoduleₓ'. -/
 @[simp]
 theorem coe_toSubmodule (S : Subalgebra R A) : (↑S.toSubmodule : Set A) = S :=
@@ -719,20 +713,14 @@ instance noZeroSMulDivisors_bot [NoZeroSMulDivisors R A] : NoZeroSMulDivisors R
 #align subalgebra.no_zero_smul_divisors_bot Subalgebra.noZeroSMulDivisors_bot
 
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 Case conversion may be inaccurate. Consider using '#align subalgebra.coe_add Subalgebra.coe_addₓ'. -/
 protected theorem coe_add (x y : S) : (↑(x + y) : A) = ↑x + ↑y :=
   rfl
 #align subalgebra.coe_add Subalgebra.coe_add
 
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 Case conversion may be inaccurate. Consider using '#align subalgebra.coe_mul Subalgebra.coe_mulₓ'. -/
 protected theorem coe_mul (x y : S) : (↑(x * y) : A) = ↑x * ↑y :=
   rfl
@@ -766,10 +754,7 @@ protected theorem coe_neg {R : Type u} {A : Type v} [CommRing R] [Ring A] [Algeb
 #align subalgebra.coe_neg Subalgebra.coe_neg
 
 /- warning: subalgebra.coe_sub -> Subalgebra.coe_sub is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align subalgebra.coe_sub Subalgebra.coe_subₓ'. -/
 protected theorem coe_sub {R : Type u} {A : Type v} [CommRing R] [Ring A] [Algebra R A]
     {S : Subalgebra R A} (x y : S) : (↑(x - y) : A) = ↑x - ↑y :=
@@ -777,10 +762,7 @@ protected theorem coe_sub {R : Type u} {A : Type v} [CommRing R] [Ring A] [Algeb
 #align subalgebra.coe_sub Subalgebra.coe_sub
 
 /- warning: subalgebra.coe_smul -> Subalgebra.coe_smul is a dubious translation:
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(SMulWithZero.toSMulZeroClass.{u2, u3} R' A (MonoidWithZero.toZero.{u2} R' (Semiring.toMonoidWithZero.{u2} R' _inst_8)) (MonoidWithZero.toZero.{u3} A (Semiring.toMonoidWithZero.{u3} A _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u3} R' A (Semiring.toMonoidWithZero.{u2} R' _inst_8) (MonoidWithZero.toZero.{u3} A (Semiring.toMonoidWithZero.{u3} A _inst_2)) (Module.toMulActionWithZero.{u2, u3} R' A _inst_8 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) _inst_10))))) r (Subtype.val.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Set.{u3} A) (Set.instMembershipSet.{u3} A) x (SetLike.coe.{u3, u3} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) S)) x))
+<too large>
 Case conversion may be inaccurate. Consider using '#align subalgebra.coe_smul Subalgebra.coe_smulₓ'. -/
 @[simp, norm_cast]
 theorem coe_smul [Semiring R'] [SMul R' R] [Module R' A] [IsScalarTower R' R A] (r : R') (x : S) :
@@ -789,10 +771,7 @@ theorem coe_smul [Semiring R'] [SMul R' R] [Module R' A] [IsScalarTower R' R A]
 #align subalgebra.coe_smul Subalgebra.coe_smul
 
 /- warning: subalgebra.coe_algebra_map -> Subalgebra.coe_algebraMap is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align subalgebra.coe_algebra_map Subalgebra.coe_algebraMapₓ'. -/
 @[simp, norm_cast]
 theorem coe_algebraMap [CommSemiring R'] [SMul R' R] [Algebra R' A] [IsScalarTower R' R A]
@@ -843,10 +822,7 @@ def val : S →ₐ[R] A := by refine_struct { toFun := (coe : S → A) } <;> int
 #align subalgebra.val Subalgebra.val
 
 /- warning: subalgebra.coe_val -> Subalgebra.coe_val is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align subalgebra.coe_val Subalgebra.coe_valₓ'. -/
 @[simp]
 theorem coe_val : (S.val : S → A) = coe :=
@@ -854,20 +830,14 @@ theorem coe_val : (S.val : S → A) = coe :=
 #align subalgebra.coe_val Subalgebra.coe_val
 
 /- warning: subalgebra.val_apply -> Subalgebra.val_apply is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align subalgebra.val_apply Subalgebra.val_applyₓ'. -/
 theorem val_apply (x : S) : S.val x = (x : A) :=
   rfl
 #align subalgebra.val_apply Subalgebra.val_apply
 
 /- warning: subalgebra.to_subsemiring_subtype -> Subalgebra.toSubsemiring_subtype is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align subalgebra.to_subsemiring_subtype Subalgebra.toSubsemiring_subtypeₓ'. -/
 @[simp]
 theorem toSubsemiring_subtype : S.toSubsemiring.Subtype = (S.val : S →+* A) :=
@@ -875,10 +845,7 @@ theorem toSubsemiring_subtype : S.toSubsemiring.Subtype = (S.val : S →+* A) :=
 #align subalgebra.to_subsemiring_subtype Subalgebra.toSubsemiring_subtype
 
 /- warning: subalgebra.to_subring_subtype -> Subalgebra.toSubring_subtype is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align subalgebra.to_subring_subtype Subalgebra.toSubring_subtypeₓ'. -/
 @[simp]
 theorem toSubring_subtype {R A : Type _} [CommRing R] [Ring A] [Algebra R A] (S : Subalgebra R A) :
@@ -887,10 +854,7 @@ theorem toSubring_subtype {R A : Type _} [CommRing R] [Ring A] [Algebra R A] (S
 #align subalgebra.to_subring_subtype Subalgebra.toSubring_subtype
 
 /- warning: subalgebra.to_submodule_equiv -> Subalgebra.toSubmoduleEquiv is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align subalgebra.to_submodule_equiv Subalgebra.toSubmoduleEquivₓ'. -/
 /-- Linear equivalence between `S : submodule R A` and `S`. Though these types are equal,
 we define it as a `linear_equiv` to avoid type equalities. -/
@@ -938,20 +902,14 @@ theorem map_map (S : Subalgebra R A) (g : B →ₐ[R] C) (f : A →ₐ[R] B) :
 -/
 
 /- warning: subalgebra.mem_map -> Subalgebra.mem_map is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align subalgebra.mem_map Subalgebra.mem_mapₓ'. -/
 theorem mem_map {S : Subalgebra R A} {f : A →ₐ[R] B} {y : B} : y ∈ map f S ↔ ∃ x ∈ S, f x = y :=
   Subsemiring.mem_map
 #align subalgebra.mem_map Subalgebra.mem_map
 
 /- warning: subalgebra.map_to_submodule -> Subalgebra.map_toSubmodule is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align subalgebra.map_to_submodule Subalgebra.map_toSubmoduleₓ'. -/
 theorem map_toSubmodule {S : Subalgebra R A} {f : A →ₐ[R] B} :
     (S.map f).toSubmodule = S.toSubmodule.map f.toLinearMap :=
@@ -966,10 +924,7 @@ theorem map_toSubsemiring {S : Subalgebra R A} {f : A →ₐ[R] B} :
 -/
 
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 Case conversion may be inaccurate. Consider using '#align subalgebra.coe_map Subalgebra.coe_mapₓ'. -/
 @[simp]
 theorem coe_map (S : Subalgebra R A) (f : A →ₐ[R] B) : (S.map f : Set B) = f '' S :=
@@ -1006,10 +961,7 @@ theorem gc_map_comap (f : A →ₐ[R] B) : GaloisConnection (map f) (comap f) :=
 #align subalgebra.gc_map_comap Subalgebra.gc_map_comap
 
 /- warning: subalgebra.mem_comap -> Subalgebra.mem_comap is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align subalgebra.mem_comap Subalgebra.mem_comapₓ'. -/
 @[simp]
 theorem mem_comap (S : Subalgebra R B) (f : A →ₐ[R] B) (x : A) : x ∈ S.comap f ↔ f x ∈ S :=
@@ -1017,10 +969,7 @@ theorem mem_comap (S : Subalgebra R B) (f : A →ₐ[R] B) (x : A) : x ∈ S.com
 #align subalgebra.mem_comap Subalgebra.mem_comap
 
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 Case conversion may be inaccurate. Consider using '#align subalgebra.coe_comap Subalgebra.coe_comapₓ'. -/
 @[simp, norm_cast]
 theorem coe_comap (S : Subalgebra R B) (f : A →ₐ[R] B) : (S.comap f : Set A) = f ⁻¹' (S : Set B) :=
@@ -1074,10 +1023,7 @@ def toSubalgebra (p : Submodule R A) (h_one : (1 : A) ∈ p)
 #align submodule.to_subalgebra Submodule.toSubalgebra
 
 /- warning: submodule.mem_to_subalgebra -> Submodule.mem_toSubalgebra is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.mem_to_subalgebra Submodule.mem_toSubalgebraₓ'. -/
 @[simp]
 theorem mem_toSubalgebra {p : Submodule R A} {h_one h_mul} {x} :
@@ -1086,10 +1032,7 @@ theorem mem_toSubalgebra {p : Submodule R A} {h_one h_mul} {x} :
 #align submodule.mem_to_subalgebra Submodule.mem_toSubalgebra
 
 /- warning: submodule.coe_to_subalgebra -> Submodule.coe_toSubalgebra is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.coe_to_subalgebra Submodule.coe_toSubalgebraₓ'. -/
 @[simp]
 theorem coe_toSubalgebra (p : Submodule R A) (h_one h_mul) :
@@ -1098,10 +1041,7 @@ theorem coe_toSubalgebra (p : Submodule R A) (h_one h_mul) :
 #align submodule.coe_to_subalgebra Submodule.coe_toSubalgebra
 
 /- warning: submodule.to_subalgebra_mk -> Submodule.toSubalgebra_mk is a dubious translation:
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_inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) s) hadd) h0) (fun {a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6477 : A} {b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6478 : A} => Submodule.add_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6477 b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6478) (Submodule.zero_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s)))))) (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) r) (Set.{u1} A) (Set.instMembershipSet.{u1} A) _a (Subsemigroup.carrier.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (Submonoid.toSubsemigroup.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemiring.toSubmonoid.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Subsemiring.mk.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Submonoid.mk.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemigroup.mk.{u1} A (MulOneClass.toMul.{u1} A 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6477 b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6478) (Submodule.zero_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s))))))) (Eq.refl.{1} Prop (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) r) (Set.{u1} A) (Set.instMembershipSet.{u1} A) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) 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u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2) (RingHom.instRingHomClassRingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2))))) (algebraMap.{u2, u1} R A _inst_1 _inst_2 _inst_3) r) (Subsemigroup.carrier.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (Submonoid.toSubsemigroup.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemiring.toSubmonoid.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Subsemiring.mk.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Submonoid.mk.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemigroup.mk.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) s) hadd) h0) (fun {a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6477 : A} {b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6478 : A} => Submodule.add_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6477 b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6478) (Submodule.zero_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s))))))) (HSMul.hSMul.{u2, u1, u1} R A A (instHSMul.{u2, u1} R A (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_2 _inst_3)) r (OfNat.ofNat.{u1} A 1 (One.toOfNat1.{u1} A (Semiring.toOne.{u1} A _inst_2)))) (Algebra.algebraMap_eq_smul_one.{u2, u1} R A _inst_1 _inst_2 _inst_3 r))) (Submodule.smul_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s (OfNat.ofNat.{u1} A 1 (One.toOfNat1.{u1} A (Semiring.toOne.{u1} A _inst_2))) r h0)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.to_subalgebra_mk Submodule.toSubalgebra_mkₓ'. -/
 @[simp]
 theorem toSubalgebra_mk (s : Set A) (h0 hadd hsmul h1 hmul) :
@@ -1114,10 +1054,7 @@ theorem toSubalgebra_mk (s : Set A) (h0 hadd hsmul h1 hmul) :
 #align submodule.to_subalgebra_mk Submodule.toSubalgebra_mk
 
 /- warning: submodule.to_subalgebra_to_submodule -> Submodule.toSubalgebra_toSubmodule is a dubious translation:
-lean 3 declaration is
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R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (OfNat.ofNat.{u2} A 1 (OfNat.mk.{u2} A 1 (One.one.{u2} A (AddMonoidWithOne.toOne.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))))) p) (h_mul : forall (x : A) (y : A), (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x p) -> (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A 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_inst_2 _inst_3)) => LE.le.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R 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(Submodule.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 p h_one h_mul)) p
+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.to_subalgebra_to_submodule Submodule.toSubalgebra_toSubmoduleₓ'. -/
 @[simp]
 theorem toSubalgebra_toSubmodule (p : Submodule R A) (h_one h_mul) :
@@ -1126,10 +1063,7 @@ theorem toSubalgebra_toSubmodule (p : Submodule R A) (h_one h_mul) :
 #align submodule.to_subalgebra_to_submodule Submodule.toSubalgebra_toSubmodule
 
 /- warning: subalgebra.to_submodule_to_subalgebra -> Subalgebra.toSubmodule_toSubalgebra is a dubious translation:
-lean 3 declaration is
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 Case conversion may be inaccurate. Consider using '#align subalgebra.to_submodule_to_subalgebra Subalgebra.toSubmodule_toSubalgebraₓ'. -/
 @[simp]
 theorem Subalgebra.toSubmodule_toSubalgebra (S : Subalgebra R A) :
@@ -1157,10 +1091,7 @@ protected def range (φ : A →ₐ[R] B) : Subalgebra R B :=
 -/
 
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 Case conversion may be inaccurate. Consider using '#align alg_hom.mem_range AlgHom.mem_rangeₓ'. -/
 @[simp]
 theorem mem_range (φ : A →ₐ[R] B) {y : B} : y ∈ φ.range ↔ ∃ x, φ x = y :=
@@ -1168,20 +1099,14 @@ theorem mem_range (φ : A →ₐ[R] B) {y : B} : y ∈ φ.range ↔ ∃ x, φ x
 #align alg_hom.mem_range AlgHom.mem_range
 
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 Case conversion may be inaccurate. Consider using '#align alg_hom.mem_range_self AlgHom.mem_range_selfₓ'. -/
 theorem mem_range_self (φ : A →ₐ[R] B) (x : A) : φ x ∈ φ.range :=
   φ.mem_range.2 ⟨x, rfl⟩
 #align alg_hom.mem_range_self AlgHom.mem_range_self
 
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 Case conversion may be inaccurate. Consider using '#align alg_hom.coe_range AlgHom.coe_rangeₓ'. -/
 @[simp]
 theorem coe_range (φ : A →ₐ[R] B) : (φ.range : Set B) = Set.range φ :=
@@ -1208,10 +1133,7 @@ theorem range_comp_le_range (f : A →ₐ[R] B) (g : B →ₐ[R] C) : (g.comp f)
 #align alg_hom.range_comp_le_range AlgHom.range_comp_le_range
 
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 Case conversion may be inaccurate. Consider using '#align alg_hom.cod_restrict AlgHom.codRestrictₓ'. -/
 /-- Restrict the codomain of an algebra homomorphism. -/
 def codRestrict (f : A →ₐ[R] B) (S : Subalgebra R B) (hf : ∀ x, f x ∈ S) : A →ₐ[R] S :=
@@ -1219,10 +1141,7 @@ def codRestrict (f : A →ₐ[R] B) (S : Subalgebra R B) (hf : ∀ x, f x ∈ S)
 #align alg_hom.cod_restrict AlgHom.codRestrict
 
 /- warning: alg_hom.val_comp_cod_restrict -> AlgHom.val_comp_codRestrict is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align alg_hom.val_comp_cod_restrict AlgHom.val_comp_codRestrictₓ'. -/
 @[simp]
 theorem val_comp_codRestrict (f : A →ₐ[R] B) (S : Subalgebra R B) (hf : ∀ x, f x ∈ S) :
@@ -1231,10 +1150,7 @@ theorem val_comp_codRestrict (f : A →ₐ[R] B) (S : Subalgebra R B) (hf : ∀
 #align alg_hom.val_comp_cod_restrict AlgHom.val_comp_codRestrict
 
 /- warning: alg_hom.coe_cod_restrict -> AlgHom.coe_codRestrict is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align alg_hom.coe_cod_restrict AlgHom.coe_codRestrictₓ'. -/
 @[simp]
 theorem coe_codRestrict (f : A →ₐ[R] B) (S : Subalgebra R B) (hf : ∀ x, f x ∈ S) (x : A) :
@@ -1243,10 +1159,7 @@ theorem coe_codRestrict (f : A →ₐ[R] B) (S : Subalgebra R B) (hf : ∀ x, f
 #align alg_hom.coe_cod_restrict AlgHom.coe_codRestrict
 
 /- warning: alg_hom.injective_cod_restrict -> AlgHom.injective_codRestrict is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align alg_hom.injective_cod_restrict AlgHom.injective_codRestrictₓ'. -/
 theorem injective_codRestrict (f : A →ₐ[R] B) (S : Subalgebra R B) (hf : ∀ x, f x ∈ S) :
     Function.Injective (f.codRestrict S hf) ↔ Function.Injective f :=
@@ -1281,10 +1194,7 @@ def equalizer (ϕ ψ : A →ₐ[R] B) : Subalgebra R A
 -/
 
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(Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toSMul.{u1, u3} R B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))))) (DistribSMul.toSMulZeroClass.{u1, u3} R B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))))) (DistribMulAction.toDistribSMul.{u1, u3} R B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} B 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_inst_2 _inst_4 _inst_3 _inst_5 (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (AlgHom.algHomClass.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5))))) ϕ x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => B) _x) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (SMulZeroClass.toSMul.{u1, u2} R A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribSMul.toSMulZeroClass.{u1, u2} R A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A 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+<too large>
 Case conversion may be inaccurate. Consider using '#align alg_hom.mem_equalizer AlgHom.mem_equalizerₓ'. -/
 @[simp]
 theorem mem_equalizer (ϕ ψ : A →ₐ[R] B) (x : A) : x ∈ ϕ.equalizer ψ ↔ ϕ x = ψ x :=
@@ -1458,10 +1368,7 @@ theorem mem_top {x : A} : x ∈ (⊤ : Subalgebra R A) :=
 #align algebra.mem_top Algebra.mem_top
 
 /- warning: algebra.top_to_submodule -> Algebra.top_toSubmodule is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align algebra.top_to_submodule Algebra.top_toSubmoduleₓ'. -/
 @[simp]
 theorem top_toSubmodule : (⊤ : Subalgebra R A).toSubmodule = ⊤ :=
@@ -1492,10 +1399,7 @@ theorem top_toSubring {R A : Type _} [CommRing R] [Ring A] [Algebra R A] :
 #align algebra.top_to_subring Algebra.top_toSubring
 
 /- warning: algebra.to_submodule_eq_top -> Algebra.toSubmodule_eq_top is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align algebra.to_submodule_eq_top Algebra.toSubmodule_eq_topₓ'. -/
 @[simp]
 theorem toSubmodule_eq_top {S : Subalgebra R A} : S.toSubmodule = ⊤ ↔ S = ⊤ :=
@@ -1588,10 +1492,7 @@ theorem mem_inf {S T : Subalgebra R A} {x : A} : x ∈ S ⊓ T ↔ x ∈ S ∧ x
 #align algebra.mem_inf Algebra.mem_inf
 
 /- warning: algebra.inf_to_submodule -> Algebra.inf_toSubmodule is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align algebra.inf_to_submodule Algebra.inf_toSubmoduleₓ'. -/
 @[simp]
 theorem inf_toSubmodule (S T : Subalgebra R A) :
@@ -1633,10 +1534,7 @@ theorem mem_sInf {S : Set (Subalgebra R A)} {x : A} : x ∈ sInf S ↔ ∀ p ∈
 #align algebra.mem_Inf Algebra.mem_sInf
 
 /- warning: algebra.Inf_to_submodule -> Algebra.sInf_toSubmodule is a dubious translation:
-lean 3 declaration is
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A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (fun (_x : RelEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) => (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) -> (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (RelEmbedding.hasCoeToFun.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (InfSet.sInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))) S)) (InfSet.sInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.hasInf.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.image.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (coeFn.{succ u2, succ u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (fun (_x : RelEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) => (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) -> (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (RelEmbedding.hasCoeToFun.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A 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+<too large>
 Case conversion may be inaccurate. Consider using '#align algebra.Inf_to_submodule Algebra.sInf_toSubmoduleₓ'. -/
 @[simp]
 theorem sInf_toSubmodule (S : Set (Subalgebra R A)) :
@@ -1678,10 +1576,7 @@ theorem mem_iInf {ι : Sort _} {S : ι → Subalgebra R A} {x : A} : (x ∈ ⨅
 #align algebra.mem_infi Algebra.mem_iInf
 
 /- warning: algebra.infi_to_submodule -> Algebra.iInf_toSubmodule is a dubious translation:
-lean 3 declaration is
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+<too large>
 Case conversion may be inaccurate. Consider using '#align algebra.infi_to_submodule Algebra.iInf_toSubmoduleₓ'. -/
 @[simp]
 theorem iInf_toSubmodule {ι : Sort _} (S : ι → Subalgebra R A) :
@@ -1707,10 +1602,7 @@ theorem mem_bot {x : A} : x ∈ (⊥ : Subalgebra R A) ↔ x ∈ Set.range (alge
 #align algebra.mem_bot Algebra.mem_bot
 
 /- warning: algebra.to_submodule_bot -> Algebra.toSubmodule_bot is a dubious translation:
-lean 3 declaration is
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+<too large>
 Case conversion may be inaccurate. Consider using '#align algebra.to_submodule_bot Algebra.toSubmodule_botₓ'. -/
 theorem toSubmodule_bot : (⊥ : Subalgebra R A).toSubmodule = R ∙ 1 :=
   by
@@ -1741,10 +1633,7 @@ theorem eq_top_iff {S : Subalgebra R A} : S = ⊤ ↔ ∀ x : A, x ∈ S :=
 #align algebra.eq_top_iff Algebra.eq_top_iff
 
 /- warning: algebra.range_top_iff_surjective -> Algebra.range_top_iff_surjective is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align algebra.range_top_iff_surjective Algebra.range_top_iff_surjectiveₓ'. -/
 theorem range_top_iff_surjective (f : A →ₐ[R] B) :
     f.range = (⊤ : Subalgebra R B) ↔ Function.Surjective f :=
@@ -1954,10 +1843,7 @@ def inclusion {S T : Subalgebra R A} (h : S ≤ T) : S →ₐ[R] T
 #align subalgebra.inclusion Subalgebra.inclusion
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align subalgebra.inclusion_injective Subalgebra.inclusion_injectiveₓ'. -/
 theorem inclusion_injective {S T : Subalgebra R A} (h : S ≤ T) : Function.Injective (inclusion h) :=
   fun _ _ => Subtype.ext ∘ Subtype.mk.inj
@@ -1975,10 +1861,7 @@ theorem inclusion_self {S : Subalgebra R A} : inclusion (le_refl S) = AlgHom.id
 #align subalgebra.inclusion_self Subalgebra.inclusion_self
 
 /- warning: subalgebra.inclusion_mk -> Subalgebra.inclusion_mk is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align subalgebra.inclusion_mk Subalgebra.inclusion_mkₓ'. -/
 @[simp]
 theorem inclusion_mk {S T : Subalgebra R A} (h : S ≤ T) (x : A) (hx : x ∈ S) :
@@ -1987,10 +1870,7 @@ theorem inclusion_mk {S T : Subalgebra R A} (h : S ≤ T) (x : A) (hx : x ∈ S)
 #align subalgebra.inclusion_mk Subalgebra.inclusion_mk
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align subalgebra.inclusion_right Subalgebra.inclusion_rightₓ'. -/
 theorem inclusion_right {S T : Subalgebra R A} (h : S ≤ T) (x : T) (m : (x : A) ∈ S) :
     inclusion h ⟨x, m⟩ = x :=
@@ -1998,10 +1878,7 @@ theorem inclusion_right {S T : Subalgebra R A} (h : S ≤ T) (x : T) (m : (x : A
 #align subalgebra.inclusion_right Subalgebra.inclusion_right
 
 /- warning: subalgebra.inclusion_inclusion -> Subalgebra.inclusion_inclusion is a dubious translation:
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(OmegaCompletePartialOrder.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) S T U hst htu)) x)
+<too large>
 Case conversion may be inaccurate. Consider using '#align subalgebra.inclusion_inclusion Subalgebra.inclusion_inclusionₓ'. -/
 @[simp]
 theorem inclusion_inclusion {S T U : Subalgebra R A} (hst : S ≤ T) (htu : T ≤ U) (x : S) :
@@ -2010,10 +1887,7 @@ theorem inclusion_inclusion {S T U : Subalgebra R A} (hst : S ≤ T) (htu : T 
 #align subalgebra.inclusion_inclusion Subalgebra.inclusion_inclusion
 
 /- warning: subalgebra.coe_inclusion -> Subalgebra.coe_inclusion is a dubious translation:
-lean 3 declaration is
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+<too large>
 Case conversion may be inaccurate. Consider using '#align subalgebra.coe_inclusion Subalgebra.coe_inclusionₓ'. -/
 @[simp]
 theorem coe_inclusion {S T : Subalgebra R A} (h : S ≤ T) (s : S) : (inclusion h s : A) = s :=
@@ -2041,10 +1915,7 @@ def equivOfEq (S T : Subalgebra R A) (h : S = T) : S ≃ₐ[R] T :=
 #align subalgebra.equiv_of_eq Subalgebra.equivOfEq
 
 /- warning: subalgebra.equiv_of_eq_symm -> Subalgebra.equivOfEq_symm is a dubious translation:
-lean 3 declaration is
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 Case conversion may be inaccurate. Consider using '#align subalgebra.equiv_of_eq_symm Subalgebra.equivOfEq_symmₓ'. -/
 @[simp]
 theorem equivOfEq_symm (S T : Subalgebra R A) (h : S = T) :
@@ -2066,10 +1937,7 @@ theorem equivOfEq_rfl (S : Subalgebra R A) : equivOfEq S S rfl = AlgEquiv.refl :
 #align subalgebra.equiv_of_eq_rfl Subalgebra.equivOfEq_rfl
 
 /- warning: subalgebra.equiv_of_eq_trans -> Subalgebra.equivOfEq_trans is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align subalgebra.equiv_of_eq_trans Subalgebra.equivOfEq_transₓ'. -/
 @[simp]
 theorem equivOfEq_trans (S T U : Subalgebra R A) (hST : S = T) (hTU : T = U) :
@@ -2109,10 +1977,7 @@ theorem coe_prod : (prod S S₁ : Set (A × B)) = S ×ˢ S₁ :=
 #align subalgebra.coe_prod Subalgebra.coe_prod
 
 /- warning: subalgebra.prod_to_submodule -> Subalgebra.prod_toSubmodule is a dubious translation:
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(NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.semiring.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)))))))) (fun (_x : RelEmbedding.{max u2 u3, max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.semiring.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (LE.le.{max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (Preorder.toHasLe.{max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (PartialOrder.toPreorder.{max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (SetLike.partialOrder.{max u2 u3, max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (Prod.{u2, u3} A B) (Subalgebra.setLike.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)))))) (LE.le.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.semiring.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (Preorder.toHasLe.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.semiring.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (PartialOrder.toPreorder.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.semiring.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) 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(CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.semiring.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)))) (RelEmbedding.hasCoeToFun.{max u2 u3, max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.semiring.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (LE.le.{max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (Preorder.toHasLe.{max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (PartialOrder.toPreorder.{max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (SetLike.partialOrder.{max u2 u3, max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (Prod.{u2, u3} A B) (Subalgebra.setLike.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)))))) (LE.le.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.semiring.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (Preorder.toHasLe.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) 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_inst_3 _inst_4 _inst_5))) (CompleteSemilatticeInf.toPartialOrder.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.semiring.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (CompleteLattice.toCompleteSemilatticeInf.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.semiring.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (Submodule.completeLattice.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.semiring.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))))))))) (Subalgebra.toSubmodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (Subalgebra.prod.{u1, u2, u3} R A B _inst_1 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u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) => LE.le.{max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (Preorder.toLE.{max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (PartialOrder.toPreorder.{max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (SetLike.instPartialOrder.{max u2 u3, max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (Prod.{u2, u3} A B) (Subalgebra.instSetLikeSubalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))))) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) => LE.le.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (Preorder.toLE.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (PartialOrder.toPreorder.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (OmegaCompletePartialOrder.toPartialOrder.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (CompleteLattice.instOmegaCompletePartialOrder.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (Submodule.completeLattice.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))))))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{max u2 u3, max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) => LE.le.{max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (Preorder.toLE.{max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (PartialOrder.toPreorder.{max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (SetLike.instPartialOrder.{max u2 u3, max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (Prod.{u2, u3} A B) (Subalgebra.instSetLikeSubalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))))) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) => LE.le.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (Preorder.toLE.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (PartialOrder.toPreorder.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (OmegaCompletePartialOrder.toPartialOrder.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (CompleteLattice.instOmegaCompletePartialOrder.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (Submodule.completeLattice.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))))))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Subalgebra.toSubmodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (Subalgebra.prod.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 S S₁)) (Submodule.prod.{u1, u2, u3} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, 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+<too large>
 Case conversion may be inaccurate. Consider using '#align subalgebra.prod_to_submodule Subalgebra.prod_toSubmoduleₓ'. -/
 theorem prod_toSubmodule : (S.Prod S₁).toSubmodule = S.toSubmodule.Prod S₁.toSubmodule :=
   rfl
@@ -2141,10 +2006,7 @@ theorem prod_top : (prod ⊤ ⊤ : Subalgebra R (A × B)) = ⊤ := by ext <;> si
 #align subalgebra.prod_top Subalgebra.prod_top
 
 /- warning: subalgebra.prod_mono -> Subalgebra.prod_mono is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align subalgebra.prod_mono Subalgebra.prod_monoₓ'. -/
 theorem prod_mono {S T : Subalgebra R A} {S₁ T₁ : Subalgebra R B} :
     S ≤ T → S₁ ≤ T₁ → prod S S₁ ≤ prod T T₁ :=
@@ -2152,10 +2014,7 @@ theorem prod_mono {S T : Subalgebra R A} {S₁ T₁ : Subalgebra R B} :
 #align subalgebra.prod_mono Subalgebra.prod_mono
 
 /- warning: subalgebra.prod_inf_prod -> Subalgebra.prod_inf_prod is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align subalgebra.prod_inf_prod Subalgebra.prod_inf_prodₓ'. -/
 @[simp]
 theorem prod_inf_prod {S T : Subalgebra R A} {S₁ T₁ : Subalgebra R B} :
@@ -2199,10 +2058,7 @@ theorem coe_iSup_of_directed [Nonempty ι] {S : ι → Subalgebra R A} (dir : Di
 #align subalgebra.coe_supr_of_directed Subalgebra.coe_iSup_of_directed
 
 /- warning: subalgebra.supr_lift -> Subalgebra.iSupLift is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align subalgebra.supr_lift Subalgebra.iSupLiftₓ'. -/
 /-- Define an algebra homomorphism on a directed supremum of subalgebras by defining
 it on each subalgebra, and proving that it agrees on the intersection of subalgebras. -/
@@ -2236,10 +2092,7 @@ variable [Nonempty ι] {K : ι → Subalgebra R A} {dir : Directed (· ≤ ·) K
   {hT : T = iSup K}
 
 /- warning: subalgebra.supr_lift_inclusion -> Subalgebra.iSupLift_inclusion is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align subalgebra.supr_lift_inclusion Subalgebra.iSupLift_inclusionₓ'. -/
 @[simp]
 theorem iSupLift_inclusion {i : ι} (x : K i) (h : K i ≤ T) :
@@ -2248,10 +2101,7 @@ theorem iSupLift_inclusion {i : ι} (x : K i) (h : K i ≤ T) :
 #align subalgebra.supr_lift_inclusion Subalgebra.iSupLift_inclusion
 
 /- warning: subalgebra.supr_lift_comp_inclusion -> Subalgebra.iSupLift_comp_inclusion is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align subalgebra.supr_lift_comp_inclusion Subalgebra.iSupLift_comp_inclusionₓ'. -/
 @[simp]
 theorem iSupLift_comp_inclusion {i : ι} (h : K i ≤ T) :
@@ -2259,10 +2109,7 @@ theorem iSupLift_comp_inclusion {i : ι} (h : K i ≤ T) :
 #align subalgebra.supr_lift_comp_inclusion Subalgebra.iSupLift_comp_inclusion
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align subalgebra.supr_lift_mk Subalgebra.iSupLift_mkₓ'. -/
 @[simp]
 theorem iSupLift_mk {i : ι} (x : K i) (hx : (x : A) ∈ T) :
@@ -2270,10 +2117,7 @@ theorem iSupLift_mk {i : ι} (x : K i) (hx : (x : A) ∈ T) :
 #align subalgebra.supr_lift_mk Subalgebra.iSupLift_mk
 
 /- warning: subalgebra.supr_lift_of_mem -> Subalgebra.iSupLift_of_mem is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align subalgebra.supr_lift_of_mem Subalgebra.iSupLift_of_memₓ'. -/
 theorem iSupLift_of_mem {i : ι} (x : T) (hx : (x : A) ∈ K i) :
     iSupLift K dir f hf T hT x = f i ⟨x, hx⟩ := by subst hT <;> exact Set.iUnionLift_of_mem x hx
@@ -2297,10 +2141,7 @@ instance [SMul A α] (S : Subalgebra R A) : SMul S α :=
   S.toSubsemiring.SMul
 
 /- warning: subalgebra.smul_def -> Subalgebra.smul_def is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align subalgebra.smul_def Subalgebra.smul_defₓ'. -/
 theorem smul_def [SMul A α] {S : Subalgebra R A} (g : S) (m : α) : g • m = (g : A) • m :=
   rfl
@@ -2329,10 +2170,7 @@ instance smulCommClass_right [SMul α β] [SMul A β] [SMulCommClass α A β] (S
 #align subalgebra.smul_comm_class_right Subalgebra.smulCommClass_right
 
 /- warning: subalgebra.is_scalar_tower_left -> Subalgebra.isScalarTower_left is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align subalgebra.is_scalar_tower_left Subalgebra.isScalarTower_leftₓ'. -/
 /-- Note that this provides `is_scalar_tower S R R` which is needed by `smul_mul_assoc`. -/
 instance isScalarTower_left [SMul α β] [SMul A α] [SMul A β] [IsScalarTower A α β]
@@ -2341,10 +2179,7 @@ instance isScalarTower_left [SMul α β] [SMul A α] [SMul A β] [IsScalarTower
 #align subalgebra.is_scalar_tower_left Subalgebra.isScalarTower_left
 
 /- warning: subalgebra.is_scalar_tower_mid -> Subalgebra.isScalarTower_mid is a dubious translation:
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_inst_10))))
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-  forall {R : Type.{u1}} {S : Type.{u2}} {T : Type.{u3}} [_inst_6 : CommSemiring.{u1} R] [_inst_7 : Semiring.{u2} S] [_inst_8 : AddCommMonoid.{u3} T] [_inst_9 : Algebra.{u1, u2} R S _inst_6 _inst_7] [_inst_10 : Module.{u1, u3} R T (CommSemiring.toSemiring.{u1} R _inst_6) _inst_8] [_inst_11 : Module.{u2, u3} S T _inst_7 _inst_8] [_inst_12 : IsScalarTower.{u1, u2, u3} R S T (Algebra.toSMul.{u1, u2} R S _inst_6 _inst_7 _inst_9) (SMulZeroClass.toSMul.{u2, u3} S T (AddMonoid.toZero.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8)) (SMulWithZero.toSMulZeroClass.{u2, u3} S T (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_7)) (AddMonoid.toZero.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8)) (MulActionWithZero.toSMulWithZero.{u2, u3} S T (Semiring.toMonoidWithZero.{u2} S _inst_7) (AddMonoid.toZero.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8)) (Module.toMulActionWithZero.{u2, u3} S T _inst_7 _inst_8 _inst_11)))) (SMulZeroClass.toSMul.{u1, u3} R T (AddMonoid.toZero.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8)) (SMulWithZero.toSMulZeroClass.{u1, u3} R T (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_6)) (AddMonoid.toZero.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8)) (MulActionWithZero.toSMulWithZero.{u1, u3} R T (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_6)) (AddMonoid.toZero.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8)) (Module.toMulActionWithZero.{u1, u3} R T (CommSemiring.toSemiring.{u1} R _inst_6) _inst_8 _inst_10))))] (S' : Subalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9), IsScalarTower.{u1, u2, u3} R (Subtype.{succ u2} S (fun (x : S) => Membership.mem.{u2, u2} S (Subalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9) S (Subalgebra.instSetLikeSubalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9)) x S')) T (Algebra.toSMul.{u1, u2} R (Subtype.{succ u2} S (fun (x : S) => Membership.mem.{u2, u2} S (Subalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9) S (Subalgebra.instSetLikeSubalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9)) x S')) _inst_6 (Subalgebra.toSemiring.{u1, u2} R S _inst_6 _inst_7 _inst_9 S') (Subalgebra.algebra.{u1, u2} R S _inst_6 _inst_7 _inst_9 S')) (Subalgebra.instSMulSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebra.{u1, u2, u3} R S _inst_6 _inst_7 _inst_9 T (SMulZeroClass.toSMul.{u2, u3} S T (AddMonoid.toZero.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8)) (SMulWithZero.toSMulZeroClass.{u2, u3} S T (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_7)) (AddMonoid.toZero.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8)) (MulActionWithZero.toSMulWithZero.{u2, u3} S T (Semiring.toMonoidWithZero.{u2} S _inst_7) (AddMonoid.toZero.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8)) (Module.toMulActionWithZero.{u2, u3} S T _inst_7 _inst_8 _inst_11)))) S') (SMulZeroClass.toSMul.{u1, u3} R T (AddMonoid.toZero.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8)) (SMulWithZero.toSMulZeroClass.{u1, u3} R T (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_6)) (AddMonoid.toZero.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8)) (MulActionWithZero.toSMulWithZero.{u1, u3} R T (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_6)) (AddMonoid.toZero.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8)) (Module.toMulActionWithZero.{u1, u3} R T (CommSemiring.toSemiring.{u1} R _inst_6) _inst_8 _inst_10))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align subalgebra.is_scalar_tower_mid Subalgebra.isScalarTower_midₓ'. -/
 instance isScalarTower_mid {R S T : Type _} [CommSemiring R] [Semiring S] [AddCommMonoid T]
     [Algebra R S] [Module R T] [Module S T] [IsScalarTower R S T] (S' : Subalgebra R S) :
@@ -2395,10 +2230,7 @@ instance toAlgebra {R A : Type _} [CommSemiring R] [CommSemiring A] [Semiring α
 #align subalgebra.to_algebra Subalgebra.toAlgebra
 
 /- warning: subalgebra.algebra_map_eq -> Subalgebra.algebraMap_eq is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align subalgebra.algebra_map_eq Subalgebra.algebraMap_eqₓ'. -/
 theorem algebraMap_eq {R A : Type _} [CommSemiring R] [CommSemiring A] [Semiring α] [Algebra R A]
     [Algebra A α] (S : Subalgebra R A) : algebraMap S α = (algebraMap A α).comp S.val :=
@@ -2590,10 +2422,7 @@ theorem centralizer_univ : centralizer R Set.univ = center R A :=
 end Centralizer
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align subalgebra.mem_of_finset_sum_eq_one_of_pow_smul_mem Subalgebra.mem_of_finset_sum_eq_one_of_pow_smul_memₓ'. -/
 /-- Suppose we are given `∑ i, lᵢ * sᵢ = 1` in `S`, and `S'` a subalgebra of `S` that contains
 `lᵢ` and `sᵢ`. To check that an `x : S` falls in `S'`, we only need to show that
@@ -2631,10 +2460,7 @@ theorem mem_of_finset_sum_eq_one_of_pow_smul_mem {S : Type _} [CommRing S] [Alge
 #align subalgebra.mem_of_finset_sum_eq_one_of_pow_smul_mem Subalgebra.mem_of_finset_sum_eq_one_of_pow_smul_mem
 
 /- warning: subalgebra.mem_of_span_eq_top_of_smul_pow_mem -> Subalgebra.mem_of_span_eq_top_of_smul_pow_mem is a dubious translation:
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Membership.mem.{u1, u1} S (Set.{u1} S) (Set.instMembershipSet.{u1} S) x s) r) n) x) S')) -> (Membership.mem.{u1, u1} S (Subalgebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)) _inst_7) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)) _inst_7) S (Subalgebra.instSetLikeSubalgebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)) _inst_7)) x S'))
+<too large>
 Case conversion may be inaccurate. Consider using '#align subalgebra.mem_of_span_eq_top_of_smul_pow_mem Subalgebra.mem_of_span_eq_top_of_smul_pow_memₓ'. -/
 theorem mem_of_span_eq_top_of_smul_pow_mem {S : Type _} [CommRing S] [Algebra R S]
     (S' : Subalgebra R S) (s : Set S) (l : s →₀ S) (hs : Finsupp.total s S S coe l = 1)

bump to nightly-2023-05-24-06

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

fbc7b476

Diff

@@ -846,7 +846,7 @@ def val : S →ₐ[R] A := by refine_struct { toFun := (coe : S → A) } <;> int
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), Eq.{succ u2} ((fun (_x : AlgHom.{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_2 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_3) => (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) -> A) (Subalgebra.val.{u1, u2} R A _inst_1 _inst_2 _inst_3 S)) (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_2 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_3) (fun (_x : AlgHom.{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_2 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_3) => (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) -> A) ([anonymous].{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_2 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_3) (Subalgebra.val.{u1, u2} R A _inst_1 _inst_2 _inst_3 S)) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) A (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) A (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) A (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) A (coeSubtype.{succ u2} A (fun (x : A) => Membership.Mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S))))))
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), Eq.{succ u2} (forall (a : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)), (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) => A) a) (FunLike.coe.{succ u2, succ u2, succ u2} (AlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_2 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_3) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (fun (_x : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) => A) _x) (SMulHomClass.toFunLike.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_2 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_3) R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) A (SMulZeroClass.toSMul.{u1, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (AddMonoid.toZero.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S)))))) (DistribSMul.toSMulZeroClass.{u1, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (AddMonoid.toAddZeroClass.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S)))))) (DistribMulAction.toDistribSMul.{u1, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S))))) (Module.toDistribMulAction.{u1, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S)))) (Algebra.toModule.{u1, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S)))))) (SMulZeroClass.toSMul.{u1, u2} R A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribSMul.toSMulZeroClass.{u1, u2} R A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (DistribMulActionHomClass.toSMulHomClass.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) 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_inst_3)) x S)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (Module.toDistribMulAction.{u1, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R 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_inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u2, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_2 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_3 (AlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A 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+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), Eq.{succ u2} (forall (a : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)), (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) => A) a) (FunLike.coe.{succ u2, succ u2, succ u2} (AlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A 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Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) => A) _x) (SMulHomClass.toFunLike.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_2 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_3) R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (Module.toDistribMulAction.{u1, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R 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_inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u2, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_2 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_3 (AlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_2 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_3) (AlgHom.algHomClass.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_2 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_3))))) (Subalgebra.val.{u1, u2} R A _inst_1 _inst_2 _inst_3 S)) (Subtype.val.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) x (SetLike.coe.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) S)))
 Case conversion may be inaccurate. Consider using '#align subalgebra.coe_val Subalgebra.coe_valₓ'. -/
 @[simp]
 theorem coe_val : (S.val : S → A) = coe :=
@@ -857,7 +857,7 @@ theorem coe_val : (S.val : S → A) = coe :=
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x : coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S), Eq.{succ u2} A (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_2 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_3) (fun (_x : AlgHom.{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_2 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_3) => (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) -> A) ([anonymous].{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_2 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_3) (Subalgebra.val.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) x) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) A (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) A (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) A (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) A (coeSubtype.{succ u2} A (fun (x : A) => Membership.Mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S))))) x)
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) => A) x) (FunLike.coe.{succ u2, succ u2, succ u2} (AlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_2 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_3) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (fun (_x : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) => A) _x) (SMulHomClass.toFunLike.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_2 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_3) R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) A (SMulZeroClass.toSMul.{u1, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (AddMonoid.toZero.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S)))))) (DistribSMul.toSMulZeroClass.{u1, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (AddMonoid.toAddZeroClass.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Subtype.{succ u2} 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R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S)))) (Algebra.toModule.{u1, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S)))))) (SMulZeroClass.toSMul.{u1, u2} R A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribSMul.toSMulZeroClass.{u1, u2} R A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (DistribMulActionHomClass.toSMulHomClass.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_2 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_3) R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S))))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Module.toDistribMulAction.{u1, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ 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_inst_2 _inst_3 S) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_2 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_3) R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (Module.toDistribMulAction.{u1, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S)))) (Algebra.toModule.{u1, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u2, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_2 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_3 (AlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_2 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_3) (AlgHom.algHomClass.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_2 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_3))))) (Subalgebra.val.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) x) (Subtype.val.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) x (SetLike.coe.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) S)) x)
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) => A) x) (FunLike.coe.{succ u2, succ u2, succ u2} (AlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_2 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_3) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (fun (_x : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Subtype.{succ u2} A (fun (x : A) => 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u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S)))) (Algebra.toModule.{u1, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_2 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_3) R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (Module.toDistribMulAction.{u1, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S)))) (Algebra.toModule.{u1, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u2, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_2 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_3 (AlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_2 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_3) (AlgHom.algHomClass.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_2 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_3))))) (Subalgebra.val.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) x) (Subtype.val.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) x (SetLike.coe.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) S)) x)
 Case conversion may be inaccurate. Consider using '#align subalgebra.val_apply Subalgebra.val_applyₓ'. -/
 theorem val_apply (x : S) : S.val x = (x : A) :=
   rfl
@@ -941,7 +941,7 @@ theorem map_map (S : Subalgebra R A) (g : B →ₐ[R] C) (f : A →ₐ[R] B) :
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3} {f : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5} {y : B}, Iff (Membership.Mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.hasMem.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.setLike.{u1, u3} R B _inst_1 _inst_4 _inst_5)) y (Subalgebra.map.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 f S)) (Exists.{succ u2} A (fun (x : A) => Exists.{0} (Membership.Mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S) (fun (H : Membership.Mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S) => Eq.{succ u3} B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (fun (_x : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) => A -> B) ([anonymous].{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) f x) y)))
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3} {f : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5} {y : B}, Iff (Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) y (Subalgebra.map.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 f S)) (Exists.{succ u2} A (fun (x : A) => And (Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S) (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) A (fun (a : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) a) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (SMulZeroClass.toSMul.{u1, u2} R A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribSMul.toSMulZeroClass.{u1, u2} R A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toSMul.{u1, u3} R B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))))) (DistribSMul.toSMulZeroClass.{u1, u3} R B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))))) (DistribMulAction.toDistribSMul.{u1, u3} R B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u2, u3, max u2 u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (AlgHom.algHomClass.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5))))) f x) y)))
+  forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3} {f : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5} {y : B}, Iff (Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) y (Subalgebra.map.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 f S)) (Exists.{succ u2} A (fun (x : A) => And (Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S) (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => B) x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) A (fun (a : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => B) a) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (SMulZeroClass.toSMul.{u1, u2} R A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribSMul.toSMulZeroClass.{u1, u2} R A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toSMul.{u1, u3} R B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))))) (DistribSMul.toSMulZeroClass.{u1, u3} R B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))))) (DistribMulAction.toDistribSMul.{u1, u3} R B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u2, u3, max u2 u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (AlgHom.algHomClass.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5))))) f x) y)))
 Case conversion may be inaccurate. Consider using '#align subalgebra.mem_map Subalgebra.mem_mapₓ'. -/
 theorem mem_map {S : Subalgebra R A} {f : A →ₐ[R] B} {y : B} : y ∈ map f S ↔ ∃ x ∈ S, f x = y :=
   Subsemiring.mem_map
@@ -969,7 +969,7 @@ theorem map_toSubsemiring {S : Subalgebra R A} {f : A →ₐ[R] B} :
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (f : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5), Eq.{succ u3} (Set.{u3} B) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Set.{u3} B) (HasLiftT.mk.{succ u3, succ u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Set.{u3} B) (CoeTCₓ.coe.{succ u3, succ u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Set.{u3} B) (SetLike.Set.hasCoeT.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.setLike.{u1, u3} R B _inst_1 _inst_4 _inst_5)))) (Subalgebra.map.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 f S)) (Set.image.{u2, u3} A B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (fun (_x : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) => A -> B) ([anonymous].{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) f) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) S))
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (f : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5), Eq.{succ u3} (Set.{u3} B) (SetLike.coe.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Subalgebra.map.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 f S)) (Set.image.{u2, u3} A B (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) _x) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (SMulZeroClass.toSMul.{u1, u2} R A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribSMul.toSMulZeroClass.{u1, u2} R A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toSMul.{u1, u3} R B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))))) (DistribSMul.toSMulZeroClass.{u1, u3} R B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))))) (DistribMulAction.toDistribSMul.{u1, u3} R B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u2, u3, max u2 u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (AlgHom.algHomClass.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5))))) f) (SetLike.coe.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) S))
+  forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (f : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5), Eq.{succ u3} (Set.{u3} B) (SetLike.coe.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Subalgebra.map.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 f S)) (Set.image.{u2, u3} A B (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => B) _x) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (SMulZeroClass.toSMul.{u1, u2} R A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribSMul.toSMulZeroClass.{u1, u2} R A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toSMul.{u1, u3} R B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))))) (DistribSMul.toSMulZeroClass.{u1, u3} R B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))))) (DistribMulAction.toDistribSMul.{u1, u3} R B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u2, u3, max u2 u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (AlgHom.algHomClass.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5))))) f) (SetLike.coe.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) S))
 Case conversion may be inaccurate. Consider using '#align subalgebra.coe_map Subalgebra.coe_mapₓ'. -/
 @[simp]
 theorem coe_map (S : Subalgebra R A) (f : A →ₐ[R] B) : (S.map f : Set B) = f '' S :=
@@ -1009,7 +1009,7 @@ theorem gc_map_comap (f : A →ₐ[R] B) : GaloisConnection (map f) (comap f) :=
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] (S : Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (f : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (x : A), Iff (Membership.Mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x (Subalgebra.comap.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 f S)) (Membership.Mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.hasMem.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.setLike.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (fun (_x : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) => A -> B) ([anonymous].{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) f x) S)
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] (S : Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (f : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (x : A), Iff (Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x (Subalgebra.comap.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 f S)) (Membership.mem.{u3, u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) x) (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) _x) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (SMulZeroClass.toSMul.{u1, u2} R A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribSMul.toSMulZeroClass.{u1, u2} R A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toSMul.{u1, u3} R B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))))) (DistribSMul.toSMulZeroClass.{u1, u3} R B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))))) (DistribMulAction.toDistribSMul.{u1, u3} R B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u2, u3, max u2 u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (AlgHom.algHomClass.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5))))) f x) S)
+  forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] (S : Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (f : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (x : A), Iff (Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x (Subalgebra.comap.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 f S)) (Membership.mem.{u3, u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => B) x) (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => B) _x) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (SMulZeroClass.toSMul.{u1, u2} R A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribSMul.toSMulZeroClass.{u1, u2} R A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toSMul.{u1, u3} R B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))))) (DistribSMul.toSMulZeroClass.{u1, u3} R B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))))) (DistribMulAction.toDistribSMul.{u1, u3} R B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u2, u3, max u2 u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (AlgHom.algHomClass.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5))))) f x) S)
 Case conversion may be inaccurate. Consider using '#align subalgebra.mem_comap Subalgebra.mem_comapₓ'. -/
 @[simp]
 theorem mem_comap (S : Subalgebra R B) (f : A →ₐ[R] B) (x : A) : x ∈ S.comap f ↔ f x ∈ S :=
@@ -1020,7 +1020,7 @@ theorem mem_comap (S : Subalgebra R B) (f : A →ₐ[R] B) (x : A) : x ∈ S.com
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] (S : Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (f : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5), Eq.{succ u2} (Set.{u2} A) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Subalgebra.comap.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 f S)) (Set.preimage.{u2, u3} A B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (fun (_x : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) => A -> B) ([anonymous].{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) f) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Set.{u3} B) (HasLiftT.mk.{succ u3, succ u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Set.{u3} B) (CoeTCₓ.coe.{succ u3, succ u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Set.{u3} B) (SetLike.Set.hasCoeT.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.setLike.{u1, u3} R B _inst_1 _inst_4 _inst_5)))) S))
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] (S : Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (f : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5), Eq.{succ u2} (Set.{u2} A) (SetLike.coe.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Subalgebra.comap.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 f S)) (Set.preimage.{u2, u3} A B (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) _x) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (SMulZeroClass.toSMul.{u1, u2} R A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribSMul.toSMulZeroClass.{u1, u2} R A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toSMul.{u1, u3} R B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))))) (DistribSMul.toSMulZeroClass.{u1, u3} R B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))))) (DistribMulAction.toDistribSMul.{u1, u3} R B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u2, u3, max u2 u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (AlgHom.algHomClass.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5))))) f) (SetLike.coe.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) S))
+  forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] (S : Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (f : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5), Eq.{succ u2} (Set.{u2} A) (SetLike.coe.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Subalgebra.comap.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 f S)) (Set.preimage.{u2, u3} A B (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => B) _x) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (SMulZeroClass.toSMul.{u1, u2} R A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribSMul.toSMulZeroClass.{u1, u2} R A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toSMul.{u1, u3} R B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))))) (DistribSMul.toSMulZeroClass.{u1, u3} R B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))))) (DistribMulAction.toDistribSMul.{u1, u3} R B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u2, u3, max u2 u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (AlgHom.algHomClass.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5))))) f) (SetLike.coe.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) S))
 Case conversion may be inaccurate. Consider using '#align subalgebra.coe_comap Subalgebra.coe_comapₓ'. -/
 @[simp, norm_cast]
 theorem coe_comap (S : Subalgebra R B) (f : A →ₐ[R] B) : (S.comap f : Set A) = f ⁻¹' (S : Set B) :=
@@ -1160,7 +1160,7 @@ protected def range (φ : A →ₐ[R] B) : Subalgebra R B :=
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] (φ : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) {y : B}, Iff (Membership.Mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.hasMem.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.setLike.{u1, u3} R B _inst_1 _inst_4 _inst_5)) y (AlgHom.range.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 φ)) (Exists.{succ u2} A (fun (x : A) => Eq.{succ u3} B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (fun (_x : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) => A -> B) ([anonymous].{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) φ x) y))
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] (φ : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) {y : B}, Iff (Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) y (AlgHom.range.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 φ)) (Exists.{succ u2} A (fun (x : A) => Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) _x) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (SMulZeroClass.toSMul.{u1, u2} R A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribSMul.toSMulZeroClass.{u1, u2} R A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toSMul.{u1, u3} R B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))))) (DistribSMul.toSMulZeroClass.{u1, u3} R B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))))) (DistribMulAction.toDistribSMul.{u1, u3} R B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u2, u3, max u2 u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (AlgHom.algHomClass.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5))))) φ x) y))
+  forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] (φ : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) {y : B}, Iff (Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) y (AlgHom.range.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 φ)) (Exists.{succ u2} A (fun (x : A) => Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => B) x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => B) _x) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (SMulZeroClass.toSMul.{u1, u2} R A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribSMul.toSMulZeroClass.{u1, u2} R A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toSMul.{u1, u3} R B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))))) (DistribSMul.toSMulZeroClass.{u1, u3} R B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))))) (DistribMulAction.toDistribSMul.{u1, u3} R B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u2, u3, max u2 u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (AlgHom.algHomClass.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5))))) φ x) y))
 Case conversion may be inaccurate. Consider using '#align alg_hom.mem_range AlgHom.mem_rangeₓ'. -/
 @[simp]
 theorem mem_range (φ : A →ₐ[R] B) {y : B} : y ∈ φ.range ↔ ∃ x, φ x = y :=
@@ -1171,7 +1171,7 @@ theorem mem_range (φ : A →ₐ[R] B) {y : B} : y ∈ φ.range ↔ ∃ x, φ x
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] (φ : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (x : A), Membership.Mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.hasMem.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.setLike.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (fun (_x : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) => A -> B) ([anonymous].{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) φ x) (AlgHom.range.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 φ)
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] (φ : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (x : A), Membership.mem.{u3, u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) x) (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) _x) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (SMulZeroClass.toSMul.{u1, u2} R A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribSMul.toSMulZeroClass.{u1, u2} R A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toSMul.{u1, u3} R B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))))) (DistribSMul.toSMulZeroClass.{u1, u3} R B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))))) (DistribMulAction.toDistribSMul.{u1, u3} R B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u2, u3, max u2 u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (AlgHom.algHomClass.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5))))) φ x) (AlgHom.range.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 φ)
+  forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] (φ : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (x : A), Membership.mem.{u3, u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => B) x) (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => B) _x) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (SMulZeroClass.toSMul.{u1, u2} R A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribSMul.toSMulZeroClass.{u1, u2} R A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toSMul.{u1, u3} R B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))))) (DistribSMul.toSMulZeroClass.{u1, u3} R B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))))) (DistribMulAction.toDistribSMul.{u1, u3} R B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u2, u3, max u2 u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (AlgHom.algHomClass.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5))))) φ x) (AlgHom.range.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 φ)
 Case conversion may be inaccurate. Consider using '#align alg_hom.mem_range_self AlgHom.mem_range_selfₓ'. -/
 theorem mem_range_self (φ : A →ₐ[R] B) (x : A) : φ x ∈ φ.range :=
   φ.mem_range.2 ⟨x, rfl⟩
@@ -1181,7 +1181,7 @@ theorem mem_range_self (φ : A →ₐ[R] B) (x : A) : φ x ∈ φ.range :=
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] (φ : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5), Eq.{succ u3} (Set.{u3} B) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Set.{u3} B) (HasLiftT.mk.{succ u3, succ u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Set.{u3} B) (CoeTCₓ.coe.{succ u3, succ u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Set.{u3} B) (SetLike.Set.hasCoeT.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.setLike.{u1, u3} R B _inst_1 _inst_4 _inst_5)))) (AlgHom.range.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 φ)) (Set.range.{u3, succ u2} B A (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (fun (_x : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) => A -> B) ([anonymous].{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) φ))
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] (φ : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5), Eq.{succ u3} (Set.{u3} B) (SetLike.coe.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (AlgHom.range.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 φ)) (Set.range.{u3, succ u2} B A (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) _x) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (SMulZeroClass.toSMul.{u1, u2} R A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribSMul.toSMulZeroClass.{u1, u2} R A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toSMul.{u1, u3} R B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))))) (DistribSMul.toSMulZeroClass.{u1, u3} R B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))))) (DistribMulAction.toDistribSMul.{u1, u3} R B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u2, u3, max u2 u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (AlgHom.algHomClass.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5))))) φ))
+  forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] (φ : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5), Eq.{succ u3} (Set.{u3} B) (SetLike.coe.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (AlgHom.range.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 φ)) (Set.range.{u3, succ u2} B A (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => B) _x) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (SMulZeroClass.toSMul.{u1, u2} R A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribSMul.toSMulZeroClass.{u1, u2} R A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toSMul.{u1, u3} R B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))))) (DistribSMul.toSMulZeroClass.{u1, u3} R B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))))) (DistribMulAction.toDistribSMul.{u1, u3} R B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u2, u3, max u2 u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (AlgHom.algHomClass.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5))))) φ))
 Case conversion may be inaccurate. Consider using '#align alg_hom.coe_range AlgHom.coe_rangeₓ'. -/
 @[simp]
 theorem coe_range (φ : A →ₐ[R] B) : (φ.range : Set B) = Set.range φ :=
@@ -1211,7 +1211,7 @@ theorem range_comp_le_range (f : A →ₐ[R] B) (g : B →ₐ[R] C) : (g.comp f)
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] (f : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (S : Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5), (forall (x : A), Membership.Mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.hasMem.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.setLike.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (fun (_x : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) => A -> B) ([anonymous].{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) f x) S) -> (AlgHom.{u1, u2, u3} R A (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.setLike.{u1, u3} R B _inst_1 _inst_4 _inst_5)) S) _inst_1 _inst_2 (Subalgebra.toSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S) _inst_3 (Subalgebra.algebra.{u1, u3} R B _inst_1 _inst_4 _inst_5 S))
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] (f : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (S : Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5), (forall (x : A), Membership.mem.{u3, u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) x) (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) _x) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (SMulZeroClass.toSMul.{u1, u2} R A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribSMul.toSMulZeroClass.{u1, u2} R A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toSMul.{u1, u3} R B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))))) (DistribSMul.toSMulZeroClass.{u1, u3} R B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))))) (DistribMulAction.toDistribSMul.{u1, u3} R B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u2, u3, max u2 u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (AlgHom.algHomClass.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5))))) f x) S) -> (AlgHom.{u1, u2, u3} R A (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) _inst_1 _inst_2 (Subalgebra.toSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S) _inst_3 (Subalgebra.algebra.{u1, u3} R B _inst_1 _inst_4 _inst_5 S))
+  forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] (f : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (S : Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5), (forall (x : A), Membership.mem.{u3, u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => B) x) (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => B) _x) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (SMulZeroClass.toSMul.{u1, u2} R A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribSMul.toSMulZeroClass.{u1, u2} R A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toSMul.{u1, u3} R B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))))) (DistribSMul.toSMulZeroClass.{u1, u3} R B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))))) (DistribMulAction.toDistribSMul.{u1, u3} R B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u2, u3, max u2 u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (AlgHom.algHomClass.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5))))) f x) S) -> (AlgHom.{u1, u2, u3} R A (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) _inst_1 _inst_2 (Subalgebra.toSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S) _inst_3 (Subalgebra.algebra.{u1, u3} R B _inst_1 _inst_4 _inst_5 S))
 Case conversion may be inaccurate. Consider using '#align alg_hom.cod_restrict AlgHom.codRestrictₓ'. -/
 /-- Restrict the codomain of an algebra homomorphism. -/
 def codRestrict (f : A →ₐ[R] B) (S : Subalgebra R B) (hf : ∀ x, f x ∈ S) : A →ₐ[R] S :=
@@ -1222,7 +1222,7 @@ def codRestrict (f : A →ₐ[R] B) (S : Subalgebra R B) (hf : ∀ x, f x ∈ S)
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] (f : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (S : Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (hf : forall (x : A), Membership.Mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.hasMem.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.setLike.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (fun (_x : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) => A -> B) ([anonymous].{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) f x) S), Eq.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (AlgHom.comp.{u1, u2, u3, u3} R A (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.setLike.{u1, u3} R B _inst_1 _inst_4 _inst_5)) S) B _inst_1 _inst_2 (Subalgebra.toSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S) _inst_4 _inst_3 (Subalgebra.algebra.{u1, u3} R B _inst_1 _inst_4 _inst_5 S) _inst_5 (Subalgebra.val.{u1, u3} R B _inst_1 _inst_4 _inst_5 S) (AlgHom.codRestrict.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 f S hf)) f
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] (f : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (S : Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (hf : forall (x : A), Membership.mem.{u3, u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) x) (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) _x) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (SMulZeroClass.toSMul.{u1, u2} R A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribSMul.toSMulZeroClass.{u1, u2} R A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toSMul.{u1, u3} R B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))))) (DistribSMul.toSMulZeroClass.{u1, u3} R B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))))) (DistribMulAction.toDistribSMul.{u1, u3} R B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u2, u3, max u2 u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (AlgHom.algHomClass.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5))))) f x) S), Eq.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (AlgHom.comp.{u1, u2, u3, u3} R A (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) B _inst_1 _inst_2 (Subalgebra.toSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S) _inst_4 _inst_3 (Subalgebra.algebra.{u1, u3} R B _inst_1 _inst_4 _inst_5 S) _inst_5 (Subalgebra.val.{u1, u3} R B _inst_1 _inst_4 _inst_5 S) (AlgHom.codRestrict.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 f S hf)) f
+  forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] (f : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (S : Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (hf : forall (x : A), Membership.mem.{u3, u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => B) x) (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => B) _x) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (SMulZeroClass.toSMul.{u1, u2} R A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribSMul.toSMulZeroClass.{u1, u2} R A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toSMul.{u1, u3} R B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))))) (DistribSMul.toSMulZeroClass.{u1, u3} R B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))))) (DistribMulAction.toDistribSMul.{u1, u3} R B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u2, u3, max u2 u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (AlgHom.algHomClass.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5))))) f x) S), Eq.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (AlgHom.comp.{u1, u2, u3, u3} R A (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) B _inst_1 _inst_2 (Subalgebra.toSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S) _inst_4 _inst_3 (Subalgebra.algebra.{u1, u3} R B _inst_1 _inst_4 _inst_5 S) _inst_5 (Subalgebra.val.{u1, u3} R B _inst_1 _inst_4 _inst_5 S) (AlgHom.codRestrict.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 f S hf)) f
 Case conversion may be inaccurate. Consider using '#align alg_hom.val_comp_cod_restrict AlgHom.val_comp_codRestrictₓ'. -/
 @[simp]
 theorem val_comp_codRestrict (f : A →ₐ[R] B) (S : Subalgebra R B) (hf : ∀ x, f x ∈ S) :
@@ -1234,7 +1234,7 @@ theorem val_comp_codRestrict (f : A →ₐ[R] B) (S : Subalgebra R B) (hf : ∀
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] (f : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (S : Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (hf : forall (x : A), Membership.Mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.hasMem.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.setLike.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (fun (_x : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) => A -> B) ([anonymous].{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) f x) S) (x : A), Eq.{succ u3} B ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.setLike.{u1, u3} R B _inst_1 _inst_4 _inst_5)) S) B (HasLiftT.mk.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.setLike.{u1, u3} R B _inst_1 _inst_4 _inst_5)) S) B (CoeTCₓ.coe.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.setLike.{u1, u3} R B _inst_1 _inst_4 _inst_5)) S) B (coeBase.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.setLike.{u1, u3} R B _inst_1 _inst_4 _inst_5)) S) B (coeSubtype.{succ u3} B (fun (x : B) => Membership.Mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.hasMem.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.setLike.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S))))) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R A (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.setLike.{u1, u3} R B _inst_1 _inst_4 _inst_5)) S) _inst_1 _inst_2 (Subalgebra.toSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S) _inst_3 (Subalgebra.algebra.{u1, u3} R B _inst_1 _inst_4 _inst_5 S)) (fun (_x : AlgHom.{u1, u2, u3} R A (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.setLike.{u1, u3} R B _inst_1 _inst_4 _inst_5)) S) _inst_1 _inst_2 (Subalgebra.toSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S) _inst_3 (Subalgebra.algebra.{u1, u3} R B _inst_1 _inst_4 _inst_5 S)) => A -> (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.setLike.{u1, u3} R B _inst_1 _inst_4 _inst_5)) S)) ([anonymous].{u1, u2, u3} R A (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.setLike.{u1, u3} R B _inst_1 _inst_4 _inst_5)) S) _inst_1 _inst_2 (Subalgebra.toSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S) _inst_3 (Subalgebra.algebra.{u1, u3} R B _inst_1 _inst_4 _inst_5 S)) (AlgHom.codRestrict.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 f S hf) x)) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (fun (_x : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) => A -> B) ([anonymous].{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) f x)
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] (f : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (S : Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (hf : forall (x : A), Membership.mem.{u3, u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) x) (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) _x) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (SMulZeroClass.toSMul.{u1, u2} R A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribSMul.toSMulZeroClass.{u1, u2} R A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toSMul.{u1, u3} R B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))))) (DistribSMul.toSMulZeroClass.{u1, u3} R B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))))) (DistribMulAction.toDistribSMul.{u1, u3} R B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u2, u3, max u2 u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (AlgHom.algHomClass.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5))))) f x) S) (x : A), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) x) (Subtype.val.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Set.{u3} B) (Set.instMembershipSet.{u3} B) x (SetLike.coe.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) S)) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} R A (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) _inst_1 _inst_2 (Subalgebra.toSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S) _inst_3 (Subalgebra.algebra.{u1, u3} R B _inst_1 _inst_4 _inst_5 S)) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) _x) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) _inst_1 _inst_2 (Subalgebra.toSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S) _inst_3 (Subalgebra.algebra.{u1, u3} R B _inst_1 _inst_4 _inst_5 S)) R A (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) (SMulZeroClass.toSMul.{u1, u2} R A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribSMul.toSMulZeroClass.{u1, u2} R A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toSMul.{u1, u3} R (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) (AddMonoid.toZero.{u3} (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) (AddCommMonoid.toAddMonoid.{u3} (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) 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u2, u3} R A (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) _inst_1 _inst_2 (Subalgebra.toSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S) _inst_3 (Subalgebra.algebra.{u1, u3} R B _inst_1 _inst_4 _inst_5 S)) (AlgHom.algHomClass.{u1, u2, u3} R A (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) _inst_1 _inst_2 (Subalgebra.toSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S) _inst_3 (Subalgebra.algebra.{u1, u3} R B _inst_1 _inst_4 _inst_5 S)))))) (AlgHom.codRestrict.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 f S hf) x)) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) _x) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (SMulZeroClass.toSMul.{u1, u2} R A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribSMul.toSMulZeroClass.{u1, u2} R A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toSMul.{u1, u3} R B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))))) (DistribSMul.toSMulZeroClass.{u1, u3} R B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))))) (DistribMulAction.toDistribSMul.{u1, u3} R B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u2, u3, max u2 u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (AlgHom.algHomClass.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5))))) f x)
+  forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] (f : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (S : Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (hf : forall (x : A), Membership.mem.{u3, u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => B) x) (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => B) _x) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (SMulZeroClass.toSMul.{u1, u2} R A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribSMul.toSMulZeroClass.{u1, u2} R A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toSMul.{u1, u3} R B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))))) (DistribSMul.toSMulZeroClass.{u1, u3} R B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))))) (DistribMulAction.toDistribSMul.{u1, u3} R B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u2, u3, max u2 u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (AlgHom.algHomClass.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5))))) f x) S) (x : A), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => B) x) (Subtype.val.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Set.{u3} B) (Set.instMembershipSet.{u3} B) x (SetLike.coe.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) S)) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} R A (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) _inst_1 _inst_2 (Subalgebra.toSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S) _inst_3 (Subalgebra.algebra.{u1, u3} R B _inst_1 _inst_4 _inst_5 S)) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) _x) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) _inst_1 _inst_2 (Subalgebra.toSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S) _inst_3 (Subalgebra.algebra.{u1, u3} R B _inst_1 _inst_4 _inst_5 S)) R A (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) (SMulZeroClass.toSMul.{u1, u2} R A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribSMul.toSMulZeroClass.{u1, u2} R A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Module.toDistribMulAction.{u1, u2} R A 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_inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) (Subalgebra.toSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) (Subalgebra.toSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S)))) (Algebra.toModule.{u1, u3} R (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) _inst_1 (Subalgebra.toSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S) (Subalgebra.algebra.{u1, u3} R B _inst_1 _inst_4 _inst_5 S))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u2, u3, max u2 u3} R A (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) _inst_1 _inst_2 (Subalgebra.toSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S) _inst_3 (Subalgebra.algebra.{u1, u3} R B _inst_1 _inst_4 _inst_5 S) (AlgHom.{u1, u2, u3} R A (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) _inst_1 _inst_2 (Subalgebra.toSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S) _inst_3 (Subalgebra.algebra.{u1, u3} R B _inst_1 _inst_4 _inst_5 S)) (AlgHom.algHomClass.{u1, u2, u3} R A (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) _inst_1 _inst_2 (Subalgebra.toSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S) _inst_3 (Subalgebra.algebra.{u1, u3} R B _inst_1 _inst_4 _inst_5 S)))))) (AlgHom.codRestrict.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 f S hf) x)) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => B) _x) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (SMulZeroClass.toSMul.{u1, u2} R A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribSMul.toSMulZeroClass.{u1, u2} R A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toSMul.{u1, u3} R B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))))) (DistribSMul.toSMulZeroClass.{u1, u3} R B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))))) (DistribMulAction.toDistribSMul.{u1, u3} R B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u2, u3, max u2 u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (AlgHom.algHomClass.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5))))) f x)
 Case conversion may be inaccurate. Consider using '#align alg_hom.coe_cod_restrict AlgHom.coe_codRestrictₓ'. -/
 @[simp]
 theorem coe_codRestrict (f : A →ₐ[R] B) (S : Subalgebra R B) (hf : ∀ x, f x ∈ S) (x : A) :
@@ -1246,7 +1246,7 @@ theorem coe_codRestrict (f : A →ₐ[R] B) (S : Subalgebra R B) (hf : ∀ x, f
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] (f : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (S : Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (hf : forall (x : A), Membership.Mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.hasMem.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.setLike.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (fun (_x : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) => A -> B) ([anonymous].{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) f x) S), Iff (Function.Injective.{succ u2, succ u3} A (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.setLike.{u1, u3} R B _inst_1 _inst_4 _inst_5)) S) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R A (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.setLike.{u1, u3} R B _inst_1 _inst_4 _inst_5)) S) _inst_1 _inst_2 (Subalgebra.toSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S) _inst_3 (Subalgebra.algebra.{u1, u3} R B _inst_1 _inst_4 _inst_5 S)) (fun (_x : AlgHom.{u1, u2, u3} R A (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.setLike.{u1, u3} R B _inst_1 _inst_4 _inst_5)) S) _inst_1 _inst_2 (Subalgebra.toSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S) _inst_3 (Subalgebra.algebra.{u1, u3} R B _inst_1 _inst_4 _inst_5 S)) => A -> (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.setLike.{u1, u3} R B _inst_1 _inst_4 _inst_5)) S)) ([anonymous].{u1, u2, u3} R A (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.setLike.{u1, u3} R B _inst_1 _inst_4 _inst_5)) S) _inst_1 _inst_2 (Subalgebra.toSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S) _inst_3 (Subalgebra.algebra.{u1, u3} R B _inst_1 _inst_4 _inst_5 S)) (AlgHom.codRestrict.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 f S hf))) (Function.Injective.{succ u2, succ u3} A B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (fun (_x : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) => A -> B) ([anonymous].{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) f))
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] (f : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (S : Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (hf : forall (x : A), Membership.mem.{u3, u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) x) (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) _x) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (SMulZeroClass.toSMul.{u1, u2} R A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribSMul.toSMulZeroClass.{u1, u2} R A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) 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(SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) (Subalgebra.toSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S))))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) (Subalgebra.toSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S)))) (Algebra.toModule.{u1, u3} R (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) _inst_1 (Subalgebra.toSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S) (Subalgebra.algebra.{u1, u3} R B _inst_1 _inst_4 _inst_5 S))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) _inst_1 _inst_2 (Subalgebra.toSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S) _inst_3 (Subalgebra.algebra.{u1, u3} R B _inst_1 _inst_4 _inst_5 S)) R A (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) (Subalgebra.toSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) (Subalgebra.toSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S)))) (Algebra.toModule.{u1, u3} R (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) _inst_1 (Subalgebra.toSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S) (Subalgebra.algebra.{u1, u3} R B _inst_1 _inst_4 _inst_5 S))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u2, u3, max u2 u3} R A (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) _inst_1 _inst_2 (Subalgebra.toSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S) _inst_3 (Subalgebra.algebra.{u1, u3} R B _inst_1 _inst_4 _inst_5 S) (AlgHom.{u1, u2, u3} R A (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) _inst_1 _inst_2 (Subalgebra.toSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S) _inst_3 (Subalgebra.algebra.{u1, u3} R B _inst_1 _inst_4 _inst_5 S)) (AlgHom.algHomClass.{u1, u2, u3} R A (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) _inst_1 _inst_2 (Subalgebra.toSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S) _inst_3 (Subalgebra.algebra.{u1, u3} R B _inst_1 _inst_4 _inst_5 S)))))) (AlgHom.codRestrict.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 f S hf))) (Function.Injective.{succ u2, succ u3} A B (FunLike.coe.{max (succ u2) (succ u3), 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toSMul.{u1, u3} R B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))))) (DistribSMul.toSMulZeroClass.{u1, u3} R B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))))) (DistribMulAction.toDistribSMul.{u1, u3} R B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u2, u3, max u2 u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (AlgHom.algHomClass.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5))))) f))
+  forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] (f : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (S : Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (hf : forall (x : A), Membership.mem.{u3, u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => B) x) (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => B) _x) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (SMulZeroClass.toSMul.{u1, u2} R A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribSMul.toSMulZeroClass.{u1, u2} R A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toSMul.{u1, u3} R B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))))) (DistribSMul.toSMulZeroClass.{u1, u3} R B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))))) (DistribMulAction.toDistribSMul.{u1, u3} R B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u2, u3, max u2 u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (AlgHom.algHomClass.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5))))) f x) S), Iff (Function.Injective.{succ u2, succ u3} A (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} R A (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) _inst_1 _inst_2 (Subalgebra.toSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S) _inst_3 (Subalgebra.algebra.{u1, u3} R B _inst_1 _inst_4 _inst_5 S)) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) _x) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) _inst_1 _inst_2 (Subalgebra.toSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S) _inst_3 (Subalgebra.algebra.{u1, u3} R B _inst_1 _inst_4 _inst_5 S)) R A (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) (SMulZeroClass.toSMul.{u1, u2} R A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribSMul.toSMulZeroClass.{u1, u2} R A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toSMul.{u1, u3} R (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) (AddMonoid.toZero.{u3} (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) (AddCommMonoid.toAddMonoid.{u3} (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) 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_inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) (Subalgebra.toSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S)))))) (DistribMulAction.toDistribSMul.{u1, u3} R (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Subtype.{succ u3} B (fun (x : B) => 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Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) _inst_1 (Subalgebra.toSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S) (Subalgebra.algebra.{u1, u3} R B _inst_1 _inst_4 _inst_5 S))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) _inst_1 _inst_2 (Subalgebra.toSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S) _inst_3 (Subalgebra.algebra.{u1, u3} R B _inst_1 _inst_4 _inst_5 S)) R A (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) (Subalgebra.toSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) (Subalgebra.toSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S)))) (Algebra.toModule.{u1, u3} R (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) _inst_1 (Subalgebra.toSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S) (Subalgebra.algebra.{u1, u3} R B _inst_1 _inst_4 _inst_5 S))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u2, u3, max u2 u3} R A (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) _inst_1 _inst_2 (Subalgebra.toSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S) _inst_3 (Subalgebra.algebra.{u1, u3} R B _inst_1 _inst_4 _inst_5 S) (AlgHom.{u1, u2, u3} R A (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) _inst_1 _inst_2 (Subalgebra.toSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S) _inst_3 (Subalgebra.algebra.{u1, u3} R B _inst_1 _inst_4 _inst_5 S)) (AlgHom.algHomClass.{u1, u2, u3} R A (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) _inst_1 _inst_2 (Subalgebra.toSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S) _inst_3 (Subalgebra.algebra.{u1, u3} R B _inst_1 _inst_4 _inst_5 S)))))) (AlgHom.codRestrict.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 f S hf))) (Function.Injective.{succ u2, succ u3} A B (FunLike.coe.{max (succ u2) (succ u3), 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toSMul.{u1, u3} R B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))))) (DistribSMul.toSMulZeroClass.{u1, u3} R B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))))) (DistribMulAction.toDistribSMul.{u1, u3} R B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (MonoidWithZero.toMonoid.{u1} R 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(AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u2, u3, max u2 u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (AlgHom.algHomClass.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5))))) f))
 Case conversion may be inaccurate. Consider using '#align alg_hom.injective_cod_restrict AlgHom.injective_codRestrictₓ'. -/
 theorem injective_codRestrict (f : A →ₐ[R] B) (S : Subalgebra R B) (hf : ∀ x, f x ∈ S) :
     Function.Injective (f.codRestrict S hf) ↔ Function.Injective f :=
@@ -1284,7 +1284,7 @@ def equalizer (ϕ ψ : A →ₐ[R] B) : Subalgebra R A
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] (ϕ : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (ψ : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (x : A), Iff (Membership.Mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x (AlgHom.equalizer.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 ϕ ψ)) (Eq.{succ u3} B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (fun (_x : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) => A -> B) ([anonymous].{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) ϕ x) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (fun (_x : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) => A -> B) ([anonymous].{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) ψ x))
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] (ϕ : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (ψ : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (x : A), Iff (Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x (AlgHom.equalizer.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 ϕ ψ)) (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) _x) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (SMulZeroClass.toSMul.{u1, u2} R A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribSMul.toSMulZeroClass.{u1, u2} R A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toSMul.{u1, u3} R B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))))) (DistribSMul.toSMulZeroClass.{u1, u3} R B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))))) (DistribMulAction.toDistribSMul.{u1, u3} R B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u2, u3, max u2 u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (AlgHom.algHomClass.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5))))) ϕ x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) _x) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (SMulZeroClass.toSMul.{u1, u2} R A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribSMul.toSMulZeroClass.{u1, u2} R A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toSMul.{u1, u3} R B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))))) (DistribSMul.toSMulZeroClass.{u1, u3} R B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))))) (DistribMulAction.toDistribSMul.{u1, u3} R B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u2, u3, max u2 u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (AlgHom.algHomClass.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5))))) ψ x))
+  forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] (ϕ : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (ψ : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (x : A), Iff (Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x (AlgHom.equalizer.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 ϕ ψ)) (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => B) x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => B) _x) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (SMulZeroClass.toSMul.{u1, u2} R A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribSMul.toSMulZeroClass.{u1, u2} R A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toSMul.{u1, u3} R B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))))) (DistribSMul.toSMulZeroClass.{u1, u3} R B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))))) (DistribMulAction.toDistribSMul.{u1, u3} R B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u2, u3, max u2 u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (AlgHom.algHomClass.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5))))) ϕ x) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => B) _x) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (SMulZeroClass.toSMul.{u1, u2} R A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribSMul.toSMulZeroClass.{u1, u2} R A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toSMul.{u1, u3} R B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))))) (DistribSMul.toSMulZeroClass.{u1, u3} R B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))))) (DistribMulAction.toDistribSMul.{u1, u3} R B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u2, u3, max u2 u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (AlgHom.algHomClass.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5))))) ψ x))
 Case conversion may be inaccurate. Consider using '#align alg_hom.mem_equalizer AlgHom.mem_equalizerₓ'. -/
 @[simp]
 theorem mem_equalizer (ϕ ψ : A →ₐ[R] B) (x : A) : x ∈ ϕ.equalizer ψ ↔ ϕ x = ψ x :=
@@ -1744,7 +1744,7 @@ theorem eq_top_iff {S : Subalgebra R A} : S = ⊤ ↔ ∀ x : A, x ∈ S :=
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] (f : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5), Iff (Eq.{succ u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (AlgHom.range.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 f) (Top.top.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (CompleteLattice.toHasTop.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.Subalgebra.completeLattice.{u1, u3} R B _inst_1 _inst_4 _inst_5)))) (Function.Surjective.{succ u2, succ u3} A B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (fun (_x : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) => A -> B) ([anonymous].{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) f))
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] (f : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5), Iff (Eq.{succ u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (AlgHom.range.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 f) (Top.top.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (CompleteLattice.toTop.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.instCompleteLatticeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)))) (Function.Surjective.{succ u2, succ u3} A B (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) _x) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (SMulZeroClass.toSMul.{u1, u2} R A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribSMul.toSMulZeroClass.{u1, u2} R A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toSMul.{u1, u3} R B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))))) (DistribSMul.toSMulZeroClass.{u1, u3} R B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))))) (DistribMulAction.toDistribSMul.{u1, u3} R B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u2, u3, max u2 u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (AlgHom.algHomClass.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5))))) f))
+  forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] (f : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5), Iff (Eq.{succ u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (AlgHom.range.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 f) (Top.top.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (CompleteLattice.toTop.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.instCompleteLatticeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)))) (Function.Surjective.{succ u2, succ u3} A B (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => B) _x) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (SMulZeroClass.toSMul.{u1, u2} R A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribSMul.toSMulZeroClass.{u1, u2} R A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toSMul.{u1, u3} R B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))))) (DistribSMul.toSMulZeroClass.{u1, u3} R B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))))) (DistribMulAction.toDistribSMul.{u1, u3} R B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u2, u3, max u2 u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (AlgHom.algHomClass.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5))))) f))
 Case conversion may be inaccurate. Consider using '#align algebra.range_top_iff_surjective Algebra.range_top_iff_surjectiveₓ'. -/
 theorem range_top_iff_surjective (f : A →ₐ[R] B) :
     f.range = (⊤ : Subalgebra R B) ↔ Function.Surjective f :=
@@ -1957,7 +1957,7 @@ def inclusion {S T : Subalgebra R A} (h : S ≤ T) : S →ₐ[R] T
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3} {T : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3} (h : LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) S T), Function.Injective.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T) (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 T)) (fun (_x : AlgHom.{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 T)) => (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) -> (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T)) ([anonymous].{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 T)) (Subalgebra.inclusion.{u1, u2} R A _inst_1 _inst_2 _inst_3 S T h))
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3} {T : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3} (h : LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) S T), Function.Injective.{succ u2, succ u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A 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+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3} {T : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3} (h : LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) S T), Function.Injective.{succ u2, succ u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A 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 Case conversion may be inaccurate. Consider using '#align subalgebra.inclusion_injective Subalgebra.inclusion_injectiveₓ'. -/
 theorem inclusion_injective {S T : Subalgebra R A} (h : S ≤ T) : Function.Injective (inclusion h) :=
   fun _ _ => Subtype.ext ∘ Subtype.mk.inj
@@ -1978,7 +1978,7 @@ theorem inclusion_self {S : Subalgebra R A} : inclusion (le_refl S) = AlgHom.id
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3} {T : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3} (h : LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) S T) (x : A) (hx : Membership.Mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S), Eq.{succ u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T) (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 T)) (fun (_x : AlgHom.{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 T)) => (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) -> (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T)) ([anonymous].{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 T)) (Subalgebra.inclusion.{u1, u2} R A _inst_1 _inst_2 _inst_3 S T h) (Subtype.mk.{succ u2} A (fun (x : A) => Membership.Mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S) x hx)) (Subtype.mk.{succ u2} A (fun (x : A) => Membership.Mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T) x (h x hx))
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3} {T : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3} (h : LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) S T) (x : A) (hx : Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T)) (Subtype.mk.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S) x hx)) (FunLike.coe.{succ u2, succ u2, succ u2} (AlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T)) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 T)) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (fun (_x : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T)) _x) (SMulHomClass.toFunLike.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T)) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 T)) R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T)) (SMulZeroClass.toSMul.{u1, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (AddMonoid.toZero.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, 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(Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, 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(Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T)) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, 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A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T)) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) (AlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T)) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 T)) (AlgHom.algHomClass.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T)) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 T)))))) (Subalgebra.inclusion.{u1, u2} R A _inst_1 _inst_2 _inst_3 S T h) (Subtype.mk.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S) x hx)) (Subtype.mk.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T) x (h x hx))
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3} {T : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3} (h : LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) S T) (x : A) (hx : Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 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(Algebra.toModule.{u1, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S))) (Module.toDistribMulAction.{u1, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T)) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T)) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T)) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T)))) (Algebra.toModule.{u1, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T)) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 T))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u2, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T)) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) (AlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T)) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 T)) (AlgHom.algHomClass.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T)) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 T)))))) (Subalgebra.inclusion.{u1, u2} R A _inst_1 _inst_2 _inst_3 S T h) (Subtype.mk.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S) x hx)) (Subtype.mk.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T) x (h x hx))
 Case conversion may be inaccurate. Consider using '#align subalgebra.inclusion_mk Subalgebra.inclusion_mkₓ'. -/
 @[simp]
 theorem inclusion_mk {S T : Subalgebra R A} (h : S ≤ T) (x : A) (hx : x ∈ S) :
@@ -1990,7 +1990,7 @@ theorem inclusion_mk {S T : Subalgebra R A} (h : S ≤ T) (x : A) (hx : x ∈ S)
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3} {T : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3} (h : LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) S T) (x : coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T) (m : Membership.Mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T) A (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T) A (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T) A (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T) A (coeSubtype.{succ u2} A (fun (x : A) => Membership.Mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T))))) x) S), Eq.{succ u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T) (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 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_inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 T)) => (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) -> (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T)) ([anonymous].{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 T)) (Subalgebra.inclusion.{u1, u2} R A _inst_1 _inst_2 _inst_3 S T h) (Subtype.mk.{succ u2} A (fun (x : A) => Membership.Mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T) A (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T) A (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T) A (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T) A (coeSubtype.{succ u2} A (fun (x : A) => Membership.Mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T))))) x) m)) x
 but is expected to have type
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_inst_3 S) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) (AlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T)) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 T)) (AlgHom.algHomClass.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T)) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 T)))))) (Subalgebra.inclusion.{u1, u2} R A _inst_1 _inst_2 _inst_3 S T h) (Subtype.mk.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S) (Subtype.val.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) x (SetLike.coe.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) T)) x) m)) x
 Case conversion may be inaccurate. Consider using '#align subalgebra.inclusion_right Subalgebra.inclusion_rightₓ'. -/
 theorem inclusion_right {S T : Subalgebra R A} (h : S ≤ T) (x : T) (m : (x : A) ∈ S) :
     inclusion h ⟨x, m⟩ = x :=
@@ -2001,7 +2001,7 @@ theorem inclusion_right {S T : Subalgebra R A} (h : S ≤ T) (x : T) (m : (x : A
 lean 3 declaration is
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R A _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) T U) (x : coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S), Eq.{succ u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) U) (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A 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 but is expected to have type
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+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3} {T : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3} {U : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3} (hst : LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) S T) (htu : LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, 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_inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x U)) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 U))) (Module.toDistribMulAction.{u1, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 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(Module.toDistribMulAction.{u1, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x U)) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x U)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x U)) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x U)) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 U)))) (Algebra.toModule.{u1, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x U)) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 U) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 U))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u2, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x U)) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 U) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 U) (AlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x U)) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 U) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 U)) (AlgHom.algHomClass.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x U)) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 U) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 U)))))) (Subalgebra.inclusion.{u1, u2} R A _inst_1 _inst_2 _inst_3 S U (le_trans.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) S T U hst htu)) x)
 Case conversion may be inaccurate. Consider using '#align subalgebra.inclusion_inclusion Subalgebra.inclusion_inclusionₓ'. -/
 @[simp]
 theorem inclusion_inclusion {S T U : Subalgebra R A} (hst : S ≤ T) (htu : T ≤ U) (x : S) :
@@ -2013,7 +2013,7 @@ theorem inclusion_inclusion {S T U : Subalgebra R A} (hst : S ≤ T) (htu : T 
 lean 3 declaration is
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 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3} {T : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3} (h : LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) S T) (s : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, 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_inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 T)) R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T)) (SMulZeroClass.toSMul.{u1, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} 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 Case conversion may be inaccurate. Consider using '#align subalgebra.coe_inclusion Subalgebra.coe_inclusionₓ'. -/
 @[simp]
 theorem coe_inclusion {S T : Subalgebra R A} (h : S ≤ T) (s : S) : (inclusion h s : A) = s :=
@@ -2239,7 +2239,7 @@ variable [Nonempty ι] {K : ι → Subalgebra R A} {dir : Directed (· ≤ ·) K
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {ι : Type.{u4}} [_inst_6 : Nonempty.{succ u4} ι] {K : ι -> (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {dir : Directed.{u2, succ u4} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) ι (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) K} {f : forall (i : ι), AlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ 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u2} R A _inst_1 _inst_2 _inst_3 (K j)) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K j)) _inst_5 (f j) (Subalgebra.inclusion.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i) (K j) h))} {T : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3} {hT : Eq.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) T (iSup.{u2, succ u4} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))) ι K)} {i : ι} (x : coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K i)) (h : LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (K i) T), Eq.{succ u3} B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) _inst_5) (fun (_x : 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T) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) _inst_5) (Subalgebra.iSupLift.{u1, u2, u3, u4} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 ι _inst_6 K dir f hf T hT) (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K i)) (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 T)) (fun (_x : 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_inst_3)) (K i)) -> (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T)) ([anonymous].{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K i)) (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 T)) (Subalgebra.inclusion.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i) T h) x)) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K i)) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) (fun (_x : AlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K i)) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) => (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K i)) -> B) ([anonymous].{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K i)) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) (f i) x)
 but is expected to have type
-  forall {R : Type.{u2}} {A : Type.{u3}} {B : Type.{u4}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u3} A] [_inst_3 : Algebra.{u2, u3} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u4} B] [_inst_5 : Algebra.{u2, u4} R B _inst_1 _inst_4] {ι : Type.{u1}} [_inst_6 : Nonempty.{succ u1} ι] {K : ι -> (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)} {dir : Directed.{u3, succ u1} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) ι (fun (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13718 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13720 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) => LE.le.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3))))) x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13718 x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13720) K} {f : forall (i : ι), AlgHom.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5} {hf : forall (i : ι) (j : ι) (h : LE.le.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3))))) (K i) (K j)), Eq.{max (succ u3) (succ u4)} (AlgHom.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) (f i) (AlgHom.comp.{u2, u3, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))) (Module.toDistribMulAction.{u2, u4} R B (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u2, u4} R B _inst_1 _inst_4 _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u4, u2, u3, u4} (AlgHom.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)))))) (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))) (Module.toDistribMulAction.{u2, u3} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => 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(Algebra.toModule.{u2, u4} R B _inst_1 _inst_4 _inst_5)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u3 u4, u2, u3, u4} (AlgHom.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)) (Module.toDistribMulAction.{u2, u3} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i))))) (Algebra.toModule.{u2, u3} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.algebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)))) (Module.toDistribMulAction.{u2, u4} R B (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u2, u4} R B _inst_1 _inst_4 _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u3, u4, max u3 u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5 (AlgHom.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) (AlgHom.algHomClass.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5))))) (f i) x)
+  forall {R : Type.{u2}} {A : Type.{u3}} {B : Type.{u4}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u3} A] [_inst_3 : Algebra.{u2, u3} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u4} B] [_inst_5 : Algebra.{u2, u4} R B _inst_1 _inst_4] {ι : Type.{u1}} [_inst_6 : Nonempty.{succ u1} ι] {K : ι -> (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)} {dir : Directed.{u3, succ u1} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) ι (fun (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13718 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13720 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) => LE.le.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3))))) x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13718 x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13720) K} {f : forall (i : ι), AlgHom.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5} {hf : forall (i : ι) (j : ι) (h : LE.le.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Subalgebra.{u2, u3} R 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_inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.algebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i))))))) (SMulZeroClass.toSMul.{u2, u4} R B (AddMonoid.toZero.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))))) (DistribSMul.toSMulZeroClass.{u2, u4} R B (AddMonoid.toAddZeroClass.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))))) (DistribMulAction.toDistribSMul.{u2, u4} R B (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))) (Module.toDistribMulAction.{u2, u4} R B (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u2, u4} R B _inst_1 _inst_4 _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u4, u2, u3, u4} (AlgHom.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)))))) (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))) (Module.toDistribMulAction.{u2, u3} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i))))) (Algebra.toModule.{u2, u3} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.algebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)))) (Module.toDistribMulAction.{u2, u4} R B (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u2, u4} R B _inst_1 _inst_4 _inst_5)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u3 u4, u2, u3, u4} (AlgHom.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)) (Module.toDistribMulAction.{u2, u3} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i))))) (Algebra.toModule.{u2, u3} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.algebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)))) (Module.toDistribMulAction.{u2, u4} R B (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u2, u4} R B _inst_1 _inst_4 _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u3, u4, max u3 u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5 (AlgHom.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) (AlgHom.algHomClass.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5))))) (f i) x)
 Case conversion may be inaccurate. Consider using '#align subalgebra.supr_lift_inclusion Subalgebra.iSupLift_inclusionₓ'. -/
 @[simp]
 theorem iSupLift_inclusion {i : ι} (x : K i) (h : K i ≤ T) :
@@ -2262,7 +2262,7 @@ theorem iSupLift_comp_inclusion {i : ι} (h : K i ≤ T) :
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {ι : Type.{u4}} [_inst_6 : Nonempty.{succ u4} ι] {K : ι -> (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {dir : Directed.{u2, succ u4} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) ι (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) K} {f : forall (i : ι), AlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i))))) (Algebra.toModule.{u2, u3} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.algebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i))))))) (SMulZeroClass.toSMul.{u2, u4} R B (AddMonoid.toZero.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))))) (DistribSMul.toSMulZeroClass.{u2, u4} R B (AddMonoid.toAddZeroClass.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))))) (DistribMulAction.toDistribSMul.{u2, u4} R B (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))) (Module.toDistribMulAction.{u2, u4} R B (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u2, u4} R B _inst_1 _inst_4 _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u4, u2, u3, u4} (AlgHom.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)))))) (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))) (Module.toDistribMulAction.{u2, u3} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i))))) (Algebra.toModule.{u2, u3} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.algebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)))) (Module.toDistribMulAction.{u2, u4} R B (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u2, u4} R B _inst_1 _inst_4 _inst_5)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u3 u4, u2, u3, u4} (AlgHom.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)) (Module.toDistribMulAction.{u2, u3} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i))))) (Algebra.toModule.{u2, u3} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.algebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)))) (Module.toDistribMulAction.{u2, u4} R B (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u2, u4} R B _inst_1 _inst_4 _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u3, u4, max u3 u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5 (AlgHom.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) (AlgHom.algHomClass.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5))))) (f i) x)
+  forall {R : Type.{u2}} {A : Type.{u3}} {B : Type.{u4}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u3} A] [_inst_3 : Algebra.{u2, u3} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u4} B] [_inst_5 : Algebra.{u2, u4} R B _inst_1 _inst_4] {ι : Type.{u1}} [_inst_6 : Nonempty.{succ u1} ι] {K : ι -> (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)} {dir : Directed.{u3, succ u1} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) ι (fun (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.14000 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.14002 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) => LE.le.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3))))) x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.14000 x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.14002) K} {f : forall (i : ι), AlgHom.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5} {hf : forall (i : ι) (j : ι) (h : LE.le.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Subalgebra.{u2, u3} R 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(Module.toDistribMulAction.{u2, u4} R B (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u2, u4} R B _inst_1 _inst_4 _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u3, u4, max u3 u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5 (AlgHom.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) (AlgHom.algHomClass.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5))))) (f i) x)
 Case conversion may be inaccurate. Consider using '#align subalgebra.supr_lift_mk Subalgebra.iSupLift_mkₓ'. -/
 @[simp]
 theorem iSupLift_mk {i : ι} (x : K i) (hx : (x : A) ∈ T) :
@@ -2273,7 +2273,7 @@ theorem iSupLift_mk {i : ι} (x : K i) (hx : (x : A) ∈ T) :
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {ι : Type.{u4}} [_inst_6 : Nonempty.{succ u4} ι] {K : ι -> (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {dir : Directed.{u2, succ u4} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) ι (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) K} {f : forall (i : ι), AlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K i)) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5} {hf : forall (i : ι) (j : ι) (h : LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (K i) (K j)), Eq.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} 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u2} R A _inst_1 _inst_2 _inst_3 (K j)) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K j)) _inst_5 (f j) (Subalgebra.inclusion.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i) (K j) h))} {T : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3} {hT : Eq.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) T (iSup.{u2, succ u4} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))) ι K)} {i : ι} (x : coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T) (hx : 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(Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) _inst_5) (fun (_x : AlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) _inst_5) => (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T) -> B) ([anonymous].{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 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 but is expected to have type
-  forall {R : Type.{u2}} {A : Type.{u3}} {B : Type.{u4}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u3} A] [_inst_3 : Algebra.{u2, u3} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u4} B] [_inst_5 : Algebra.{u2, u4} R B _inst_1 _inst_4] {ι : Type.{u1}} [_inst_6 : Nonempty.{succ u1} ι] {K : ι -> (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)} {dir : Directed.{u3, succ u1} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) ι (fun (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.14155 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.14157 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) => LE.le.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) 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+  forall {R : Type.{u2}} {A : Type.{u3}} {B : Type.{u4}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u3} A] [_inst_3 : Algebra.{u2, u3} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u4} B] [_inst_5 : Algebra.{u2, u4} R B _inst_1 _inst_4] {ι : Type.{u1}} [_inst_6 : Nonempty.{succ u1} ι] {K : ι -> (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)} {dir : Directed.{u3, succ u1} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) ι (fun (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.14155 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.14157 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) => LE.le.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) 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(Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R 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_inst_3 (K i)) (Subalgebra.algebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)))) (Module.toDistribMulAction.{u2, u4} R B (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u2, u4} R B _inst_1 _inst_4 _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u3, u4, max u3 u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5 (AlgHom.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) (AlgHom.algHomClass.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5))))) (f i) (Subtype.mk.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i)) (Subtype.val.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Set.{u3} A) (Set.instMembershipSet.{u3} A) x (SetLike.coe.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) T)) x) hx))
 Case conversion may be inaccurate. Consider using '#align subalgebra.supr_lift_of_mem Subalgebra.iSupLift_of_memₓ'. -/
 theorem iSupLift_of_mem {i : ι} (x : T) (hx : (x : A) ∈ K i) :
     iSupLift K dir f hf T hT x = f i ⟨x, hx⟩ := by subst hT <;> exact Set.iUnionLift_of_mem x hx
@@ -2634,7 +2634,7 @@ theorem mem_of_finset_sum_eq_one_of_pow_smul_mem {S : Type _} [CommRing S] [Alge
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {S : Type.{u2}} [_inst_6 : CommRing.{u2} S] [_inst_7 : Algebra.{u1, u2} R S _inst_1 (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6))] (S' : Subalgebra.{u1, u2} R S _inst_1 (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_7) (s : Set.{u2} S) (l : Finsupp.{u2, u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} S) Type.{u2} (Set.hasCoeToSort.{u2} S) s) S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} S (NonAssocRing.toNonUnitalNonAssocRing.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_6))))))), (Eq.{succ u2} S (coeFn.{succ u2, succ u2} (LinearMap.{u2, u2, u2, u2} S S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)))) 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(Semiring.toModule.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)))) => (Finsupp.{u2, u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} S) Type.{u2} (Set.hasCoeToSort.{u2} S) s) S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6))))))) -> S) (LinearMap.hasCoeToFun.{u2, u2, u2, u2} S S (Finsupp.{u2, u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} S) Type.{u2} (Set.hasCoeToSort.{u2} S) s) S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6))))))) S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) (Finsupp.addCommMonoid.{u2, u2} (coeSort.{succ u2, succ (succ 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 but is expected to have type
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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6))))) (Semiring.toModule.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)))) (Semiring.toModule.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6))) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6))))) (Finsupp.total.{u1, u1, u1} (Set.Elem.{u1} S s) S S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_6))))) (Semiring.toModule.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6))) (Subtype.val.{succ u1} S (fun (x : S) => Membership.mem.{u1, u1} S (Set.{u1} S) (Set.instMembershipSet.{u1} S) x s))) l) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6))))) => S) l) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6))))) => S) l) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6))))) => S) l) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6))))) => S) l) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6))))) => S) l) _inst_6)))))) -> (HasSubset.Subset.{u1} (Set.{u1} S) (Set.instHasSubsetSet.{u1} S) s (SetLike.coe.{u1, u1} (Subalgebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)) _inst_7) S (Subalgebra.instSetLikeSubalgebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)) _inst_7) S')) -> (forall (i : Set.Elem.{u1} S s), Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : Set.Elem.{u1} S s) => S) i) (Subalgebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)) _inst_7) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)) _inst_7) S (Subalgebra.instSetLikeSubalgebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)) _inst_7)) (FunLike.coe.{succ u1, succ u1, succ u1} (Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (CommMonoidWithZero.toZero.{u1} S (CommSemiring.toCommMonoidWithZero.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)))) (Set.Elem.{u1} S s) (fun (_x : Set.Elem.{u1} S s) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : Set.Elem.{u1} S s) => S) _x) (Finsupp.funLike.{u1, u1} (Set.Elem.{u1} S s) S (CommMonoidWithZero.toZero.{u1} S (CommSemiring.toCommMonoidWithZero.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)))) l i) S') -> (forall (x : S), (forall (r : Set.Elem.{u1} S s), Exists.{1} Nat (fun (n : Nat) => Membership.mem.{u1, u1} S (Subalgebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)) _inst_7) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)) _inst_7) S (Subalgebra.instSetLikeSubalgebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)) _inst_7)) (HSMul.hSMul.{u1, u1, u1} S S S (instHSMul.{u1, u1} S S (Algebra.toSMul.{u1, u1} S S (CommRing.toCommSemiring.{u1} S _inst_6) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)) (Algebra.id.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)))) (HPow.hPow.{u1, 0, u1} S Nat S (instHPow.{u1, 0} S Nat (Monoid.Pow.{u1} S (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)))))) (Subtype.val.{succ u1} S (fun (x : S) => Membership.mem.{u1, u1} S (Set.{u1} S) (Set.instMembershipSet.{u1} S) x s) r) n) x) S')) -> (Membership.mem.{u1, u1} S (Subalgebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)) _inst_7) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)) _inst_7) S (Subalgebra.instSetLikeSubalgebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)) _inst_7)) x S'))
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {S : Type.{u1}} [_inst_6 : CommRing.{u1} S] [_inst_7 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6))] (S' : Subalgebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)) _inst_7) (s : Set.{u1} S) (l : Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (CommMonoidWithZero.toZero.{u1} S (CommSemiring.toCommMonoidWithZero.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)))), (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6))))) => S) l) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} S S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)))) (Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6))))) S (Finsupp.addCommMonoid.{u1, u1} (Set.Elem.{u1} S s) S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_6))))) (Finsupp.module.{u1, u1, u1} (Set.Elem.{u1} S s) S S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6))))) (Semiring.toModule.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)))) (Semiring.toModule.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)))) (Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6))))) (fun (_x : Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6))))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6))))) => S) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} S S (Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6))))) S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)) (Finsupp.addCommMonoid.{u1, u1} (Set.Elem.{u1} S s) S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_6))))) (Finsupp.module.{u1, u1, u1} (Set.Elem.{u1} S s) S S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6))))) (Semiring.toModule.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)))) (Semiring.toModule.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6))) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6))))) (Finsupp.total.{u1, u1, u1} (Set.Elem.{u1} S s) S S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_6))))) (Semiring.toModule.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6))) (Subtype.val.{succ u1} S (fun (x : S) => Membership.mem.{u1, u1} S (Set.{u1} S) (Set.instMembershipSet.{u1} S) x s))) l) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6))))) => S) l) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6))))) => S) l) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6))))) => S) l) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6))))) => S) l) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6))))) => S) l) _inst_6)))))) -> (HasSubset.Subset.{u1} (Set.{u1} S) (Set.instHasSubsetSet.{u1} S) s (SetLike.coe.{u1, u1} (Subalgebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)) _inst_7) S (Subalgebra.instSetLikeSubalgebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)) _inst_7) S')) -> (forall (i : Set.Elem.{u1} S s), Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : Set.Elem.{u1} S s) => S) i) (Subalgebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)) _inst_7) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)) _inst_7) S (Subalgebra.instSetLikeSubalgebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)) _inst_7)) (FunLike.coe.{succ u1, succ u1, succ u1} (Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (CommMonoidWithZero.toZero.{u1} S (CommSemiring.toCommMonoidWithZero.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)))) (Set.Elem.{u1} S s) (fun (_x : Set.Elem.{u1} S s) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : Set.Elem.{u1} S s) => S) _x) (Finsupp.funLike.{u1, u1} (Set.Elem.{u1} S s) S (CommMonoidWithZero.toZero.{u1} S (CommSemiring.toCommMonoidWithZero.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)))) l i) S') -> (forall (x : S), (forall (r : Set.Elem.{u1} S s), Exists.{1} Nat (fun (n : Nat) => Membership.mem.{u1, u1} S (Subalgebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)) _inst_7) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)) _inst_7) S (Subalgebra.instSetLikeSubalgebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)) _inst_7)) (HSMul.hSMul.{u1, u1, u1} S S S (instHSMul.{u1, u1} S S (Algebra.toSMul.{u1, u1} S S (CommRing.toCommSemiring.{u1} S _inst_6) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)) (Algebra.id.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)))) (HPow.hPow.{u1, 0, u1} S Nat S (instHPow.{u1, 0} S Nat (Monoid.Pow.{u1} S (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)))))) (Subtype.val.{succ u1} S (fun (x : S) => Membership.mem.{u1, u1} S (Set.{u1} S) (Set.instMembershipSet.{u1} S) x s) r) n) x) S')) -> (Membership.mem.{u1, u1} S (Subalgebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)) _inst_7) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)) _inst_7) S (Subalgebra.instSetLikeSubalgebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)) _inst_7)) x S'))
 Case conversion may be inaccurate. Consider using '#align subalgebra.mem_of_span_eq_top_of_smul_pow_mem Subalgebra.mem_of_span_eq_top_of_smul_pow_memₓ'. -/
 theorem mem_of_span_eq_top_of_smul_pow_mem {S : Type _} [CommRing S] [Algebra R S]
     (S' : Subalgebra R S) (s : Set S) (l : s →₀ S) (hs : Finsupp.total s S S coe l = 1)

bump to nightly-2023-05-23-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/75e7fca56381d056096ce5d05e938f63a6567828

ed98987c

Diff

@@ -710,7 +710,7 @@ end
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) [_inst_8 : NoZeroSMulDivisors.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u2} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))], NoZeroSMulDivisors.{u1, u2} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (ZeroMemClass.zero.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (AddSubmonoidClass.to_zeroMemClass.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SubsemiringClass.to_addSubmonoidClass.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Semiring.toNonAssocSemiring.{u2} A _inst_2) (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Subalgebra.subsemiringClass.{u1, u2} R A _inst_1 _inst_2 _inst_3))) S) (SetLike.smul.{u1, u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) R A (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Subalgebra.smulMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3) S)
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) [_inst_8 : NoZeroSMulDivisors.{u1, u2} R A (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3)], NoZeroSMulDivisors.{u1, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (ZeroMemClass.zero.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (AddSubmonoidClass.toZeroMemClass.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SubsemiringClass.toAddSubmonoidClass.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Semiring.toNonAssocSemiring.{u2} A _inst_2) (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Subalgebra.SubsemiringClass.{u1, u2} R A _inst_1 _inst_2 _inst_3))) S) (Algebra.toSMul.{u1, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S))
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) [_inst_8 : NoZeroSMulDivisors.{u1, u2} R A (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3)], NoZeroSMulDivisors.{u1, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (ZeroMemClass.zero.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (AddSubmonoidClass.toZeroMemClass.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SubsemiringClass.toAddSubmonoidClass.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Semiring.toNonAssocSemiring.{u2} A _inst_2) (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Subalgebra.SubsemiringClass.{u1, u2} R A _inst_1 _inst_2 _inst_3))) S) (Algebra.toSMul.{u1, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S))
 Case conversion may be inaccurate. Consider using '#align subalgebra.no_zero_smul_divisors_bot Subalgebra.noZeroSMulDivisors_botₓ'. -/
 instance noZeroSMulDivisors_bot [NoZeroSMulDivisors R A] : NoZeroSMulDivisors R S :=
   ⟨fun c x h =>
@@ -834,7 +834,7 @@ protected theorem coe_eq_one {x : S} : (x : A) = 1 ↔ x = 1 :=
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), AlgHom.{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_2 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_3
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), AlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_2 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_3
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), AlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_2 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_3
 Case conversion may be inaccurate. Consider using '#align subalgebra.val Subalgebra.valₓ'. -/
 -- todo: standardize on the names these morphisms
 -- compare with submodule.subtype
@@ -846,7 +846,7 @@ def val : S →ₐ[R] A := by refine_struct { toFun := (coe : S → A) } <;> int
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), Eq.{succ u2} ((fun (_x : AlgHom.{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_2 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_3) => (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) -> A) (Subalgebra.val.{u1, u2} R A _inst_1 _inst_2 _inst_3 S)) (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_2 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_3) (fun (_x : AlgHom.{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_2 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_3) => (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) -> A) ([anonymous].{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_2 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_3) (Subalgebra.val.{u1, u2} R A _inst_1 _inst_2 _inst_3 S)) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) A (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) A (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) A (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) A (coeSubtype.{succ u2} A (fun (x : A) => Membership.Mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S))))))
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), Eq.{succ u2} (forall (a : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)), (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) => A) a) (FunLike.coe.{succ u2, succ u2, succ u2} (AlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_2 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_3) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (fun (_x : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) => A) _x) (SMulHomClass.toFunLike.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_2 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_3) R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) A (SMulZeroClass.toSMul.{u1, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (AddMonoid.toZero.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A 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+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), Eq.{succ u2} (forall (a : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)), (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) => A) a) (FunLike.coe.{succ u2, succ u2, succ u2} (AlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A 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R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S)))) (Algebra.toModule.{u1, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S)))))) (SMulZeroClass.toSMul.{u1, u2} R A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribSMul.toSMulZeroClass.{u1, u2} R A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (DistribMulActionHomClass.toSMulHomClass.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_2 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_3) R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S))))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Module.toDistribMulAction.{u1, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S)))) (Algebra.toModule.{u1, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_2 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_3) R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (Module.toDistribMulAction.{u1, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S)))) (Algebra.toModule.{u1, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u2, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_2 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_3 (AlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_2 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_3) (AlgHom.algHomClass.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_2 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_3))))) (Subalgebra.val.{u1, u2} R A _inst_1 _inst_2 _inst_3 S)) (Subtype.val.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) x (SetLike.coe.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) S)))
 Case conversion may be inaccurate. Consider using '#align subalgebra.coe_val Subalgebra.coe_valₓ'. -/
 @[simp]
 theorem coe_val : (S.val : S → A) = coe :=
@@ -857,7 +857,7 @@ theorem coe_val : (S.val : S → A) = coe :=
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x : coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S), Eq.{succ u2} A (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_2 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_3) (fun (_x : AlgHom.{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_2 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_3) => (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) -> A) ([anonymous].{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_2 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_3) (Subalgebra.val.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) x) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) A (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) A (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) A (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) A (coeSubtype.{succ u2} A (fun (x : A) => Membership.Mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S))))) x)
 but is expected to have type
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+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) => A) x) (FunLike.coe.{succ u2, succ u2, succ u2} (AlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 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R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S)))) (Algebra.toModule.{u1, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S)))))) (SMulZeroClass.toSMul.{u1, u2} R A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribSMul.toSMulZeroClass.{u1, u2} R A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (DistribMulActionHomClass.toSMulHomClass.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_2 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_3) R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S))))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Module.toDistribMulAction.{u1, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ 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_inst_2 _inst_3 S) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_2 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_3) R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (Module.toDistribMulAction.{u1, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S)))) (Algebra.toModule.{u1, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u2, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_2 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_3 (AlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_2 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_3) (AlgHom.algHomClass.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_2 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_3))))) (Subalgebra.val.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) x) (Subtype.val.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) x (SetLike.coe.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) S)) x)
 Case conversion may be inaccurate. Consider using '#align subalgebra.val_apply Subalgebra.val_applyₓ'. -/
 theorem val_apply (x : S) : S.val x = (x : A) :=
   rfl
@@ -867,7 +867,7 @@ theorem val_apply (x : S) : S.val x = (x : A) :=
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), Eq.{succ u2} (RingHom.{u2, u2} (coeSort.{succ u2, succ (succ u2)} (Subsemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subsemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) A (Subsemiring.setLike.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Subalgebra.toSubsemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S)) A (Subsemiring.toNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2) (Subalgebra.toSubsemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (Subsemiring.subtype.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2) (Subalgebra.toSubsemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S)) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (AlgHom.{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_2 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_3) (RingHom.{u2, u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) A (Semiring.toNonAssocSemiring.{u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (HasLiftT.mk.{succ u2, succ u2} (AlgHom.{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_2 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_3) (RingHom.{u2, u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) A (Semiring.toNonAssocSemiring.{u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (CoeTCₓ.coe.{succ u2, succ u2} (AlgHom.{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_2 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_3) (RingHom.{u2, u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) A (Semiring.toNonAssocSemiring.{u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHom.hasCoeT.{u2, u2, u2} (AlgHom.{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_2 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_3) (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) A (Semiring.toNonAssocSemiring.{u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (AlgHomClass.toRingHomClass.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_2 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_3) R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_2 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_3 (AlgHom.algHomClass.{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_2 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_3))))) (Subalgebra.val.{u1, u2} R A _inst_1 _inst_2 _inst_3 S))
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), Eq.{succ u2} (RingHom.{u2, u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subsemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (SetLike.instMembership.{u2, u2} (Subsemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) A (Subsemiring.instSetLikeSubsemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) x (Subalgebra.toSubsemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S))) A (Subsemiring.toNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2) (Subalgebra.toSubsemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (Subsemiring.subtype.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2) (Subalgebra.toSubsemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S)) (RingHomClass.toRingHom.{u2, u2, u2} (AlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_2 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_3) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) A (Subsemiring.toNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2) (Subalgebra.toSubsemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (AlgHomClass.toRingHomClass.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_2 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_3) R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_2 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_3 (AlgHom.algHomClass.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_2 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_3)) (Subalgebra.val.{u1, u2} R A _inst_1 _inst_2 _inst_3 S))
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), Eq.{succ u2} (RingHom.{u2, u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subsemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (SetLike.instMembership.{u2, u2} (Subsemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) A (Subsemiring.instSetLikeSubsemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) x (Subalgebra.toSubsemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S))) A (Subsemiring.toNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2) (Subalgebra.toSubsemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (Subsemiring.subtype.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2) (Subalgebra.toSubsemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S)) (RingHomClass.toRingHom.{u2, u2, u2} (AlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_2 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_3) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) A (Subsemiring.toNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2) (Subalgebra.toSubsemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (AlgHomClass.toRingHomClass.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_2 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_3) R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_2 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_3 (AlgHom.algHomClass.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_2 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_3)) (Subalgebra.val.{u1, u2} R A _inst_1 _inst_2 _inst_3 S))
 Case conversion may be inaccurate. Consider using '#align subalgebra.to_subsemiring_subtype Subalgebra.toSubsemiring_subtypeₓ'. -/
 @[simp]
 theorem toSubsemiring_subtype : S.toSubsemiring.Subtype = (S.val : S →+* A) :=
@@ -878,7 +878,7 @@ theorem toSubsemiring_subtype : S.toSubsemiring.Subtype = (S.val : S →+* A) :=
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_8 : CommRing.{u1} R] [_inst_9 : Ring.{u2} A] [_inst_10 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9)] (S : Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10), Eq.{succ u2} (RingHom.{u2, u2} (coeSort.{succ u2, succ (succ u2)} (Subring.{u2} A _inst_9) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subring.{u2} A _inst_9) A (Subring.setLike.{u2} A _inst_9)) (Subalgebra.toSubring.{u1, u2} R A _inst_8 _inst_9 _inst_10 S)) A (NonAssocRing.toNonAssocSemiring.{u2} (coeSort.{succ u2, succ (succ u2)} (Subring.{u2} A _inst_9) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subring.{u2} A _inst_9) A (Subring.setLike.{u2} A _inst_9)) (Subalgebra.toSubring.{u1, u2} R A _inst_8 _inst_9 _inst_10 S)) (Ring.toNonAssocRing.{u2} (coeSort.{succ u2, succ (succ u2)} (Subring.{u2} A _inst_9) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subring.{u2} A _inst_9) A (Subring.setLike.{u2} A _inst_9)) (Subalgebra.toSubring.{u1, u2} R A _inst_8 _inst_9 _inst_10 S)) (Subring.toRing.{u2} A _inst_9 (Subalgebra.toSubring.{u1, u2} R A _inst_8 _inst_9 _inst_10 S)))) (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A _inst_9))) (Subring.subtype.{u2} A _inst_9 (Subalgebra.toSubring.{u1, u2} R A _inst_8 _inst_9 _inst_10 S)) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (AlgHom.{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) A (Subalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10)) S) A (CommRing.toCommSemiring.{u1} R _inst_8) (Subalgebra.toSemiring.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10 S) (Ring.toSemiring.{u2} A _inst_9) (Subalgebra.algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10 S) _inst_10) (RingHom.{u2, u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) A (Subalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10)) S) A (NonAssocRing.toNonAssocSemiring.{u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A 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(CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) A (Subalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10)) S) A (CommRing.toCommSemiring.{u1} R _inst_8) (Subalgebra.toSemiring.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10 S) (Ring.toSemiring.{u2} A _inst_9) (Subalgebra.algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10 S) _inst_10) (RingHom.{u2, u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) A (Subalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10)) S) A (NonAssocRing.toNonAssocSemiring.{u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) A (Subalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10)) S) (Ring.toNonAssocRing.{u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) A (Subalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10)) S) (Subalgebra.toRing.{u1, u2} R A _inst_8 _inst_9 _inst_10 S))) (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A _inst_9))) (CoeTCₓ.coe.{succ u2, succ u2} (AlgHom.{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) A (Subalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10)) S) A (CommRing.toCommSemiring.{u1} R _inst_8) (Subalgebra.toSemiring.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10 S) (Ring.toSemiring.{u2} A _inst_9) (Subalgebra.algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10 S) _inst_10) (RingHom.{u2, u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) 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_inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) A (Subalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10)) S) (Subalgebra.toRing.{u1, u2} R A _inst_8 _inst_9 _inst_10 S))) (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A _inst_9))) (RingHom.hasCoeT.{u2, u2, u2} (AlgHom.{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) A (Subalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10)) S) A (CommRing.toCommSemiring.{u1} R _inst_8) (Subalgebra.toSemiring.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10 S) (Ring.toSemiring.{u2} A _inst_9) (Subalgebra.algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10 S) _inst_10) (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) A (Subalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10)) S) A (NonAssocRing.toNonAssocSemiring.{u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) A (Subalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10)) S) (Ring.toNonAssocRing.{u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) A (Subalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10)) S) (Subalgebra.toRing.{u1, u2} R A _inst_8 _inst_9 _inst_10 S))) (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A _inst_9)) (AlgHomClass.toRingHomClass.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) A (Subalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10)) S) A (CommRing.toCommSemiring.{u1} R _inst_8) (Subalgebra.toSemiring.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10 S) (Ring.toSemiring.{u2} A _inst_9) (Subalgebra.algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10 S) _inst_10) R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) A (Subalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10)) S) A (CommRing.toCommSemiring.{u1} R _inst_8) (Subalgebra.toSemiring.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10 S) (Ring.toSemiring.{u2} A _inst_9) (Subalgebra.algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10 S) _inst_10 (AlgHom.algHomClass.{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) A (Subalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10)) S) A (CommRing.toCommSemiring.{u1} R _inst_8) (Subalgebra.toSemiring.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10 S) (Ring.toSemiring.{u2} A _inst_9) (Subalgebra.algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10 S) _inst_10))))) (Subalgebra.val.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10 S))
 but is expected to have type
-  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_8 : CommRing.{u2} R] [_inst_9 : Ring.{u1} A] [_inst_10 : Algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9)] (S : Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10), Eq.{succ u1} (RingHom.{u1, u1} (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subring.{u1} A _inst_9) (SetLike.instMembership.{u1, u1} (Subring.{u1} A _inst_9) A (Subring.instSetLikeSubring.{u1} A _inst_9)) x (Subalgebra.toSubring.{u2, u1} R A _inst_8 _inst_9 _inst_10 S))) A (Subsemiring.toNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_9)) (Subring.toSubsemiring.{u1} A _inst_9 (Subalgebra.toSubring.{u2, u1} R A _inst_8 _inst_9 _inst_10 S))) (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_9))) (Subring.subtype.{u1} A _inst_9 (Subalgebra.toSubring.{u2, u1} R A _inst_8 _inst_9 _inst_10 S)) (RingHomClass.toRingHom.{u1, u1, u1} (AlgHom.{u2, u1, u1} R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10)) x S)) A (CommRing.toCommSemiring.{u2} R _inst_8) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10 S) (Ring.toSemiring.{u1} A _inst_9) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10 S) _inst_10) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10)) x S)) A (Subsemiring.toNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_9)) (Subalgebra.toSubsemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10 S)) (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_9)) (AlgHomClass.toRingHomClass.{u1, u2, u1, u1} (AlgHom.{u2, u1, u1} R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10)) x S)) A (CommRing.toCommSemiring.{u2} R _inst_8) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10 S) (Ring.toSemiring.{u1} A _inst_9) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10 S) _inst_10) R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10)) x S)) A (CommRing.toCommSemiring.{u2} R _inst_8) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10 S) (Ring.toSemiring.{u1} A _inst_9) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10 S) _inst_10 (AlgHom.algHomClass.{u2, u1, u1} R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10)) x S)) A (CommRing.toCommSemiring.{u2} R _inst_8) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10 S) (Ring.toSemiring.{u1} A _inst_9) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10 S) _inst_10)) (Subalgebra.val.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10 S))
+  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_8 : CommRing.{u2} R] [_inst_9 : Ring.{u1} A] [_inst_10 : Algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9)] (S : Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10), Eq.{succ u1} (RingHom.{u1, u1} (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subring.{u1} A _inst_9) (SetLike.instMembership.{u1, u1} (Subring.{u1} A _inst_9) A (Subring.instSetLikeSubring.{u1} A _inst_9)) x (Subalgebra.toSubring.{u2, u1} R A _inst_8 _inst_9 _inst_10 S))) A (Subsemiring.toNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_9)) (Subring.toSubsemiring.{u1} A _inst_9 (Subalgebra.toSubring.{u2, u1} R A _inst_8 _inst_9 _inst_10 S))) (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_9))) (Subring.subtype.{u1} A _inst_9 (Subalgebra.toSubring.{u2, u1} R A _inst_8 _inst_9 _inst_10 S)) (RingHomClass.toRingHom.{u1, u1, u1} (AlgHom.{u2, u1, u1} R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10)) x S)) A (CommRing.toCommSemiring.{u2} R _inst_8) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10 S) (Ring.toSemiring.{u1} A _inst_9) (Subalgebra.algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10 S) _inst_10) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10)) x S)) A (Subsemiring.toNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_9)) (Subalgebra.toSubsemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10 S)) (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_9)) (AlgHomClass.toRingHomClass.{u1, u2, u1, u1} (AlgHom.{u2, u1, u1} R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10)) x S)) A (CommRing.toCommSemiring.{u2} R _inst_8) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10 S) (Ring.toSemiring.{u1} A _inst_9) (Subalgebra.algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10 S) _inst_10) R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10)) x S)) A (CommRing.toCommSemiring.{u2} R _inst_8) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10 S) (Ring.toSemiring.{u1} A _inst_9) (Subalgebra.algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10 S) _inst_10 (AlgHom.algHomClass.{u2, u1, u1} R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10)) x S)) A (CommRing.toCommSemiring.{u2} R _inst_8) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10 S) (Ring.toSemiring.{u1} A _inst_9) (Subalgebra.algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10 S) _inst_10)) (Subalgebra.val.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10 S))
 Case conversion may be inaccurate. Consider using '#align subalgebra.to_subring_subtype Subalgebra.toSubring_subtypeₓ'. -/
 @[simp]
 theorem toSubring_subtype {R A : Type _} [CommRing R] [Ring A] [Algebra R A] (S : Subalgebra R A) :
@@ -1101,7 +1101,7 @@ theorem coe_toSubalgebra (p : Submodule R A) (h_one h_mul) :
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (s : Set.{u2} A) (h0 : Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) (OfNat.ofNat.{u2} A 0 (OfNat.mk.{u2} A 0 (Zero.zero.{u2} A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))))))) s) (hadd : forall {a : A} {b : A}, (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) a s) -> (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) b s) -> (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (AddZeroClass.toHasAdd.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))))) a b) s)) (hsmul : forall (c : R) {x : A}, (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) x s) -> (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) (SMul.smul.{u1, u2} R A (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) c x) s)) (h1 : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (OfNat.ofNat.{u2} A 1 (OfNat.mk.{u2} A 1 (One.one.{u2} A (AddMonoidWithOne.toOne.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))))) (Submodule.mk.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) s hadd h0 hsmul)) (hmul : forall (x : A) (y : A), (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (Submodule.mk.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) s hadd h0 hsmul)) -> (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) y (Submodule.mk.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) s hadd h0 hsmul)) -> (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A 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_inst_2)))))))) s) (id_tag Tactic.IdTag.rw (Eq.{1} Prop (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) s) (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) (SMul.smul.{u1, u2} R A (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A 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(OfNat.ofNat.{u2} A 1 (OfNat.mk.{u2} A 1 (One.one.{u2} A (AddMonoidWithOne.toOne.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))))) (Algebra.algebraMap_eq_smul_one.{u1, u2} R A _inst_1 _inst_2 _inst_3 r))) (hsmul r (OfNat.ofNat.{u2} A 1 (OfNat.mk.{u2} A 1 (One.one.{u2} A (AddMonoidWithOne.toOne.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))))) h1)))
 but is expected to have type
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(Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) (OfNat.ofNat.{u1} A 1 (One.toOfNat1.{u1} A (Semiring.toOne.{u1} A _inst_2))) s) (hadd : forall (a : A) (b : A), (Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) s) hadd) h0) (fun {a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6476 : A} {b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6477 : A} => Submodule.add_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6476 b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6477) (Submodule.zero_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s))))))) (Eq.ndrec.{0, 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(CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2) (RingHom.instRingHomClassRingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2))))) (algebraMap.{u2, u1} R A _inst_1 _inst_2 _inst_3) r) (fun (_a : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) r) => Eq.{1} Prop (Membership.mem.{u1, u1} ((fun 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R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2) (RingHom.instRingHomClassRingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2))))) (algebraMap.{u2, u1} R A _inst_1 _inst_2 _inst_3) r) (Subsemigroup.carrier.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (Submonoid.toSubsemigroup.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemiring.toSubmonoid.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Subsemiring.mk.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Submonoid.mk.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemigroup.mk.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) s) hadd) h0) (fun {a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6476 : A} {b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6477 : A} => Submodule.add_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6476 b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6477) (Submodule.zero_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s)))))) (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) r) (Set.{u1} A) (Set.instMembershipSet.{u1} A) _a (Subsemigroup.carrier.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (Submonoid.toSubsemigroup.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemiring.toSubmonoid.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Subsemiring.mk.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Submonoid.mk.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemigroup.mk.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) s) hadd) h0) (fun {a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6476 : A} {b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6477 : A} => Submodule.add_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6476 b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6477) (Submodule.zero_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s))))))) (Eq.refl.{1} Prop (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) r) (Set.{u1} A) (Set.instMembershipSet.{u1} A) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2) (RingHom.instRingHomClassRingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2))))) (algebraMap.{u2, u1} R A _inst_1 _inst_2 _inst_3) r) (Subsemigroup.carrier.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (Submonoid.toSubsemigroup.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemiring.toSubmonoid.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Subsemiring.mk.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Submonoid.mk.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemigroup.mk.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) s) hadd) h0) (fun {a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6476 : A} {b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6477 : A} => Submodule.add_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6476 b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6477) (Submodule.zero_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s))))))) (HSMul.hSMul.{u2, u1, u1} R A A (instHSMul.{u2, u1} R A (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_2 _inst_3)) r (OfNat.ofNat.{u1} A 1 (One.toOfNat1.{u1} A (Semiring.toOne.{u1} A _inst_2)))) (Algebra.algebraMap_eq_smul_one.{u2, u1} R A _inst_1 _inst_2 _inst_3 r))) (Submodule.smul_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s (OfNat.ofNat.{u1} A 1 (One.toOfNat1.{u1} A (Semiring.toOne.{u1} A _inst_2))) r h0)))
+  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u1} A] [_inst_3 : Algebra.{u2, u1} R A _inst_1 _inst_2] (s : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (h0 : Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) (OfNat.ofNat.{u1} A 1 (One.toOfNat1.{u1} A (Semiring.toOne.{u1} A _inst_2))) s) (hadd : forall (a : A) (b : A), (Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) a s) -> (Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) b s) -> (Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u1, u1, u1} A A A (instHMul.{u1} A (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) a b) s)), Eq.{succ u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 s h0 hadd) (Subalgebra.mk.{u2, u1} R A _inst_1 _inst_2 _inst_3 (Subsemiring.mk.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Submonoid.mk.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemigroup.mk.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) s) hadd) h0) (fun {a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6477 : A} {b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6478 : A} => Submodule.add_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s 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_inst_2)) R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2) (RingHom.instRingHomClassRingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2))))) (algebraMap.{u2, u1} R A _inst_1 _inst_2 _inst_3) r) (Subsemigroup.carrier.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (Submonoid.toSubsemigroup.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemiring.toSubmonoid.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Subsemiring.mk.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Submonoid.mk.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemigroup.mk.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) s) hadd) h0) (fun {a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6477 : A} {b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6478 : A} => Submodule.add_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6477 b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6478) (Submodule.zero_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s)))))) (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) r) (Set.{u1} A) (Set.instMembershipSet.{u1} A) (HSMul.hSMul.{u2, u1, u1} R A A (instHSMul.{u2, u1} R A (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_2 _inst_3)) r (OfNat.ofNat.{u1} A 1 (One.toOfNat1.{u1} A (Semiring.toOne.{u1} A _inst_2)))) (Subsemigroup.carrier.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (Submonoid.toSubsemigroup.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemiring.toSubmonoid.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Subsemiring.mk.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Submonoid.mk.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemigroup.mk.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) s) hadd) h0) (fun {a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6477 : A} {b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6478 : A} => Submodule.add_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6477 b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6478) (Submodule.zero_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s)))))) (id.{0} (Eq.{1} Prop (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) r) (Set.{u1} A) (Set.instMembershipSet.{u1} A) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2) (RingHom.instRingHomClassRingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R 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u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2) (RingHom.instRingHomClassRingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2))))) (algebraMap.{u2, u1} R A _inst_1 _inst_2 _inst_3) r) (Subsemigroup.carrier.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (Submonoid.toSubsemigroup.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemiring.toSubmonoid.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Subsemiring.mk.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Submonoid.mk.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemigroup.mk.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) s) hadd) h0) (fun {a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6477 : A} {b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6478 : A} => Submodule.add_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6477 b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6478) (Submodule.zero_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s))))))) (HSMul.hSMul.{u2, u1, u1} R A A (instHSMul.{u2, u1} R A (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_2 _inst_3)) r (OfNat.ofNat.{u1} A 1 (One.toOfNat1.{u1} A (Semiring.toOne.{u1} A _inst_2)))) (Algebra.algebraMap_eq_smul_one.{u2, u1} R A _inst_1 _inst_2 _inst_3 r))) (Submodule.smul_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s (OfNat.ofNat.{u1} A 1 (One.toOfNat1.{u1} A (Semiring.toOne.{u1} A _inst_2))) r h0)))
 Case conversion may be inaccurate. Consider using '#align submodule.to_subalgebra_mk Submodule.toSubalgebra_mkₓ'. -/
 @[simp]
 theorem toSubalgebra_mk (s : Set A) (h0 hadd hsmul h1 hmul) :
@@ -1211,7 +1211,7 @@ theorem range_comp_le_range (f : A →ₐ[R] B) (g : B →ₐ[R] C) : (g.comp f)
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] (f : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (S : Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5), (forall (x : A), Membership.Mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.hasMem.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.setLike.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (fun (_x : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) => A -> B) ([anonymous].{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) f x) S) -> (AlgHom.{u1, u2, u3} R A (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.setLike.{u1, u3} R B _inst_1 _inst_4 _inst_5)) S) _inst_1 _inst_2 (Subalgebra.toSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S) _inst_3 (Subalgebra.algebra.{u1, u3} R B _inst_1 _inst_4 _inst_5 S))
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] (f : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (S : Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5), (forall (x : A), Membership.mem.{u3, u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) x) (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) _x) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (SMulZeroClass.toSMul.{u1, u2} R A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribSMul.toSMulZeroClass.{u1, u2} R A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toSMul.{u1, u3} R B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))))) (DistribSMul.toSMulZeroClass.{u1, u3} R B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))))) (DistribMulAction.toDistribSMul.{u1, u3} R B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u2, u3, max u2 u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (AlgHom.algHomClass.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5))))) f x) S) -> (AlgHom.{u1, u2, u3} R A (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) _inst_1 _inst_2 (Subalgebra.toSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S) _inst_3 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S))
+  forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] (f : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (S : Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5), (forall (x : A), Membership.mem.{u3, u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) x) (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) _x) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (SMulZeroClass.toSMul.{u1, u2} R A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribSMul.toSMulZeroClass.{u1, u2} R A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toSMul.{u1, u3} R B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))))) (DistribSMul.toSMulZeroClass.{u1, u3} R B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))))) (DistribMulAction.toDistribSMul.{u1, u3} R B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u2, u3, max u2 u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (AlgHom.algHomClass.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5))))) f x) S) -> (AlgHom.{u1, u2, u3} R A (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) _inst_1 _inst_2 (Subalgebra.toSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S) _inst_3 (Subalgebra.algebra.{u1, u3} R B _inst_1 _inst_4 _inst_5 S))
 Case conversion may be inaccurate. Consider using '#align alg_hom.cod_restrict AlgHom.codRestrictₓ'. -/
 /-- Restrict the codomain of an algebra homomorphism. -/
 def codRestrict (f : A →ₐ[R] B) (S : Subalgebra R B) (hf : ∀ x, f x ∈ S) : A →ₐ[R] S :=
@@ -1222,7 +1222,7 @@ def codRestrict (f : A →ₐ[R] B) (S : Subalgebra R B) (hf : ∀ x, f x ∈ S)
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] (f : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (S : Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (hf : forall (x : A), Membership.Mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.hasMem.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.setLike.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (fun (_x : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) => A -> B) ([anonymous].{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) f x) S), Eq.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (AlgHom.comp.{u1, u2, u3, u3} R A (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.setLike.{u1, u3} R B _inst_1 _inst_4 _inst_5)) S) B _inst_1 _inst_2 (Subalgebra.toSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S) _inst_4 _inst_3 (Subalgebra.algebra.{u1, u3} R B _inst_1 _inst_4 _inst_5 S) _inst_5 (Subalgebra.val.{u1, u3} R B _inst_1 _inst_4 _inst_5 S) (AlgHom.codRestrict.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 f S hf)) f
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] (f : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (S : Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (hf : forall (x : A), Membership.mem.{u3, u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) x) (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) _x) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (SMulZeroClass.toSMul.{u1, u2} R A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribSMul.toSMulZeroClass.{u1, u2} R A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toSMul.{u1, u3} R B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))))) (DistribSMul.toSMulZeroClass.{u1, u3} R B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))))) (DistribMulAction.toDistribSMul.{u1, u3} R B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u2, u3, max u2 u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (AlgHom.algHomClass.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5))))) f x) S), Eq.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (AlgHom.comp.{u1, u2, u3, u3} R A (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) B _inst_1 _inst_2 (Subalgebra.toSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S) _inst_4 _inst_3 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S) _inst_5 (Subalgebra.val.{u1, u3} R B _inst_1 _inst_4 _inst_5 S) (AlgHom.codRestrict.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 f S hf)) f
+  forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] (f : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (S : Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (hf : forall (x : A), Membership.mem.{u3, u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) x) (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) _x) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (SMulZeroClass.toSMul.{u1, u2} R A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribSMul.toSMulZeroClass.{u1, u2} R A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toSMul.{u1, u3} R B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))))) (DistribSMul.toSMulZeroClass.{u1, u3} R B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))))) (DistribMulAction.toDistribSMul.{u1, u3} R B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u2, u3, max u2 u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (AlgHom.algHomClass.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5))))) f x) S), Eq.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (AlgHom.comp.{u1, u2, u3, u3} R A (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) B _inst_1 _inst_2 (Subalgebra.toSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S) _inst_4 _inst_3 (Subalgebra.algebra.{u1, u3} R B _inst_1 _inst_4 _inst_5 S) _inst_5 (Subalgebra.val.{u1, u3} R B _inst_1 _inst_4 _inst_5 S) (AlgHom.codRestrict.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 f S hf)) f
 Case conversion may be inaccurate. Consider using '#align alg_hom.val_comp_cod_restrict AlgHom.val_comp_codRestrictₓ'. -/
 @[simp]
 theorem val_comp_codRestrict (f : A →ₐ[R] B) (S : Subalgebra R B) (hf : ∀ x, f x ∈ S) :
@@ -1234,7 +1234,7 @@ theorem val_comp_codRestrict (f : A →ₐ[R] B) (S : Subalgebra R B) (hf : ∀
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] (f : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (S : Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (hf : forall (x : A), Membership.Mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.hasMem.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.setLike.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (fun (_x : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) => A -> B) ([anonymous].{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) f x) S) (x : A), Eq.{succ u3} B ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.setLike.{u1, u3} R B _inst_1 _inst_4 _inst_5)) S) B (HasLiftT.mk.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.setLike.{u1, u3} R B _inst_1 _inst_4 _inst_5)) S) B (CoeTCₓ.coe.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.setLike.{u1, u3} R B _inst_1 _inst_4 _inst_5)) S) B (coeBase.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.setLike.{u1, u3} R B _inst_1 _inst_4 _inst_5)) S) B (coeSubtype.{succ u3} B (fun (x : B) => Membership.Mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.hasMem.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.setLike.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S))))) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R A (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.setLike.{u1, u3} R B _inst_1 _inst_4 _inst_5)) S) _inst_1 _inst_2 (Subalgebra.toSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S) _inst_3 (Subalgebra.algebra.{u1, u3} R B _inst_1 _inst_4 _inst_5 S)) (fun (_x : AlgHom.{u1, u2, u3} R A (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.setLike.{u1, u3} R B _inst_1 _inst_4 _inst_5)) S) _inst_1 _inst_2 (Subalgebra.toSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S) _inst_3 (Subalgebra.algebra.{u1, u3} R B _inst_1 _inst_4 _inst_5 S)) => A -> (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.setLike.{u1, u3} R B _inst_1 _inst_4 _inst_5)) S)) ([anonymous].{u1, u2, u3} R A (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.setLike.{u1, u3} R B _inst_1 _inst_4 _inst_5)) S) _inst_1 _inst_2 (Subalgebra.toSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S) _inst_3 (Subalgebra.algebra.{u1, u3} R B _inst_1 _inst_4 _inst_5 S)) (AlgHom.codRestrict.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 f S hf) x)) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (fun (_x : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) => A -> B) ([anonymous].{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) f x)
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] (f : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (S : Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (hf : forall (x : A), Membership.mem.{u3, u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) x) (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) _x) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (SMulZeroClass.toSMul.{u1, u2} R A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribSMul.toSMulZeroClass.{u1, u2} R A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toSMul.{u1, u3} R B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))))) (DistribSMul.toSMulZeroClass.{u1, u3} R B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))))) (DistribMulAction.toDistribSMul.{u1, u3} R B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u2, u3, max u2 u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) 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Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) (Subalgebra.toSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) (Subalgebra.toSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S)))) (Algebra.toModule.{u1, u3} R (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) _inst_1 (Subalgebra.toSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u2, u3, max u2 u3} R A (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) _inst_1 _inst_2 (Subalgebra.toSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S) _inst_3 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S) (AlgHom.{u1, u2, u3} R A (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) _inst_1 _inst_2 (Subalgebra.toSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S) _inst_3 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S)) (AlgHom.algHomClass.{u1, u2, u3} R A (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) _inst_1 _inst_2 (Subalgebra.toSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S) _inst_3 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S)))))) (AlgHom.codRestrict.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 f S hf) x)) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) _x) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (SMulZeroClass.toSMul.{u1, u2} R A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribSMul.toSMulZeroClass.{u1, u2} R A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toSMul.{u1, u3} R B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))))) (DistribSMul.toSMulZeroClass.{u1, u3} R B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))))) (DistribMulAction.toDistribSMul.{u1, u3} R B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u2, u3, max u2 u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (AlgHom.algHomClass.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5))))) f x)
+  forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] (f : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (S : Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (hf : forall (x : A), Membership.mem.{u3, u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) x) (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) _x) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (SMulZeroClass.toSMul.{u1, u2} R A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribSMul.toSMulZeroClass.{u1, u2} R A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toSMul.{u1, u3} R B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))))) (DistribSMul.toSMulZeroClass.{u1, u3} R B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))))) (DistribMulAction.toDistribSMul.{u1, u3} R B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B 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(Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) (Subalgebra.toSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S)))) (Algebra.toModule.{u1, u3} R (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) _inst_1 (Subalgebra.toSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S) (Subalgebra.algebra.{u1, u3} R B _inst_1 _inst_4 _inst_5 S))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) _inst_1 _inst_2 (Subalgebra.toSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S) _inst_3 (Subalgebra.algebra.{u1, u3} R B _inst_1 _inst_4 _inst_5 S)) R A (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) (Subalgebra.toSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) (Subalgebra.toSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S)))) (Algebra.toModule.{u1, u3} R (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) _inst_1 (Subalgebra.toSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S) (Subalgebra.algebra.{u1, u3} R B _inst_1 _inst_4 _inst_5 S))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u2, u3, max u2 u3} R A (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) _inst_1 _inst_2 (Subalgebra.toSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S) _inst_3 (Subalgebra.algebra.{u1, u3} R B _inst_1 _inst_4 _inst_5 S) (AlgHom.{u1, u2, u3} R A (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) _inst_1 _inst_2 (Subalgebra.toSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S) _inst_3 (Subalgebra.algebra.{u1, u3} R B _inst_1 _inst_4 _inst_5 S)) (AlgHom.algHomClass.{u1, u2, u3} R A (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) _inst_1 _inst_2 (Subalgebra.toSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S) _inst_3 (Subalgebra.algebra.{u1, u3} R B _inst_1 _inst_4 _inst_5 S)))))) (AlgHom.codRestrict.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 f S hf) x)) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) _x) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (SMulZeroClass.toSMul.{u1, u2} R A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribSMul.toSMulZeroClass.{u1, u2} R A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toSMul.{u1, u3} R B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))))) (DistribSMul.toSMulZeroClass.{u1, u3} R B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))))) (DistribMulAction.toDistribSMul.{u1, u3} R B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u2, u3, max u2 u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (AlgHom.algHomClass.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5))))) f x)
 Case conversion may be inaccurate. Consider using '#align alg_hom.coe_cod_restrict AlgHom.coe_codRestrictₓ'. -/
 @[simp]
 theorem coe_codRestrict (f : A →ₐ[R] B) (S : Subalgebra R B) (hf : ∀ x, f x ∈ S) (x : A) :
@@ -1246,7 +1246,7 @@ theorem coe_codRestrict (f : A →ₐ[R] B) (S : Subalgebra R B) (hf : ∀ x, f
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] (f : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (S : Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (hf : forall (x : A), Membership.Mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.hasMem.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.setLike.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (fun (_x : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) => A -> B) ([anonymous].{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) f x) S), Iff (Function.Injective.{succ u2, succ u3} A (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.setLike.{u1, u3} R B _inst_1 _inst_4 _inst_5)) S) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R A (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.setLike.{u1, u3} R B _inst_1 _inst_4 _inst_5)) S) _inst_1 _inst_2 (Subalgebra.toSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S) _inst_3 (Subalgebra.algebra.{u1, u3} R B _inst_1 _inst_4 _inst_5 S)) (fun (_x : AlgHom.{u1, u2, u3} R A (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.setLike.{u1, u3} R B _inst_1 _inst_4 _inst_5)) S) _inst_1 _inst_2 (Subalgebra.toSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S) _inst_3 (Subalgebra.algebra.{u1, u3} R B _inst_1 _inst_4 _inst_5 S)) => A -> (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.setLike.{u1, u3} R B _inst_1 _inst_4 _inst_5)) S)) ([anonymous].{u1, u2, u3} R A (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.setLike.{u1, u3} R B _inst_1 _inst_4 _inst_5)) S) _inst_1 _inst_2 (Subalgebra.toSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S) _inst_3 (Subalgebra.algebra.{u1, u3} R B _inst_1 _inst_4 _inst_5 S)) (AlgHom.codRestrict.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 f S hf))) (Function.Injective.{succ u2, succ u3} A B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (fun (_x : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) => A -> B) ([anonymous].{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) f))
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] (f : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (S : Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (hf : forall (x : A), Membership.mem.{u3, u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) x) (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) _x) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (SMulZeroClass.toSMul.{u1, u2} R A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribSMul.toSMulZeroClass.{u1, u2} R A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toSMul.{u1, u3} R B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))))) (DistribSMul.toSMulZeroClass.{u1, u3} R B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))))) (DistribMulAction.toDistribSMul.{u1, u3} R B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u2, u3, max u2 u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (AlgHom.algHomClass.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5))))) f x) S), Iff (Function.Injective.{succ u2, succ u3} A (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} R A (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) _inst_1 _inst_2 (Subalgebra.toSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S) _inst_3 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S)) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) _x) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) _inst_1 _inst_2 (Subalgebra.toSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S) _inst_3 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S)) R A (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) (SMulZeroClass.toSMul.{u1, u2} R A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribSMul.toSMulZeroClass.{u1, u2} R A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toSMul.{u1, u3} R (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) (AddMonoid.toZero.{u3} (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) (AddCommMonoid.toAddMonoid.{u3} (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) (Subalgebra.toSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S)))))) (DistribSMul.toSMulZeroClass.{u1, u3} R (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) (AddMonoid.toAddZeroClass.{u3} (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) 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(Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) _inst_1 _inst_2 (Subalgebra.toSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S) _inst_3 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S)) (AlgHom.algHomClass.{u1, u2, u3} R A (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) _inst_1 _inst_2 (Subalgebra.toSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S) _inst_3 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S)))))) (AlgHom.codRestrict.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 f S hf))) (Function.Injective.{succ u2, succ u3} A B (FunLike.coe.{max (succ u2) (succ 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toSMul.{u1, u3} R B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))))) (DistribSMul.toSMulZeroClass.{u1, u3} R B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))))) (DistribMulAction.toDistribSMul.{u1, u3} R B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u2, u3, max u2 u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (AlgHom.algHomClass.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5))))) f))
+  forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] (f : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (S : Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (hf : forall (x : A), Membership.mem.{u3, u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) x) (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) _x) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (SMulZeroClass.toSMul.{u1, u2} R A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribSMul.toSMulZeroClass.{u1, u2} R A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toSMul.{u1, u3} R B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))))) (DistribSMul.toSMulZeroClass.{u1, u3} R B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))))) (DistribMulAction.toDistribSMul.{u1, u3} R B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u2, u3, max u2 u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (AlgHom.algHomClass.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5))))) f x) S), Iff (Function.Injective.{succ u2, succ u3} A (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} R A (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) _inst_1 _inst_2 (Subalgebra.toSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S) _inst_3 (Subalgebra.algebra.{u1, u3} R B _inst_1 _inst_4 _inst_5 S)) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) _x) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) _inst_1 _inst_2 (Subalgebra.toSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S) _inst_3 (Subalgebra.algebra.{u1, u3} R B _inst_1 _inst_4 _inst_5 S)) R A (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) (SMulZeroClass.toSMul.{u1, u2} R A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribSMul.toSMulZeroClass.{u1, u2} R A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toSMul.{u1, u3} R (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) (AddMonoid.toZero.{u3} (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) (AddCommMonoid.toAddMonoid.{u3} (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) 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(Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) (Subalgebra.toSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S)))) (Algebra.toModule.{u1, u3} R (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) _inst_1 (Subalgebra.toSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S) (Subalgebra.algebra.{u1, u3} R B _inst_1 _inst_4 _inst_5 S))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u2, u3, max u2 u3} R A (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) _inst_1 _inst_2 (Subalgebra.toSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S) _inst_3 (Subalgebra.algebra.{u1, u3} R B _inst_1 _inst_4 _inst_5 S) (AlgHom.{u1, u2, u3} R A (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) _inst_1 _inst_2 (Subalgebra.toSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S) _inst_3 (Subalgebra.algebra.{u1, u3} R B _inst_1 _inst_4 _inst_5 S)) (AlgHom.algHomClass.{u1, u2, u3} R A (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) _inst_1 _inst_2 (Subalgebra.toSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S) _inst_3 (Subalgebra.algebra.{u1, u3} R B _inst_1 _inst_4 _inst_5 S)))))) (AlgHom.codRestrict.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 f S hf))) (Function.Injective.{succ u2, succ u3} A B (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) _x) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (SMulZeroClass.toSMul.{u1, u2} R A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribSMul.toSMulZeroClass.{u1, u2} R A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toSMul.{u1, u3} R B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))))) (DistribSMul.toSMulZeroClass.{u1, u3} R B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))))) (DistribMulAction.toDistribSMul.{u1, u3} R B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u2, u3, max u2 u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (AlgHom.algHomClass.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5))))) f))
 Case conversion may be inaccurate. Consider using '#align alg_hom.injective_cod_restrict AlgHom.injective_codRestrictₓ'. -/
 theorem injective_codRestrict (f : A →ₐ[R] B) (S : Subalgebra R B) (hf : ∀ x, f x ∈ S) :
     Function.Injective (f.codRestrict S hf) ↔ Function.Injective f :=
@@ -1257,7 +1257,7 @@ theorem injective_codRestrict (f : A →ₐ[R] B) (S : Subalgebra R B) (hf : ∀
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] (f : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5), AlgHom.{u1, u2, u3} R A (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.setLike.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (AlgHom.range.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 f)) _inst_1 _inst_2 (Subalgebra.toSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 (AlgHom.range.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 f)) _inst_3 (Subalgebra.algebra.{u1, u3} R B _inst_1 _inst_4 _inst_5 (AlgHom.range.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 f))
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] (f : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5), AlgHom.{u1, u2, u3} R A (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x (AlgHom.range.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 f))) _inst_1 _inst_2 (Subalgebra.toSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 (AlgHom.range.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 f)) _inst_3 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 (AlgHom.range.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 f))
+  forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] (f : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5), AlgHom.{u1, u2, u3} R A (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x (AlgHom.range.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 f))) _inst_1 _inst_2 (Subalgebra.toSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 (AlgHom.range.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 f)) _inst_3 (Subalgebra.algebra.{u1, u3} R B _inst_1 _inst_4 _inst_5 (AlgHom.range.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 f))
 Case conversion may be inaccurate. Consider using '#align alg_hom.range_restrict AlgHom.rangeRestrictₓ'. -/
 /-- Restrict the codomain of a alg_hom `f` to `f.range`.
 
@@ -1363,7 +1363,7 @@ theorem ofInjective_apply (f : A →ₐ[R] B) (hf : Function.Injective f) (x : A
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {E : Type.{u2}} {F : Type.{u3}} [_inst_6 : DivisionRing.{u2} E] [_inst_7 : Semiring.{u3} F] [_inst_8 : Nontrivial.{u3} F] [_inst_9 : Algebra.{u1, u2} R E _inst_1 (Ring.toSemiring.{u2} E (DivisionRing.toRing.{u2} E _inst_6))] [_inst_10 : Algebra.{u1, u3} R F _inst_1 _inst_7] (f : AlgHom.{u1, u2, u3} R E F _inst_1 (Ring.toSemiring.{u2} E (DivisionRing.toRing.{u2} E _inst_6)) _inst_7 _inst_9 _inst_10), AlgEquiv.{u1, u2, u3} R E (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u1, u3} R F _inst_1 _inst_7 _inst_10) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u1, u3} R F _inst_1 _inst_7 _inst_10) F (Subalgebra.setLike.{u1, u3} R F _inst_1 _inst_7 _inst_10)) (AlgHom.range.{u1, u2, u3} R E F _inst_1 (Ring.toSemiring.{u2} E (DivisionRing.toRing.{u2} E _inst_6)) _inst_9 _inst_7 _inst_10 f)) _inst_1 (Ring.toSemiring.{u2} E (DivisionRing.toRing.{u2} E _inst_6)) (Subalgebra.toSemiring.{u1, u3} R F _inst_1 _inst_7 _inst_10 (AlgHom.range.{u1, u2, u3} R E F _inst_1 (Ring.toSemiring.{u2} E (DivisionRing.toRing.{u2} E _inst_6)) _inst_9 _inst_7 _inst_10 f)) _inst_9 (Subalgebra.algebra.{u1, u3} R F _inst_1 _inst_7 _inst_10 (AlgHom.range.{u1, u2, u3} R E F _inst_1 (Ring.toSemiring.{u2} E (DivisionRing.toRing.{u2} E _inst_6)) _inst_9 _inst_7 _inst_10 f))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {E : Type.{u2}} {F : Type.{u3}} [_inst_6 : DivisionRing.{u2} E] [_inst_7 : Semiring.{u3} F] [_inst_8 : Nontrivial.{u3} F] [_inst_9 : Algebra.{u1, u2} R E _inst_1 (DivisionSemiring.toSemiring.{u2} E (DivisionRing.toDivisionSemiring.{u2} E _inst_6))] [_inst_10 : Algebra.{u1, u3} R F _inst_1 _inst_7] (f : AlgHom.{u1, u2, u3} R E F _inst_1 (DivisionSemiring.toSemiring.{u2} E (DivisionRing.toDivisionSemiring.{u2} E _inst_6)) _inst_7 _inst_9 _inst_10), AlgEquiv.{u1, u2, u3} R E (Subtype.{succ u3} F (fun (x : F) => Membership.mem.{u3, u3} F (Subalgebra.{u1, u3} R F _inst_1 _inst_7 _inst_10) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R F _inst_1 _inst_7 _inst_10) F (Subalgebra.instSetLikeSubalgebra.{u1, u3} R F _inst_1 _inst_7 _inst_10)) x (AlgHom.range.{u1, u2, u3} R E F _inst_1 (DivisionSemiring.toSemiring.{u2} E (DivisionRing.toDivisionSemiring.{u2} E _inst_6)) _inst_9 _inst_7 _inst_10 f))) _inst_1 (DivisionSemiring.toSemiring.{u2} E (DivisionRing.toDivisionSemiring.{u2} E _inst_6)) (Subalgebra.toSemiring.{u1, u3} R F _inst_1 _inst_7 _inst_10 (AlgHom.range.{u1, u2, u3} R E F _inst_1 (DivisionSemiring.toSemiring.{u2} E (DivisionRing.toDivisionSemiring.{u2} E _inst_6)) _inst_9 _inst_7 _inst_10 f)) _inst_9 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u3} R F _inst_1 _inst_7 _inst_10 (AlgHom.range.{u1, u2, u3} R E F _inst_1 (DivisionSemiring.toSemiring.{u2} E (DivisionRing.toDivisionSemiring.{u2} E _inst_6)) _inst_9 _inst_7 _inst_10 f))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {E : Type.{u2}} {F : Type.{u3}} [_inst_6 : DivisionRing.{u2} E] [_inst_7 : Semiring.{u3} F] [_inst_8 : Nontrivial.{u3} F] [_inst_9 : Algebra.{u1, u2} R E _inst_1 (DivisionSemiring.toSemiring.{u2} E (DivisionRing.toDivisionSemiring.{u2} E _inst_6))] [_inst_10 : Algebra.{u1, u3} R F _inst_1 _inst_7] (f : AlgHom.{u1, u2, u3} R E F _inst_1 (DivisionSemiring.toSemiring.{u2} E (DivisionRing.toDivisionSemiring.{u2} E _inst_6)) _inst_7 _inst_9 _inst_10), AlgEquiv.{u1, u2, u3} R E (Subtype.{succ u3} F (fun (x : F) => Membership.mem.{u3, u3} F (Subalgebra.{u1, u3} R F _inst_1 _inst_7 _inst_10) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R F _inst_1 _inst_7 _inst_10) F (Subalgebra.instSetLikeSubalgebra.{u1, u3} R F _inst_1 _inst_7 _inst_10)) x (AlgHom.range.{u1, u2, u3} R E F _inst_1 (DivisionSemiring.toSemiring.{u2} E (DivisionRing.toDivisionSemiring.{u2} E _inst_6)) _inst_9 _inst_7 _inst_10 f))) _inst_1 (DivisionSemiring.toSemiring.{u2} E (DivisionRing.toDivisionSemiring.{u2} E _inst_6)) (Subalgebra.toSemiring.{u1, u3} R F _inst_1 _inst_7 _inst_10 (AlgHom.range.{u1, u2, u3} R E F _inst_1 (DivisionSemiring.toSemiring.{u2} E (DivisionRing.toDivisionSemiring.{u2} E _inst_6)) _inst_9 _inst_7 _inst_10 f)) _inst_9 (Subalgebra.algebra.{u1, u3} R F _inst_1 _inst_7 _inst_10 (AlgHom.range.{u1, u2, u3} R E F _inst_1 (DivisionSemiring.toSemiring.{u2} E (DivisionRing.toDivisionSemiring.{u2} E _inst_6)) _inst_9 _inst_7 _inst_10 f))
 Case conversion may be inaccurate. Consider using '#align alg_equiv.of_injective_field AlgEquiv.ofInjectiveFieldₓ'. -/
 /-- Restrict an algebra homomorphism between fields to an algebra isomorphism -/
 noncomputable def ofInjectiveField {E F : Type _} [DivisionRing E] [Semiring F] [Nontrivial F]
@@ -1375,7 +1375,7 @@ noncomputable def ofInjectiveField {E F : Type _} [DivisionRing E] [Semiring F]
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Semiring.{u3} B] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_3] (e : AlgEquiv.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5) (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4), AlgEquiv.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4)) S) (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u1, u3} R B _inst_1 _inst_3 _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_3 _inst_5) B (Subalgebra.setLike.{u1, u3} R B _inst_1 _inst_3 _inst_5)) (Subalgebra.map.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 (AlgEquiv.toAlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 e) S)) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_4 S) (Subalgebra.toSemiring.{u1, u3} R B _inst_1 _inst_3 _inst_5 (Subalgebra.map.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 (AlgEquiv.toAlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 e) S)) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 S) (Subalgebra.algebra.{u1, u3} R B _inst_1 _inst_3 _inst_5 (Subalgebra.map.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 (AlgEquiv.toAlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 e) S))
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Semiring.{u3} B] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_3] (e : AlgEquiv.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5) (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4), AlgEquiv.{u1, u2, u3} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4)) x S)) (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_3 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_3 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_3 _inst_5)) x (Subalgebra.map.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 (AlgEquiv.toAlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 e) S))) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_4 S) (Subalgebra.toSemiring.{u1, u3} R B _inst_1 _inst_3 _inst_5 (Subalgebra.map.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 (AlgEquiv.toAlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 e) S)) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_4 S) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u3} R B _inst_1 _inst_3 _inst_5 (Subalgebra.map.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 (AlgEquiv.toAlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 e) S))
+  forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Semiring.{u3} B] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_3] (e : AlgEquiv.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5) (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4), AlgEquiv.{u1, u2, u3} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4)) x S)) (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_3 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_3 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_3 _inst_5)) x (Subalgebra.map.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 (AlgEquiv.toAlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 e) S))) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_4 S) (Subalgebra.toSemiring.{u1, u3} R B _inst_1 _inst_3 _inst_5 (Subalgebra.map.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 (AlgEquiv.toAlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 e) S)) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 S) (Subalgebra.algebra.{u1, u3} R B _inst_1 _inst_3 _inst_5 (Subalgebra.map.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 (AlgEquiv.toAlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 e) S))
 Case conversion may be inaccurate. Consider using '#align alg_equiv.subalgebra_map AlgEquiv.subalgebraMapₓ'. -/
 /-- Given an equivalence `e : A ≃ₐ[R] B` of `R`-algebras and a subalgebra `S` of `A`,
 `subalgebra_map` is the induced equivalence between `S` and `S.map e` -/
@@ -1800,7 +1800,7 @@ theorem comap_top (f : A →ₐ[R] B) : (⊤ : Subalgebra R B).comap f = ⊤ :=
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], AlgHom.{u1, u2, u2} R A (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Top.top.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toHasTop.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) _inst_1 _inst_2 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (Top.top.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toHasTop.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) _inst_3 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (Top.top.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toHasTop.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))))
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], AlgHom.{u1, u2, u2} R A (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x (Top.top.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toTop.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) _inst_1 _inst_2 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (Top.top.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toTop.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) _inst_3 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (Top.top.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toTop.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))))
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], AlgHom.{u1, u2, u2} R A (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x (Top.top.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toTop.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) _inst_1 _inst_2 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (Top.top.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toTop.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) _inst_3 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (Top.top.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toTop.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))))
 Case conversion may be inaccurate. Consider using '#align algebra.to_top Algebra.toTopₓ'. -/
 /-- `alg_hom` to `⊤ : subalgebra R A`. -/
 def toTop : A →ₐ[R] (⊤ : Subalgebra R A) :=
@@ -1838,7 +1838,7 @@ theorem bijective_algebraMap_iff {R A : Type _} [Field R] [Semiring A] [Nontrivi
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], (Function.Injective.{succ u1, succ u2} R A (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3))) -> (AlgEquiv.{u1, u2, u1} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Bot.bot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toHasBot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) R _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (Bot.bot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toHasBot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (CommSemiring.toSemiring.{u1} R _inst_1) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (Bot.bot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toHasBot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Algebra.id.{u1} R _inst_1))
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], (Function.Injective.{succ u1, succ u2} R A (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3))) -> (AlgEquiv.{u1, u2, u1} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x (Bot.bot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toBot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) R _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (Bot.bot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toBot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (CommSemiring.toSemiring.{u1} R _inst_1) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (Bot.bot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toBot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Algebra.id.{u1} R _inst_1))
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], (Function.Injective.{succ u1, succ u2} R A (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3))) -> (AlgEquiv.{u1, u2, u1} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x (Bot.bot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toBot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) R _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (Bot.bot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toBot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (CommSemiring.toSemiring.{u1} R _inst_1) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (Bot.bot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toBot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Algebra.id.{u1} R _inst_1))
 Case conversion may be inaccurate. Consider using '#align algebra.bot_equiv_of_injective Algebra.botEquivOfInjectiveₓ'. -/
 /-- The bottom subalgebra is isomorphic to the base ring. -/
 noncomputable def botEquivOfInjective (h : Function.Injective (algebraMap R A)) :
@@ -1854,7 +1854,7 @@ noncomputable def botEquivOfInjective (h : Function.Injective (algebraMap R A))
 lean 3 declaration is
   forall (F : Type.{u1}) (R : Type.{u2}) [_inst_6 : Field.{u1} F] [_inst_7 : Semiring.{u2} R] [_inst_8 : Nontrivial.{u2} R] [_inst_9 : Algebra.{u1, u2} F R (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_6)) _inst_7], AlgEquiv.{u1, u2, u1} F (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} F R (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_6)) _inst_7 _inst_9) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} F R (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_6)) _inst_7 _inst_9) R (Subalgebra.setLike.{u1, u2} F R (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_6)) _inst_7 _inst_9)) (Bot.bot.{u2} (Subalgebra.{u1, u2} F R (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_6)) _inst_7 _inst_9) (CompleteLattice.toHasBot.{u2} (Subalgebra.{u1, u2} F R (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_6)) _inst_7 _inst_9) (Algebra.Subalgebra.completeLattice.{u1, u2} F R (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_6)) _inst_7 _inst_9)))) F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_6)) (Subalgebra.toSemiring.{u1, u2} F R (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_6)) _inst_7 _inst_9 (Bot.bot.{u2} (Subalgebra.{u1, u2} F R (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_6)) _inst_7 _inst_9) (CompleteLattice.toHasBot.{u2} (Subalgebra.{u1, u2} F R (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_6)) _inst_7 _inst_9) (Algebra.Subalgebra.completeLattice.{u1, u2} F R (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_6)) _inst_7 _inst_9)))) (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_6))) (Subalgebra.algebra.{u1, u2} F R (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_6)) _inst_7 _inst_9 (Bot.bot.{u2} (Subalgebra.{u1, u2} F R (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_6)) _inst_7 _inst_9) (CompleteLattice.toHasBot.{u2} (Subalgebra.{u1, u2} F R (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_6)) _inst_7 _inst_9) (Algebra.Subalgebra.completeLattice.{u1, u2} F R (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_6)) _inst_7 _inst_9)))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_6)))
 but is expected to have type
-  forall (F : Type.{u1}) (R : Type.{u2}) [_inst_6 : Field.{u1} F] [_inst_7 : Semiring.{u2} R] [_inst_8 : Nontrivial.{u2} R] [_inst_9 : Algebra.{u1, u2} F R (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_6)) _inst_7], AlgEquiv.{u1, u2, u1} F (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Subalgebra.{u1, u2} F R (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_6)) _inst_7 _inst_9) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} F R (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_6)) _inst_7 _inst_9) R (Subalgebra.instSetLikeSubalgebra.{u1, u2} F R (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_6)) _inst_7 _inst_9)) x (Bot.bot.{u2} (Subalgebra.{u1, u2} F R (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_6)) _inst_7 _inst_9) (CompleteLattice.toBot.{u2} (Subalgebra.{u1, u2} F R (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_6)) _inst_7 _inst_9) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} F R (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_6)) _inst_7 _inst_9))))) F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_6)) (Subalgebra.toSemiring.{u1, u2} F R (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_6)) _inst_7 _inst_9 (Bot.bot.{u2} (Subalgebra.{u1, u2} F R (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_6)) _inst_7 _inst_9) (CompleteLattice.toBot.{u2} (Subalgebra.{u1, u2} F R (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_6)) _inst_7 _inst_9) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} F R (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_6)) _inst_7 _inst_9)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_6))) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} F R (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_6)) _inst_7 _inst_9 (Bot.bot.{u2} (Subalgebra.{u1, u2} F R (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_6)) _inst_7 _inst_9) (CompleteLattice.toBot.{u2} (Subalgebra.{u1, u2} F R (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_6)) _inst_7 _inst_9) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} F R (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_6)) _inst_7 _inst_9)))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_6)))
+  forall (F : Type.{u1}) (R : Type.{u2}) [_inst_6 : Field.{u1} F] [_inst_7 : Semiring.{u2} R] [_inst_8 : Nontrivial.{u2} R] [_inst_9 : Algebra.{u1, u2} F R (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_6)) _inst_7], AlgEquiv.{u1, u2, u1} F (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Subalgebra.{u1, u2} F R (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_6)) _inst_7 _inst_9) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} F R (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_6)) _inst_7 _inst_9) R (Subalgebra.instSetLikeSubalgebra.{u1, u2} F R (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_6)) _inst_7 _inst_9)) x (Bot.bot.{u2} (Subalgebra.{u1, u2} F R (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_6)) _inst_7 _inst_9) (CompleteLattice.toBot.{u2} (Subalgebra.{u1, u2} F R (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_6)) _inst_7 _inst_9) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} F R (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_6)) _inst_7 _inst_9))))) F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_6)) (Subalgebra.toSemiring.{u1, u2} F R (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_6)) _inst_7 _inst_9 (Bot.bot.{u2} (Subalgebra.{u1, u2} F R (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_6)) _inst_7 _inst_9) (CompleteLattice.toBot.{u2} (Subalgebra.{u1, u2} F R (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_6)) _inst_7 _inst_9) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} F R (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_6)) _inst_7 _inst_9)))) (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_6))) (Subalgebra.algebra.{u1, u2} F R (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_6)) _inst_7 _inst_9 (Bot.bot.{u2} (Subalgebra.{u1, u2} F R (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_6)) _inst_7 _inst_9) (CompleteLattice.toBot.{u2} (Subalgebra.{u1, u2} F R (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_6)) _inst_7 _inst_9) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} F R (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_6)) _inst_7 _inst_9)))) (Algebra.id.{u1} F (Semifield.toCommSemiring.{u1} F (Field.toSemifield.{u1} F _inst_6)))
 Case conversion may be inaccurate. Consider using '#align algebra.bot_equiv Algebra.botEquivₓ'. -/
 /-- The bottom subalgebra is isomorphic to the field. -/
 @[simps symm_apply]
@@ -1879,7 +1879,7 @@ variable (S : Subalgebra R A)
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], AlgEquiv.{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Top.top.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toHasTop.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (Top.top.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toHasTop.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) _inst_2 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (Top.top.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toHasTop.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) _inst_3
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], AlgEquiv.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x (Top.top.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toTop.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (Top.top.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toTop.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) _inst_2 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (Top.top.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toTop.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) _inst_3
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], AlgEquiv.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x (Top.top.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toTop.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (Top.top.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toTop.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) _inst_2 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (Top.top.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toTop.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) _inst_3
 Case conversion may be inaccurate. Consider using '#align subalgebra.top_equiv Subalgebra.topEquivₓ'. -/
 /-- The top subalgebra is isomorphic to the algebra.
 
@@ -1917,11 +1917,15 @@ instance AlgEquiv.subsingleton_right [Subsingleton (Subalgebra R B)] : Subsingle
 #align alg_equiv.subsingleton_right AlgEquiv.subsingleton_right
 -/
 
-#print Subalgebra.range_val /-
+/- warning: subalgebra.range_val -> Subalgebra.range_val is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), Eq.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (AlgHom.range.{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_2 _inst_3 (Subalgebra.val.{u1, u2} R A _inst_1 _inst_2 _inst_3 S)) S
+but is expected to have type
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), Eq.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (AlgHom.range.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_2 _inst_3 (Subalgebra.val.{u1, u2} R A _inst_1 _inst_2 _inst_3 S)) S
+Case conversion may be inaccurate. Consider using '#align subalgebra.range_val Subalgebra.range_valₓ'. -/
 theorem range_val : S.val.range = S :=
   ext <| Set.ext_iff.1 <| S.val.coe_range.trans Subtype.range_val
 #align subalgebra.range_val Subalgebra.range_val
--/
 
 instance : Unique (Subalgebra R R) :=
   { Algebra.Subalgebra.inhabited with
@@ -1934,7 +1938,7 @@ instance : Unique (Subalgebra R R) :=
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3} {T : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3}, (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) S T) -> (AlgHom.{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 T))
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3} {T : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3}, (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) S T) -> (AlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T)) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T))
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3} {T : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3}, (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) S T) -> (AlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T)) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 T))
 Case conversion may be inaccurate. Consider using '#align subalgebra.inclusion Subalgebra.inclusionₓ'. -/
 /-- The map `S → T` when `S` is a subalgebra contained in the subalgebra `T`.
 
@@ -1953,7 +1957,7 @@ def inclusion {S T : Subalgebra R A} (h : S ≤ T) : S →ₐ[R] T
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3} {T : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3} (h : LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) S T), Function.Injective.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T) (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 T)) (fun (_x : AlgHom.{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 T)) => (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) -> (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T)) ([anonymous].{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 T)) (Subalgebra.inclusion.{u1, u2} R A _inst_1 _inst_2 _inst_3 S T h))
 but is expected to have type
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+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3} {T : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3} (h : LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) S T), Function.Injective.{succ u2, succ u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A 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 Case conversion may be inaccurate. Consider using '#align subalgebra.inclusion_injective Subalgebra.inclusion_injectiveₓ'. -/
 theorem inclusion_injective {S T : Subalgebra R A} (h : S ≤ T) : Function.Injective (inclusion h) :=
   fun _ _ => Subtype.ext ∘ Subtype.mk.inj
@@ -1963,7 +1967,7 @@ theorem inclusion_injective {S T : Subalgebra R A} (h : S ≤ T) : Function.Inje
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3}, Eq.{succ u2} (AlgHom.{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S)) (Subalgebra.inclusion.{u1, u2} R A _inst_1 _inst_2 _inst_3 S S (le_refl.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) S)) (AlgHom.id.{u1, u2} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S))
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3}, Eq.{succ u2} (AlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S)) (Subalgebra.inclusion.{u1, u2} R A _inst_1 _inst_2 _inst_3 S S (le_refl.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) S)) (AlgHom.id.{u1, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S))
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3}, Eq.{succ u2} (AlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S)) (Subalgebra.inclusion.{u1, u2} R A _inst_1 _inst_2 _inst_3 S S (le_refl.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) S)) (AlgHom.id.{u1, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S))
 Case conversion may be inaccurate. Consider using '#align subalgebra.inclusion_self Subalgebra.inclusion_selfₓ'. -/
 @[simp]
 theorem inclusion_self {S : Subalgebra R A} : inclusion (le_refl S) = AlgHom.id R S :=
@@ -1974,7 +1978,7 @@ theorem inclusion_self {S : Subalgebra R A} : inclusion (le_refl S) = AlgHom.id
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3} {T : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3} (h : LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) S T) (x : A) (hx : Membership.Mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S), Eq.{succ u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T) (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 T)) (fun (_x : AlgHom.{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 T)) => (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) -> (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T)) ([anonymous].{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 T)) (Subalgebra.inclusion.{u1, u2} R A _inst_1 _inst_2 _inst_3 S T h) (Subtype.mk.{succ u2} A (fun (x : A) => Membership.Mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S) x hx)) (Subtype.mk.{succ u2} A (fun (x : A) => Membership.Mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T) x (h x hx))
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3} {T : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3} (h : LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) S T) (x : A) (hx : Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T)) (Subtype.mk.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S) x hx)) (FunLike.coe.{succ u2, succ u2, succ u2} (AlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T)) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T)) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (fun (_x : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) 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u2} R A _inst_1 _inst_2 _inst_3)) x T)) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T)) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T)) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T)))) (Algebra.toModule.{u1, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T)) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 T))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T)) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 T)) R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T)) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T)) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T)) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T))) (Module.toDistribMulAction.{u1, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S)))) (Algebra.toModule.{u1, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S))) (Module.toDistribMulAction.{u1, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T)) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} 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(SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T)) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 T))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u2, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T)) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) (AlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T)) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 T)) (AlgHom.algHomClass.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T)) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 T)))))) (Subalgebra.inclusion.{u1, u2} R A _inst_1 _inst_2 _inst_3 S T h) (Subtype.mk.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S) x hx)) (Subtype.mk.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T) x (h x hx))
 Case conversion may be inaccurate. Consider using '#align subalgebra.inclusion_mk Subalgebra.inclusion_mkₓ'. -/
 @[simp]
 theorem inclusion_mk {S T : Subalgebra R A} (h : S ≤ T) (x : A) (hx : x ∈ S) :
@@ -1986,7 +1990,7 @@ theorem inclusion_mk {S T : Subalgebra R A} (h : S ≤ T) (x : A) (hx : x ∈ S)
 lean 3 declaration is
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Membership.Mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T) A (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T) A (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A 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(SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T)) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T)) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T)))) (Algebra.toModule.{u1, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T)) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 T))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T)) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 T)) R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T)) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T)) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S)))) (Algebra.toModule.{u1, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S))) (Module.toDistribMulAction.{u1, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T)) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) 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(AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u2, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T)) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) (AlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T)) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 T)) (AlgHom.algHomClass.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T)) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 T)))))) (Subalgebra.inclusion.{u1, u2} R A _inst_1 _inst_2 _inst_3 S T h) (Subtype.mk.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S) (Subtype.val.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) x (SetLike.coe.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) T)) x) m)) x
 Case conversion may be inaccurate. Consider using '#align subalgebra.inclusion_right Subalgebra.inclusion_rightₓ'. -/
 theorem inclusion_right {S T : Subalgebra R A} (h : S ≤ T) (x : T) (m : (x : A) ∈ S) :
     inclusion h ⟨x, m⟩ = x :=
@@ -1997,7 +2001,7 @@ theorem inclusion_right {S T : Subalgebra R A} (h : S ≤ T) (x : T) (m : (x : A
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3} {T : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3} {U : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3} (hst : LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) S T) (htu : LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} 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 but is expected to have type
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A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x U)) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x U)) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 U)))) (Algebra.toModule.{u1, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x U)) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 U) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 U))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u2, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x U)) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 U) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 U) (AlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x U)) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 U) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 U)) (AlgHom.algHomClass.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x U)) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 U) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 U)))))) (Subalgebra.inclusion.{u1, u2} R A _inst_1 _inst_2 _inst_3 S U (le_trans.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) S T U hst htu)) x)
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3} {T : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3} {U : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3} (hst : LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) S T) (htu : LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, 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(Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 U)) R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x U)) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x U)) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x U)) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 U))) (Module.toDistribMulAction.{u1, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 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(Module.toDistribMulAction.{u1, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x U)) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x U)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x U)) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x U)) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 U)))) (Algebra.toModule.{u1, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x U)) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 U) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 U))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u2, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x U)) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 U) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 U) (AlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x U)) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 U) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 U)) (AlgHom.algHomClass.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x U)) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 U) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 U)))))) (Subalgebra.inclusion.{u1, u2} R A _inst_1 _inst_2 _inst_3 S U (le_trans.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) S T U hst htu)) x)
 Case conversion may be inaccurate. Consider using '#align subalgebra.inclusion_inclusion Subalgebra.inclusion_inclusionₓ'. -/
 @[simp]
 theorem inclusion_inclusion {S T U : Subalgebra R A} (hst : S ≤ T) (htu : T ≤ U) (x : S) :
@@ -2009,7 +2013,7 @@ theorem inclusion_inclusion {S T U : Subalgebra R A} (hst : S ≤ T) (htu : T 
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3} {T : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3} (h : LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) S T) (s : coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S), Eq.{succ u2} A ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T) A (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T) A (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T) A (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 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 but is expected to have type
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+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3} {T : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3} (h : LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) S T) (s : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, 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_inst_2 _inst_3)) x T)) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T)))) (Algebra.toModule.{u1, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T)) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 T))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u2, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T)) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) (AlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T)) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 T)) (AlgHom.algHomClass.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T)) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 T)))))) (Subalgebra.inclusion.{u1, u2} R A _inst_1 _inst_2 _inst_3 S T h) s)) (Subtype.val.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) x (SetLike.coe.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) S)) s)
 Case conversion may be inaccurate. Consider using '#align subalgebra.coe_inclusion Subalgebra.coe_inclusionₓ'. -/
 @[simp]
 theorem coe_inclusion {S T : Subalgebra R A} (h : S ≤ T) (s : S) : (inclusion h s : A) = s :=
@@ -2020,7 +2024,7 @@ theorem coe_inclusion {S T : Subalgebra R A} (h : S ≤ T) (s : S) : (inclusion
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (T : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), (Eq.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) S T) -> (AlgEquiv.{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 T))
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (T : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), (Eq.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) S T) -> (AlgEquiv.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T)) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T))
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (T : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), (Eq.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) S T) -> (AlgEquiv.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T)) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 T))
 Case conversion may be inaccurate. Consider using '#align subalgebra.equiv_of_eq Subalgebra.equivOfEqₓ'. -/
 /-- Two subalgebras that are equal are also equivalent as algebras.
 
@@ -2040,7 +2044,7 @@ def equivOfEq (S T : Subalgebra R A) (h : S = T) : S ≃ₐ[R] T :=
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (T : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (h : Eq.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) S T), Eq.{succ u2} (AlgEquiv.{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T) (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S)) (AlgEquiv.symm.{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) (Subalgebra.equivOfEq.{u1, u2} R A _inst_1 _inst_2 _inst_3 S T h)) (Subalgebra.equivOfEq.{u1, u2} R A _inst_1 _inst_2 _inst_3 T S (Eq.symm.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) S T h))
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (T : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (h : Eq.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) S T), Eq.{succ u2} (AlgEquiv.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T)) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S)) (AlgEquiv.symm.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T)) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) (Subalgebra.equivOfEq.{u1, u2} R A _inst_1 _inst_2 _inst_3 S T h)) (Subalgebra.equivOfEq.{u1, u2} R A _inst_1 _inst_2 _inst_3 T S (Eq.symm.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) S T h))
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (T : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (h : Eq.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) S T), Eq.{succ u2} (AlgEquiv.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T)) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S)) (AlgEquiv.symm.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T)) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) (Subalgebra.equivOfEq.{u1, u2} R A _inst_1 _inst_2 _inst_3 S T h)) (Subalgebra.equivOfEq.{u1, u2} R A _inst_1 _inst_2 _inst_3 T S (Eq.symm.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) S T h))
 Case conversion may be inaccurate. Consider using '#align subalgebra.equiv_of_eq_symm Subalgebra.equivOfEq_symmₓ'. -/
 @[simp]
 theorem equivOfEq_symm (S T : Subalgebra R A) (h : S = T) :
@@ -2052,7 +2056,7 @@ theorem equivOfEq_symm (S T : Subalgebra R A) (h : S = T) :
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), Eq.{succ u2} (AlgEquiv.{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S)) (Subalgebra.equivOfEq.{u1, u2} R A _inst_1 _inst_2 _inst_3 S S (rfl.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) S)) (AlgEquiv.refl.{u1, u2} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S))
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), Eq.{succ u2} (AlgEquiv.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S)) (Subalgebra.equivOfEq.{u1, u2} R A _inst_1 _inst_2 _inst_3 S S (rfl.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) S)) (AlgEquiv.refl.{u1, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S))
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), Eq.{succ u2} (AlgEquiv.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S)) (Subalgebra.equivOfEq.{u1, u2} R A _inst_1 _inst_2 _inst_3 S S (rfl.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) S)) (AlgEquiv.refl.{u1, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S))
 Case conversion may be inaccurate. Consider using '#align subalgebra.equiv_of_eq_rfl Subalgebra.equivOfEq_rflₓ'. -/
 @[simp]
 theorem equivOfEq_rfl (S : Subalgebra R A) : equivOfEq S S rfl = AlgEquiv.refl :=
@@ -2065,7 +2069,7 @@ theorem equivOfEq_rfl (S : Subalgebra R A) : equivOfEq S S rfl = AlgEquiv.refl :
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (T : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (U : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (hST : Eq.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) S T) (hTU : Eq.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) T U), Eq.{succ u2} (AlgEquiv.{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) U) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 U) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 U)) (AlgEquiv.trans.{u1, u2, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T) (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) U) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 U) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 U) (Subalgebra.equivOfEq.{u1, u2} R A _inst_1 _inst_2 _inst_3 S T hST) (Subalgebra.equivOfEq.{u1, u2} R A _inst_1 _inst_2 _inst_3 T U hTU)) (Subalgebra.equivOfEq.{u1, u2} R A _inst_1 _inst_2 _inst_3 S U (trans.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Eq.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IsPreorder.to_isTrans.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Eq.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IsEquiv.to_isPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Eq.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (eq_isEquiv.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) S T U hST hTU))
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (T : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (U : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (hST : Eq.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) S T) (hTU : Eq.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) T U), Eq.{succ u2} (AlgEquiv.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x U)) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 U) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 U)) (AlgEquiv.trans.{u1, u2, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T)) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x U)) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 U) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 U) (Subalgebra.equivOfEq.{u1, u2} R A _inst_1 _inst_2 _inst_3 S T hST) (Subalgebra.equivOfEq.{u1, u2} R A _inst_1 _inst_2 _inst_3 T U hTU)) (Subalgebra.equivOfEq.{u1, u2} R A _inst_1 _inst_2 _inst_3 S U (Eq.trans.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) S T U hST hTU))
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (T : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (U : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (hST : Eq.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) S T) (hTU : Eq.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) T U), Eq.{succ u2} (AlgEquiv.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x U)) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 U) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 U)) (AlgEquiv.trans.{u1, u2, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T)) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x U)) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 U) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 U) (Subalgebra.equivOfEq.{u1, u2} R A _inst_1 _inst_2 _inst_3 S T hST) (Subalgebra.equivOfEq.{u1, u2} R A _inst_1 _inst_2 _inst_3 T U hTU)) (Subalgebra.equivOfEq.{u1, u2} R A _inst_1 _inst_2 _inst_3 S U (Eq.trans.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) S T U hST hTU))
 Case conversion may be inaccurate. Consider using '#align subalgebra.equiv_of_eq_trans Subalgebra.equivOfEq_transₓ'. -/
 @[simp]
 theorem equivOfEq_trans (S T U : Subalgebra R A) (hST : S = T) (hTU : T = U) :
@@ -2169,7 +2173,7 @@ variable {ι : Type _}
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {ι : Type.{u3}} [_inst_6 : Nonempty.{succ u3} ι] {S : ι -> (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)}, (Directed.{u2, succ u3} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) ι (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) S) -> (Eq.{succ u2} (Set.{u2} A) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (iSup.{u2, succ u3} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))) ι S)) (Set.iUnion.{u2, succ u3} A ι (fun (i : ι) => (fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (S i))))
 but is expected to have type
-  forall {R : Type.{u2}} {A : Type.{u3}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u3} A] [_inst_3 : Algebra.{u2, u3} R A _inst_1 _inst_2] {ι : Type.{u1}} [_inst_6 : Nonempty.{succ u1} ι] {S : ι -> (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)}, (Directed.{u3, succ u1} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) ι (fun (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.12746 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.12748 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) => LE.le.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3))))) x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.12746 x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.12748) S) -> (Eq.{succ u3} (Set.{u3} A) (SetLike.coe.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (iSup.{u3, succ u1} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3))) ι S)) (Set.iUnion.{u3, succ u1} A ι (fun (i : ι) => SetLike.coe.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (S i))))
+  forall {R : Type.{u2}} {A : Type.{u3}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u3} A] [_inst_3 : Algebra.{u2, u3} R A _inst_1 _inst_2] {ι : Type.{u1}} [_inst_6 : Nonempty.{succ u1} ι] {S : ι -> (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)}, (Directed.{u3, succ u1} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) ι (fun (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.12747 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.12749 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) => LE.le.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3))))) x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.12747 x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.12749) S) -> (Eq.{succ u3} (Set.{u3} A) (SetLike.coe.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (iSup.{u3, succ u1} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3))) ι S)) (Set.iUnion.{u3, succ u1} A ι (fun (i : ι) => SetLike.coe.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (S i))))
 Case conversion may be inaccurate. Consider using '#align subalgebra.coe_supr_of_directed Subalgebra.coe_iSup_of_directedₓ'. -/
 theorem coe_iSup_of_directed [Nonempty ι] {S : ι → Subalgebra R A} (dir : Directed (· ≤ ·) S) :
     ↑(iSup S) = ⋃ i, (S i : Set A) :=
@@ -2198,7 +2202,7 @@ theorem coe_iSup_of_directed [Nonempty ι] {S : ι → Subalgebra R A} (dir : Di
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {ι : Type.{u4}} [_inst_6 : Nonempty.{succ u4} ι] (K : ι -> (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)), (Directed.{u2, succ u4} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) ι (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) K) -> (forall (f : forall (i : ι), AlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K i)) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5), (forall (i : ι) (j : ι) (h : LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (K i) (K j)), Eq.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K i)) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) (f i) (AlgHom.comp.{u1, u2, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K i)) (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K j)) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K j)) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K j)) _inst_5 (f j) (Subalgebra.inclusion.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i) (K j) h))) -> (forall (T : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), (Eq.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) T (iSup.{u2, succ u4} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))) ι K)) -> (AlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) _inst_5)))
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {ι : Type.{u4}} [_inst_6 : Nonempty.{succ u4} ι] (K : ι -> (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)), (Directed.{u2, succ u4} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) ι (fun (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13129 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13131 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13129 x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13131) K) -> (forall (f : forall (i : ι), AlgHom.{u1, u2, u3} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5), (forall (i : ι) (j : ι) (h : LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (K i) (K j)), Eq.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) (f i) (AlgHom.comp.{u1, u2, u2, u3} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x (K j))) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K j)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K j)) _inst_5 (f j) (Subalgebra.inclusion.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i) (K j) h))) -> (forall (T : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), (Eq.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) T (iSup.{u2, succ u4} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))) ι K)) -> (AlgHom.{u1, u2, u3} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T)) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) _inst_5)))
+  forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {ι : Type.{u4}} [_inst_6 : Nonempty.{succ u4} ι] (K : ι -> (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)), (Directed.{u2, succ u4} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) ι (fun (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13130 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13132 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13130 x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13132) K) -> (forall (f : forall (i : ι), AlgHom.{u1, u2, u3} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5), (forall (i : ι) (j : ι) (h : LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (K i) (K j)), Eq.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) (f i) (AlgHom.comp.{u1, u2, u2, u3} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x (K j))) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K j)) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K j)) _inst_5 (f j) (Subalgebra.inclusion.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i) (K j) h))) -> (forall (T : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), (Eq.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) T (iSup.{u2, succ u4} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))) ι K)) -> (AlgHom.{u1, u2, u3} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T)) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) _inst_5)))
 Case conversion may be inaccurate. Consider using '#align subalgebra.supr_lift Subalgebra.iSupLiftₓ'. -/
 /-- Define an algebra homomorphism on a directed supremum of subalgebras by defining
 it on each subalgebra, and proving that it agrees on the intersection of subalgebras. -/
@@ -2235,7 +2239,7 @@ variable [Nonempty ι] {K : ι → Subalgebra R A} {dir : Directed (· ≤ ·) K
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {ι : Type.{u4}} [_inst_6 : Nonempty.{succ u4} ι] {K : ι -> (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {dir : Directed.{u2, succ u4} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) ι (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) K} {f : forall (i : ι), AlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ 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(Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)))) (Module.toDistribMulAction.{u2, u4} R B (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u2, u4} R B _inst_1 _inst_4 _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u3, u4, max u3 u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5 (AlgHom.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) (AlgHom.algHomClass.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A 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+  forall {R : Type.{u2}} {A : Type.{u3}} {B : Type.{u4}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u3} A] [_inst_3 : Algebra.{u2, u3} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u4} B] [_inst_5 : Algebra.{u2, u4} R B _inst_1 _inst_4] {ι : Type.{u1}} [_inst_6 : Nonempty.{succ u1} ι] {K : ι -> (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)} {dir : Directed.{u3, succ u1} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) ι (fun (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13718 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13720 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) => LE.le.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3))))) x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13718 x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13720) K} {f : forall (i : ι), AlgHom.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5} {hf : forall (i : ι) (j : ι) (h : LE.le.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Subalgebra.{u2, u3} R 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Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i))))) (Algebra.toModule.{u2, u3} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.algebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)))) (Module.toDistribMulAction.{u2, u4} R B (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u2, u4} R B _inst_1 _inst_4 _inst_5)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u3 u4, u2, u3, u4} (AlgHom.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)) (Module.toDistribMulAction.{u2, u3} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i))))) (Algebra.toModule.{u2, u3} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.algebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)))) (Module.toDistribMulAction.{u2, u4} R B (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u2, u4} R B _inst_1 _inst_4 _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u3, u4, max u3 u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5 (AlgHom.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) (AlgHom.algHomClass.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5))))) (f i) x)
 Case conversion may be inaccurate. Consider using '#align subalgebra.supr_lift_inclusion Subalgebra.iSupLift_inclusionₓ'. -/
 @[simp]
 theorem iSupLift_inclusion {i : ι} (x : K i) (h : K i ≤ T) :
@@ -2247,7 +2251,7 @@ theorem iSupLift_inclusion {i : ι} (x : K i) (h : K i ≤ T) :
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {ι : Type.{u4}} [_inst_6 : Nonempty.{succ u4} ι] {K : ι -> (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {dir : Directed.{u2, succ u4} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) ι (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) K} {f : forall (i : ι), AlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K i)) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5} {hf : forall (i : ι) (j : ι) (h : LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (K i) (K j)), Eq.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K i)) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) (f i) (AlgHom.comp.{u1, u2, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K i)) (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K j)) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K j)) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K j)) _inst_5 (f j) (Subalgebra.inclusion.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i) (K j) h))} {T : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3} {hT : Eq.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) T (iSup.{u2, succ u4} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))) ι K)} {i : ι} (h : LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (K i) T), Eq.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K i)) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) (AlgHom.comp.{u1, u2, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K i)) (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) _inst_5 (Subalgebra.iSupLift.{u1, u2, u3, u4} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 ι _inst_6 K dir f hf T hT) (Subalgebra.inclusion.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i) T h)) (f i)
 but is expected to have type
-  forall {R : Type.{u2}} {A : Type.{u3}} {B : Type.{u4}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u3} A] [_inst_3 : Algebra.{u2, u3} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u4} B] [_inst_5 : Algebra.{u2, u4} R B _inst_1 _inst_4] {ι : Type.{u1}} [_inst_6 : Nonempty.{succ u1} ι] {K : ι -> (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)} {dir : Directed.{u3, succ u1} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) ι (fun (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13872 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13874 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) => LE.le.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3))))) x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13872 x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13874) K} {f : forall (i : ι), AlgHom.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5} {hf : forall (i : ι) (j : ι) (h : LE.le.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3))))) (K i) (K j)), Eq.{max (succ u3) (succ u4)} (AlgHom.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) (f i) (AlgHom.comp.{u2, u3, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K j))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K j)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K j)) _inst_5 (f j) (Subalgebra.inclusion.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i) (K j) h))} {T : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3} {hT : Eq.{succ u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) T (iSup.{u3, succ u1} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3))) ι K)} {i : ι} (h : LE.le.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3))))) (K i) T), Eq.{max (succ u3) (succ u4)} (AlgHom.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) (AlgHom.comp.{u2, u3, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x T)) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 T) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 T) _inst_5 (Subalgebra.iSupLift.{u2, u3, u4, u1} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 ι _inst_6 K dir f hf T hT) (Subalgebra.inclusion.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i) T h)) (f i)
+  forall {R : Type.{u2}} {A : Type.{u3}} {B : Type.{u4}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u3} A] [_inst_3 : Algebra.{u2, u3} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u4} B] [_inst_5 : Algebra.{u2, u4} R B _inst_1 _inst_4] {ι : Type.{u1}} [_inst_6 : Nonempty.{succ u1} ι] {K : ι -> (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)} {dir : Directed.{u3, succ u1} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) ι (fun (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13873 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13875 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) => LE.le.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3))))) x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13873 x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13875) K} {f : forall (i : ι), AlgHom.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5} {hf : forall (i : ι) (j : ι) (h : LE.le.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3))))) (K i) (K j)), Eq.{max (succ u3) (succ u4)} (AlgHom.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) (f i) (AlgHom.comp.{u2, u3, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K j))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K j)) _inst_4 (Subalgebra.algebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.algebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K j)) _inst_5 (f j) (Subalgebra.inclusion.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i) (K j) h))} {T : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3} {hT : Eq.{succ u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) T (iSup.{u3, succ u1} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3))) ι K)} {i : ι} (h : LE.le.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3))))) (K i) T), Eq.{max (succ u3) (succ u4)} (AlgHom.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) (AlgHom.comp.{u2, u3, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x T)) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 T) _inst_4 (Subalgebra.algebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.algebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 T) _inst_5 (Subalgebra.iSupLift.{u2, u3, u4, u1} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 ι _inst_6 K dir f hf T hT) (Subalgebra.inclusion.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i) T h)) (f i)
 Case conversion may be inaccurate. Consider using '#align subalgebra.supr_lift_comp_inclusion Subalgebra.iSupLift_comp_inclusionₓ'. -/
 @[simp]
 theorem iSupLift_comp_inclusion {i : ι} (h : K i ≤ T) :
@@ -2258,7 +2262,7 @@ theorem iSupLift_comp_inclusion {i : ι} (h : K i ≤ T) :
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {ι : Type.{u4}} [_inst_6 : Nonempty.{succ u4} ι] {K : ι -> (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {dir : Directed.{u2, succ u4} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) ι (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) K} {f : forall (i : ι), AlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ 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i)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)) (Module.toDistribMulAction.{u2, u3} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i))))) (Algebra.toModule.{u2, u3} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.algebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)))) (Module.toDistribMulAction.{u2, u4} R B (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u2, u4} R B _inst_1 _inst_4 _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u3, u4, max u3 u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5 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 Case conversion may be inaccurate. Consider using '#align subalgebra.supr_lift_mk Subalgebra.iSupLift_mkₓ'. -/
 @[simp]
 theorem iSupLift_mk {i : ι} (x : K i) (hx : (x : A) ∈ T) :
@@ -2269,7 +2273,7 @@ theorem iSupLift_mk {i : ι} (x : K i) (hx : (x : A) ∈ T) :
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {ι : Type.{u4}} [_inst_6 : Nonempty.{succ u4} ι] {K : ι -> (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {dir : Directed.{u2, succ u4} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) ι (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) K} {f : forall (i : ι), AlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ 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 but is expected to have type
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+  forall {R : Type.{u2}} {A : Type.{u3}} {B : Type.{u4}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u3} A] [_inst_3 : Algebra.{u2, u3} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u4} B] [_inst_5 : Algebra.{u2, u4} R B _inst_1 _inst_4] {ι : Type.{u1}} [_inst_6 : Nonempty.{succ u1} ι] {K : ι -> (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)} {dir : Directed.{u3, succ u1} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) ι (fun (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.14155 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.14157 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) => LE.le.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) 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_inst_1 _inst_2 _inst_3)) x (K i))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)))))) (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))) (Module.toDistribMulAction.{u2, u3} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i))))) (Algebra.toModule.{u2, u3} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.algebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)))) (Module.toDistribMulAction.{u2, u4} R B (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u2, u4} R B _inst_1 _inst_4 _inst_5)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u3 u4, u2, u3, u4} (AlgHom.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)) (Module.toDistribMulAction.{u2, u3} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i))))) (Algebra.toModule.{u2, u3} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.algebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)))) (Module.toDistribMulAction.{u2, u4} R B (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u2, u4} R B _inst_1 _inst_4 _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u3, u4, max u3 u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5 (AlgHom.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) (AlgHom.algHomClass.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5))))) (f i) (Subtype.mk.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i)) (Subtype.val.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Set.{u3} A) (Set.instMembershipSet.{u3} A) x (SetLike.coe.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) T)) x) hx))
 Case conversion may be inaccurate. Consider using '#align subalgebra.supr_lift_of_mem Subalgebra.iSupLift_of_memₓ'. -/
 theorem iSupLift_of_mem {i : ι} (x : T) (hx : (x : A) ∈ K i) :
     iSupLift K dir f hf T hT x = f i ⟨x, hx⟩ := by subst hT <;> exact Set.iUnionLift_of_mem x hx
@@ -2340,7 +2344,7 @@ instance isScalarTower_left [SMul α β] [SMul A α] [SMul A β] [IsScalarTower
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} {T : Type.{u3}} [_inst_6 : CommSemiring.{u1} R] [_inst_7 : Semiring.{u2} S] [_inst_8 : AddCommMonoid.{u3} T] [_inst_9 : Algebra.{u1, u2} R S _inst_6 _inst_7] [_inst_10 : Module.{u1, u3} R T (CommSemiring.toSemiring.{u1} R _inst_6) _inst_8] [_inst_11 : Module.{u2, u3} S T _inst_7 _inst_8] [_inst_12 : IsScalarTower.{u1, u2, u3} R S T (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_7)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_6))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_7)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_6)) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_7)))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_7))) (Algebra.toModule.{u1, u2} R S _inst_6 _inst_7 _inst_9))))) (SMulZeroClass.toHasSmul.{u2, u3} S T (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8))) (SMulWithZero.toSmulZeroClass.{u2, u3} S T (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_7)))) (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8))) (MulActionWithZero.toSMulWithZero.{u2, u3} S T (Semiring.toMonoidWithZero.{u2} S _inst_7) (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8))) (Module.toMulActionWithZero.{u2, u3} S T _inst_7 _inst_8 _inst_11)))) (SMulZeroClass.toHasSmul.{u1, u3} R T (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8))) (SMulWithZero.toSmulZeroClass.{u1, u3} R T (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_6))))) (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8))) (MulActionWithZero.toSMulWithZero.{u1, u3} R T (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_6)) (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8))) (Module.toMulActionWithZero.{u1, u3} R T (CommSemiring.toSemiring.{u1} R _inst_6) _inst_8 _inst_10))))] (S' : Subalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9), IsScalarTower.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9) S (Subalgebra.setLike.{u1, u2} R S _inst_6 _inst_7 _inst_9)) S') T (SetLike.smul.{u1, u2, u2} (Subalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9) R S (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_7)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_6))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_7)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_6)) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_7)))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_7))) (Algebra.toModule.{u1, u2} R S _inst_6 _inst_7 _inst_9))))) (Subalgebra.setLike.{u1, u2} R S _inst_6 _inst_7 _inst_9) (Subalgebra.smulMemClass.{u1, u2} R S _inst_6 _inst_7 _inst_9) S') (Subalgebra.hasSmul.{u1, u2, u3} R S _inst_6 _inst_7 _inst_9 T (SMulZeroClass.toHasSmul.{u2, u3} S T (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8))) (SMulWithZero.toSmulZeroClass.{u2, u3} S T (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_7)))) (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8))) (MulActionWithZero.toSMulWithZero.{u2, u3} S T (Semiring.toMonoidWithZero.{u2} S _inst_7) (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8))) (Module.toMulActionWithZero.{u2, u3} S T _inst_7 _inst_8 _inst_11)))) S') (SMulZeroClass.toHasSmul.{u1, u3} R T (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8))) (SMulWithZero.toSmulZeroClass.{u1, u3} R T (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_6))))) (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8))) (MulActionWithZero.toSMulWithZero.{u1, u3} R T (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_6)) (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8))) (Module.toMulActionWithZero.{u1, u3} R T (CommSemiring.toSemiring.{u1} R _inst_6) _inst_8 _inst_10))))
 but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u2}} {T : Type.{u3}} [_inst_6 : CommSemiring.{u1} R] [_inst_7 : Semiring.{u2} S] [_inst_8 : AddCommMonoid.{u3} T] [_inst_9 : Algebra.{u1, u2} R S _inst_6 _inst_7] [_inst_10 : Module.{u1, u3} R T (CommSemiring.toSemiring.{u1} R _inst_6) _inst_8] [_inst_11 : Module.{u2, u3} S T _inst_7 _inst_8] [_inst_12 : IsScalarTower.{u1, u2, u3} R S T (Algebra.toSMul.{u1, u2} R S _inst_6 _inst_7 _inst_9) (SMulZeroClass.toSMul.{u2, u3} S T (AddMonoid.toZero.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8)) (SMulWithZero.toSMulZeroClass.{u2, u3} S T (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_7)) (AddMonoid.toZero.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8)) (MulActionWithZero.toSMulWithZero.{u2, u3} S T (Semiring.toMonoidWithZero.{u2} S _inst_7) (AddMonoid.toZero.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8)) (Module.toMulActionWithZero.{u2, u3} S T _inst_7 _inst_8 _inst_11)))) (SMulZeroClass.toSMul.{u1, u3} R T (AddMonoid.toZero.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8)) (SMulWithZero.toSMulZeroClass.{u1, u3} R T (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_6)) (AddMonoid.toZero.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8)) (MulActionWithZero.toSMulWithZero.{u1, u3} R T (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_6)) (AddMonoid.toZero.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8)) (Module.toMulActionWithZero.{u1, u3} R T (CommSemiring.toSemiring.{u1} R _inst_6) _inst_8 _inst_10))))] (S' : Subalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9), IsScalarTower.{u1, u2, u3} R (Subtype.{succ u2} S (fun (x : S) => Membership.mem.{u2, u2} S (Subalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9) S (Subalgebra.instSetLikeSubalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9)) x S')) T (Algebra.toSMul.{u1, u2} R (Subtype.{succ u2} S (fun (x : S) => Membership.mem.{u2, u2} S (Subalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9) S (Subalgebra.instSetLikeSubalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9)) x S')) _inst_6 (Subalgebra.toSemiring.{u1, u2} R S _inst_6 _inst_7 _inst_9 S') (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R S _inst_6 _inst_7 _inst_9 S')) (Subalgebra.instSMulSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebra.{u1, u2, u3} R S _inst_6 _inst_7 _inst_9 T (SMulZeroClass.toSMul.{u2, u3} S T (AddMonoid.toZero.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8)) (SMulWithZero.toSMulZeroClass.{u2, u3} S T (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_7)) (AddMonoid.toZero.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8)) (MulActionWithZero.toSMulWithZero.{u2, u3} S T (Semiring.toMonoidWithZero.{u2} S _inst_7) (AddMonoid.toZero.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8)) (Module.toMulActionWithZero.{u2, u3} S T _inst_7 _inst_8 _inst_11)))) S') (SMulZeroClass.toSMul.{u1, u3} R T (AddMonoid.toZero.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8)) (SMulWithZero.toSMulZeroClass.{u1, u3} R T (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_6)) (AddMonoid.toZero.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8)) (MulActionWithZero.toSMulWithZero.{u1, u3} R T (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_6)) (AddMonoid.toZero.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8)) (Module.toMulActionWithZero.{u1, u3} R T (CommSemiring.toSemiring.{u1} R _inst_6) _inst_8 _inst_10))))
+  forall {R : Type.{u1}} {S : Type.{u2}} {T : Type.{u3}} [_inst_6 : CommSemiring.{u1} R] [_inst_7 : Semiring.{u2} S] [_inst_8 : AddCommMonoid.{u3} T] [_inst_9 : Algebra.{u1, u2} R S _inst_6 _inst_7] [_inst_10 : Module.{u1, u3} R T (CommSemiring.toSemiring.{u1} R _inst_6) _inst_8] [_inst_11 : Module.{u2, u3} S T _inst_7 _inst_8] [_inst_12 : IsScalarTower.{u1, u2, u3} R S T (Algebra.toSMul.{u1, u2} R S _inst_6 _inst_7 _inst_9) (SMulZeroClass.toSMul.{u2, u3} S T (AddMonoid.toZero.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8)) (SMulWithZero.toSMulZeroClass.{u2, u3} S T (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_7)) (AddMonoid.toZero.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8)) (MulActionWithZero.toSMulWithZero.{u2, u3} S T (Semiring.toMonoidWithZero.{u2} S _inst_7) (AddMonoid.toZero.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8)) (Module.toMulActionWithZero.{u2, u3} S T _inst_7 _inst_8 _inst_11)))) (SMulZeroClass.toSMul.{u1, u3} R T (AddMonoid.toZero.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8)) (SMulWithZero.toSMulZeroClass.{u1, u3} R T (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_6)) (AddMonoid.toZero.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8)) (MulActionWithZero.toSMulWithZero.{u1, u3} R T (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_6)) (AddMonoid.toZero.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8)) (Module.toMulActionWithZero.{u1, u3} R T (CommSemiring.toSemiring.{u1} R _inst_6) _inst_8 _inst_10))))] (S' : Subalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9), IsScalarTower.{u1, u2, u3} R (Subtype.{succ u2} S (fun (x : S) => Membership.mem.{u2, u2} S (Subalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9) S (Subalgebra.instSetLikeSubalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9)) x S')) T (Algebra.toSMul.{u1, u2} R (Subtype.{succ u2} S (fun (x : S) => Membership.mem.{u2, u2} S (Subalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9) S (Subalgebra.instSetLikeSubalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9)) x S')) _inst_6 (Subalgebra.toSemiring.{u1, u2} R S _inst_6 _inst_7 _inst_9 S') (Subalgebra.algebra.{u1, u2} R S _inst_6 _inst_7 _inst_9 S')) (Subalgebra.instSMulSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebra.{u1, u2, u3} R S _inst_6 _inst_7 _inst_9 T (SMulZeroClass.toSMul.{u2, u3} S T (AddMonoid.toZero.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8)) (SMulWithZero.toSMulZeroClass.{u2, u3} S T (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_7)) (AddMonoid.toZero.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8)) (MulActionWithZero.toSMulWithZero.{u2, u3} S T (Semiring.toMonoidWithZero.{u2} S _inst_7) (AddMonoid.toZero.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8)) (Module.toMulActionWithZero.{u2, u3} S T _inst_7 _inst_8 _inst_11)))) S') (SMulZeroClass.toSMul.{u1, u3} R T (AddMonoid.toZero.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8)) (SMulWithZero.toSMulZeroClass.{u1, u3} R T (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_6)) (AddMonoid.toZero.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8)) (MulActionWithZero.toSMulWithZero.{u1, u3} R T (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_6)) (AddMonoid.toZero.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8)) (Module.toMulActionWithZero.{u1, u3} R T (CommSemiring.toSemiring.{u1} R _inst_6) _inst_8 _inst_10))))
 Case conversion may be inaccurate. Consider using '#align subalgebra.is_scalar_tower_mid Subalgebra.isScalarTower_midₓ'. -/
 instance isScalarTower_mid {R S T : Type _} [CommSemiring R] [Semiring S] [AddCommMonoid T]
     [Algebra R S] [Module R T] [Module S T] [IsScalarTower R S T] (S' : Subalgebra R S) :
@@ -2394,7 +2398,7 @@ instance toAlgebra {R A : Type _} [CommSemiring R] [CommSemiring A] [Semiring α
 lean 3 declaration is
   forall {α : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} [_inst_6 : CommSemiring.{u2} R] [_inst_7 : CommSemiring.{u3} A] [_inst_8 : Semiring.{u1} α] [_inst_9 : Algebra.{u2, u3} R A _inst_6 (CommSemiring.toSemiring.{u3} A _inst_7)] [_inst_10 : Algebra.{u3, u1} A α _inst_7 _inst_8] (S : Subalgebra.{u2, u3} R A _inst_6 (CommSemiring.toSemiring.{u3} A _inst_7) _inst_9), Eq.{max (succ u3) (succ u1)} (RingHom.{u3, u1} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A _inst_6 (CommSemiring.toSemiring.{u3} A _inst_7) _inst_9) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A _inst_6 (CommSemiring.toSemiring.{u3} A _inst_7) _inst_9) A (Subalgebra.setLike.{u2, u3} R A _inst_6 (CommSemiring.toSemiring.{u3} A _inst_7) _inst_9)) S) α (Semiring.toNonAssocSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A _inst_6 (CommSemiring.toSemiring.{u3} A _inst_7) _inst_9) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A _inst_6 (CommSemiring.toSemiring.{u3} A _inst_7) _inst_9) A (Subalgebra.setLike.{u2, u3} R A _inst_6 (CommSemiring.toSemiring.{u3} A _inst_7) _inst_9)) S) (CommSemiring.toSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A _inst_6 (CommSemiring.toSemiring.{u3} A _inst_7) _inst_9) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A _inst_6 (CommSemiring.toSemiring.{u3} A _inst_7) _inst_9) A (Subalgebra.setLike.{u2, u3} R A _inst_6 (CommSemiring.toSemiring.{u3} A _inst_7) _inst_9)) S) (Subalgebra.toCommSemiring.{u2, u3} R A _inst_6 _inst_7 _inst_9 S))) (Semiring.toNonAssocSemiring.{u1} α _inst_8)) (algebraMap.{u3, u1} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A _inst_6 (CommSemiring.toSemiring.{u3} A _inst_7) _inst_9) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A _inst_6 (CommSemiring.toSemiring.{u3} A _inst_7) _inst_9) A (Subalgebra.setLike.{u2, u3} R A _inst_6 (CommSemiring.toSemiring.{u3} A _inst_7) _inst_9)) S) α (Subalgebra.toCommSemiring.{u2, u3} R A _inst_6 _inst_7 _inst_9 S) _inst_8 (Subalgebra.toAlgebra.{u1, u2, u3} α R A _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 S)) (RingHom.comp.{u3, u3, u1} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A _inst_6 (CommSemiring.toSemiring.{u3} A _inst_7) _inst_9) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A _inst_6 (CommSemiring.toSemiring.{u3} A _inst_7) _inst_9) A (Subalgebra.setLike.{u2, u3} R A _inst_6 (CommSemiring.toSemiring.{u3} A _inst_7) _inst_9)) S) A α (Semiring.toNonAssocSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A _inst_6 (CommSemiring.toSemiring.{u3} A _inst_7) _inst_9) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A _inst_6 (CommSemiring.toSemiring.{u3} A _inst_7) _inst_9) A (Subalgebra.setLike.{u2, u3} R A _inst_6 (CommSemiring.toSemiring.{u3} A _inst_7) _inst_9)) S) (CommSemiring.toSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A _inst_6 (CommSemiring.toSemiring.{u3} A _inst_7) _inst_9) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A _inst_6 (CommSemiring.toSemiring.{u3} A _inst_7) _inst_9) A (Subalgebra.setLike.{u2, u3} R A _inst_6 (CommSemiring.toSemiring.{u3} A _inst_7) _inst_9)) S) (Subalgebra.toCommSemiring.{u2, u3} R A _inst_6 _inst_7 _inst_9 S))) (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_7)) (Semiring.toNonAssocSemiring.{u1} α _inst_8) (algebraMap.{u3, u1} A α _inst_7 _inst_8 _inst_10) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (AlgHom.{u2, u3, u3} R (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A _inst_6 (CommSemiring.toSemiring.{u3} A _inst_7) _inst_9) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A _inst_6 (CommSemiring.toSemiring.{u3} A _inst_7) _inst_9) A (Subalgebra.setLike.{u2, u3} R A _inst_6 (CommSemiring.toSemiring.{u3} A _inst_7) _inst_9)) S) A _inst_6 (Subalgebra.toSemiring.{u2, u3} R A _inst_6 (CommSemiring.toSemiring.{u3} A _inst_7) _inst_9 S) (CommSemiring.toSemiring.{u3} A _inst_7) (Subalgebra.algebra.{u2, u3} R A _inst_6 (CommSemiring.toSemiring.{u3} A _inst_7) _inst_9 S) _inst_9) (RingHom.{u3, u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A _inst_6 (CommSemiring.toSemiring.{u3} A _inst_7) _inst_9) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A _inst_6 (CommSemiring.toSemiring.{u3} A _inst_7) _inst_9) A (Subalgebra.setLike.{u2, u3} R A _inst_6 (CommSemiring.toSemiring.{u3} A _inst_7) _inst_9)) S) A (Semiring.toNonAssocSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A _inst_6 (CommSemiring.toSemiring.{u3} A _inst_7) _inst_9) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A _inst_6 (CommSemiring.toSemiring.{u3} A _inst_7) _inst_9) A (Subalgebra.setLike.{u2, u3} R A _inst_6 (CommSemiring.toSemiring.{u3} A _inst_7) _inst_9)) S) (CommSemiring.toSemiring.{u3} 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u3} R A _inst_6 (CommSemiring.toSemiring.{u3} A _inst_7) _inst_9) A (Subalgebra.setLike.{u2, u3} R A _inst_6 (CommSemiring.toSemiring.{u3} A _inst_7) _inst_9)) S) (Subalgebra.toCommSemiring.{u2, u3} R A _inst_6 _inst_7 _inst_9 S))) (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_7))) (RingHom.hasCoeT.{u3, u3, u3} (AlgHom.{u2, u3, u3} R (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A _inst_6 (CommSemiring.toSemiring.{u3} A _inst_7) _inst_9) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A _inst_6 (CommSemiring.toSemiring.{u3} A _inst_7) _inst_9) A (Subalgebra.setLike.{u2, u3} R A _inst_6 (CommSemiring.toSemiring.{u3} A _inst_7) _inst_9)) S) A _inst_6 (Subalgebra.toSemiring.{u2, u3} R A _inst_6 (CommSemiring.toSemiring.{u3} A _inst_7) _inst_9 S) (CommSemiring.toSemiring.{u3} A _inst_7) (Subalgebra.algebra.{u2, u3} R A _inst_6 (CommSemiring.toSemiring.{u3} A _inst_7) _inst_9 S) _inst_9) (coeSort.{succ u3, succ (succ u3)} 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(CommSemiring.toSemiring.{u3} A _inst_7) _inst_9)) S) (Subalgebra.toCommSemiring.{u2, u3} R A _inst_6 _inst_7 _inst_9 S))) (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_7)) (AlgHomClass.toRingHomClass.{u3, u2, u3, u3} (AlgHom.{u2, u3, u3} R (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A _inst_6 (CommSemiring.toSemiring.{u3} A _inst_7) _inst_9) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u2, u3} R A _inst_6 (CommSemiring.toSemiring.{u3} A _inst_7) _inst_9) A (Subalgebra.setLike.{u2, u3} R A _inst_6 (CommSemiring.toSemiring.{u3} A _inst_7) _inst_9)) S) A _inst_6 (Subalgebra.toSemiring.{u2, u3} R A _inst_6 (CommSemiring.toSemiring.{u3} A _inst_7) _inst_9 S) (CommSemiring.toSemiring.{u3} A _inst_7) (Subalgebra.algebra.{u2, u3} R A _inst_6 (CommSemiring.toSemiring.{u3} A _inst_7) _inst_9 S) _inst_9) R (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u2, u3} R A _inst_6 (CommSemiring.toSemiring.{u3} A _inst_7) _inst_9) Type.{u3} 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(Subalgebra.algebra.{u2, u3} R A _inst_6 (CommSemiring.toSemiring.{u3} A _inst_7) _inst_9 S) _inst_9))))) (Subalgebra.val.{u2, u3} R A _inst_6 (CommSemiring.toSemiring.{u3} A _inst_7) _inst_9 S)))
 but is expected to have type
-  forall {α : Type.{u1}} {R : Type.{u3}} {A : Type.{u2}} [_inst_6 : CommSemiring.{u3} R] [_inst_7 : CommSemiring.{u2} A] [_inst_8 : Semiring.{u1} α] [_inst_9 : Algebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7)] [_inst_10 : Algebra.{u2, u1} A α _inst_7 _inst_8] (S : Subalgebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9), Eq.{max (succ u1) (succ u2)} (RingHom.{u2, u1} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9) (SetLike.instMembership.{u2, u2} (Subalgebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9) A (Subalgebra.instSetLikeSubalgebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9)) x S)) α (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9) (SetLike.instMembership.{u2, u2} (Subalgebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9) A (Subalgebra.instSetLikeSubalgebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9)) x S)) (CommSemiring.toSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9) (SetLike.instMembership.{u2, u2} (Subalgebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9) A (Subalgebra.instSetLikeSubalgebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9)) x S)) (Subalgebra.toCommSemiring.{u3, u2} R A _inst_6 _inst_7 _inst_9 S))) (Semiring.toNonAssocSemiring.{u1} α _inst_8)) (algebraMap.{u2, u1} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9) (SetLike.instMembership.{u2, u2} (Subalgebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9) A (Subalgebra.instSetLikeSubalgebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9)) x S)) α (Subalgebra.toCommSemiring.{u3, u2} R A _inst_6 _inst_7 _inst_9 S) _inst_8 (Subalgebra.toAlgebra.{u1, u3, u2} α R A _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 S)) (RingHom.comp.{u2, u2, u1} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9) (SetLike.instMembership.{u2, u2} (Subalgebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9) A (Subalgebra.instSetLikeSubalgebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9)) x S)) A α (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9) (SetLike.instMembership.{u2, u2} (Subalgebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9) A (Subalgebra.instSetLikeSubalgebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9)) x S)) (CommSemiring.toSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9) (SetLike.instMembership.{u2, u2} (Subalgebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9) A (Subalgebra.instSetLikeSubalgebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9)) x S)) (Subalgebra.toCommSemiring.{u3, u2} R A _inst_6 _inst_7 _inst_9 S))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_7)) (Semiring.toNonAssocSemiring.{u1} α _inst_8) (algebraMap.{u2, u1} A α _inst_7 _inst_8 _inst_10) (RingHomClass.toRingHom.{u2, u2, u2} (AlgHom.{u3, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9) (SetLike.instMembership.{u2, u2} (Subalgebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9) A (Subalgebra.instSetLikeSubalgebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9)) x S)) A _inst_6 (Subalgebra.toSemiring.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9 S) (CommSemiring.toSemiring.{u2} A _inst_7) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9 S) _inst_9) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9) (SetLike.instMembership.{u2, u2} (Subalgebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9) A (Subalgebra.instSetLikeSubalgebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9)) x S)) A (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9) (SetLike.instMembership.{u2, u2} (Subalgebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9) A (Subalgebra.instSetLikeSubalgebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9)) x S)) (CommSemiring.toSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9) (SetLike.instMembership.{u2, u2} (Subalgebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9) A (Subalgebra.instSetLikeSubalgebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9)) x S)) (Subalgebra.toCommSemiring.{u3, u2} R A _inst_6 _inst_7 _inst_9 S))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_7)) (AlgHomClass.toRingHomClass.{u2, u3, u2, u2} (AlgHom.{u3, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9) (SetLike.instMembership.{u2, u2} (Subalgebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9) A (Subalgebra.instSetLikeSubalgebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9)) x S)) A _inst_6 (Subalgebra.toSemiring.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9 S) (CommSemiring.toSemiring.{u2} A _inst_7) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9 S) _inst_9) R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9) (SetLike.instMembership.{u2, u2} (Subalgebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9) A (Subalgebra.instSetLikeSubalgebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9)) x S)) A _inst_6 (CommSemiring.toSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9) (SetLike.instMembership.{u2, u2} (Subalgebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9) A (Subalgebra.instSetLikeSubalgebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9)) x S)) (Subalgebra.toCommSemiring.{u3, u2} R A _inst_6 _inst_7 _inst_9 S)) (CommSemiring.toSemiring.{u2} A _inst_7) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9 S) _inst_9 (AlgHom.algHomClass.{u3, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9) (SetLike.instMembership.{u2, u2} (Subalgebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9) A (Subalgebra.instSetLikeSubalgebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9)) x S)) A _inst_6 (Subalgebra.toSemiring.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9 S) (CommSemiring.toSemiring.{u2} A _inst_7) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9 S) _inst_9)) (Subalgebra.val.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9 S)))
+  forall {α : Type.{u1}} {R : Type.{u3}} {A : Type.{u2}} [_inst_6 : CommSemiring.{u3} R] [_inst_7 : CommSemiring.{u2} A] [_inst_8 : Semiring.{u1} α] [_inst_9 : Algebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7)] [_inst_10 : Algebra.{u2, u1} A α _inst_7 _inst_8] (S : Subalgebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9), Eq.{max (succ u1) (succ u2)} (RingHom.{u2, u1} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9) (SetLike.instMembership.{u2, u2} (Subalgebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9) A (Subalgebra.instSetLikeSubalgebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9)) x S)) α (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9) (SetLike.instMembership.{u2, u2} (Subalgebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9) A (Subalgebra.instSetLikeSubalgebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9)) x S)) (CommSemiring.toSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9) (SetLike.instMembership.{u2, u2} (Subalgebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9) A (Subalgebra.instSetLikeSubalgebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9)) x S)) (Subalgebra.toCommSemiring.{u3, u2} R A _inst_6 _inst_7 _inst_9 S))) (Semiring.toNonAssocSemiring.{u1} α _inst_8)) (algebraMap.{u2, u1} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9) (SetLike.instMembership.{u2, u2} (Subalgebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9) A (Subalgebra.instSetLikeSubalgebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9)) x S)) α (Subalgebra.toCommSemiring.{u3, u2} R A _inst_6 _inst_7 _inst_9 S) _inst_8 (Subalgebra.toAlgebra.{u1, u3, u2} α R A _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 S)) (RingHom.comp.{u2, u2, u1} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9) (SetLike.instMembership.{u2, u2} (Subalgebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9) A (Subalgebra.instSetLikeSubalgebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9)) x S)) A α (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9) (SetLike.instMembership.{u2, u2} (Subalgebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9) A (Subalgebra.instSetLikeSubalgebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9)) x S)) (CommSemiring.toSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9) (SetLike.instMembership.{u2, u2} (Subalgebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9) A (Subalgebra.instSetLikeSubalgebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9)) x S)) (Subalgebra.toCommSemiring.{u3, u2} R A _inst_6 _inst_7 _inst_9 S))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_7)) (Semiring.toNonAssocSemiring.{u1} α _inst_8) (algebraMap.{u2, u1} A α _inst_7 _inst_8 _inst_10) (RingHomClass.toRingHom.{u2, u2, u2} (AlgHom.{u3, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9) (SetLike.instMembership.{u2, u2} (Subalgebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9) A (Subalgebra.instSetLikeSubalgebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9)) x S)) A _inst_6 (Subalgebra.toSemiring.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9 S) (CommSemiring.toSemiring.{u2} A _inst_7) (Subalgebra.algebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9 S) _inst_9) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9) (SetLike.instMembership.{u2, u2} (Subalgebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9) A (Subalgebra.instSetLikeSubalgebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9)) x S)) A (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9) (SetLike.instMembership.{u2, u2} (Subalgebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9) A (Subalgebra.instSetLikeSubalgebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9)) x S)) (CommSemiring.toSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9) (SetLike.instMembership.{u2, u2} (Subalgebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9) A (Subalgebra.instSetLikeSubalgebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9)) x S)) (Subalgebra.toCommSemiring.{u3, u2} R A _inst_6 _inst_7 _inst_9 S))) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_7)) (AlgHomClass.toRingHomClass.{u2, u3, u2, u2} (AlgHom.{u3, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9) (SetLike.instMembership.{u2, u2} (Subalgebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9) A (Subalgebra.instSetLikeSubalgebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9)) x S)) A _inst_6 (Subalgebra.toSemiring.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9 S) (CommSemiring.toSemiring.{u2} A _inst_7) (Subalgebra.algebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9 S) _inst_9) R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9) (SetLike.instMembership.{u2, u2} (Subalgebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9) A (Subalgebra.instSetLikeSubalgebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9)) x S)) A _inst_6 (CommSemiring.toSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9) (SetLike.instMembership.{u2, u2} (Subalgebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9) A (Subalgebra.instSetLikeSubalgebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9)) x S)) (Subalgebra.toCommSemiring.{u3, u2} R A _inst_6 _inst_7 _inst_9 S)) (CommSemiring.toSemiring.{u2} A _inst_7) (Subalgebra.algebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9 S) _inst_9 (AlgHom.algHomClass.{u3, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9) (SetLike.instMembership.{u2, u2} (Subalgebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9) A (Subalgebra.instSetLikeSubalgebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9)) x S)) A _inst_6 (Subalgebra.toSemiring.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9 S) (CommSemiring.toSemiring.{u2} A _inst_7) (Subalgebra.algebra.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9 S) _inst_9)) (Subalgebra.val.{u3, u2} R A _inst_6 (CommSemiring.toSemiring.{u2} A _inst_7) _inst_9 S)))
 Case conversion may be inaccurate. Consider using '#align subalgebra.algebra_map_eq Subalgebra.algebraMap_eqₓ'. -/
 theorem algebraMap_eq {R A : Type _} [CommSemiring R] [CommSemiring A] [Semiring α] [Algebra R A]
     [Algebra A α] (S : Subalgebra R A) : algebraMap S α = (algebraMap A α).comp S.val :=

bump to nightly-2023-05-19-16

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

a31df521

Diff

@@ -164,7 +164,7 @@ variable (S : Subalgebra R A)
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (r : R), Membership.Mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) S
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (r : R), Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) S
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (r : R), Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) r) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) S
 Case conversion may be inaccurate. Consider using '#align subalgebra.algebra_map_mem Subalgebra.algebraMap_memₓ'. -/
 theorem algebraMap_mem (r : R) : algebraMap R A r ∈ S :=
   S.algebraMap_mem' r
@@ -184,7 +184,7 @@ theorem rangeS_le : (algebraMap R A).srange ≤ S.toSubsemiring := fun x ⟨r, h
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), HasSubset.Subset.{u2} (Set.{u2} A) (Set.hasSubset.{u2} A) (Set.range.{u2, succ u1} A R (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) S)
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), HasSubset.Subset.{u2} (Set.{u2} A) (Set.instHasSubsetSet.{u2} A) (Set.range.{u2, succ u1} A R (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (SetLike.coe.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) S)
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), HasSubset.Subset.{u2} (Set.{u2} A) (Set.instHasSubsetSet.{u2} A) (Set.range.{u2, succ u1} A R (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (SetLike.coe.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) S)
 Case conversion may be inaccurate. Consider using '#align subalgebra.range_subset Subalgebra.range_subsetₓ'. -/
 theorem range_subset : Set.range (algebraMap R A) ⊆ S := fun x ⟨r, hr⟩ => hr ▸ S.algebraMap_mem r
 #align subalgebra.range_subset Subalgebra.range_subset
@@ -193,7 +193,7 @@ theorem range_subset : Set.range (algebraMap R A) ⊆ S := fun x ⟨r, hr⟩ =>
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), LE.le.{u2} (Set.{u2} A) (Set.hasLe.{u2} A) (Set.range.{u2, succ u1} A R (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) S)
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), LE.le.{u2} (Set.{u2} A) (Set.instLESet.{u2} A) (Set.range.{u2, succ u1} A R (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (SetLike.coe.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) S)
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), LE.le.{u2} (Set.{u2} A) (Set.instLESet.{u2} A) (Set.range.{u2, succ u1} A R (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (SetLike.coe.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) S)
 Case conversion may be inaccurate. Consider using '#align subalgebra.range_le Subalgebra.range_leₓ'. -/
 theorem range_le : Set.range (algebraMap R A) ≤ S :=
   S.range_subset
@@ -640,7 +640,7 @@ def toSubmodule : Subalgebra R A ↪o Submodule R A
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) {x : A}, Iff (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (coeFn.{succ u2, succ u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (fun (_x : RelEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) => (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) -> (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (RelEmbedding.hasCoeToFun.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) S)) (Membership.Mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) {x : A}, Iff (Membership.mem.{u2, u2} A ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) (SetLike.instMembership.{u2, u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (FunLike.coe.{succ u2, succ u2, succ u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (fun (_x : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) _x) (RelHomClass.toFunLike.{u2, u2, u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) S)) (Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) {x : A}, Iff (Membership.mem.{u2, u2} A ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) (SetLike.instMembership.{u2, u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (FunLike.coe.{succ u2, succ u2, succ u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (fun (_x : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) _x) (RelHomClass.toFunLike.{u2, u2, u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) S)) (Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)
 Case conversion may be inaccurate. Consider using '#align subalgebra.mem_to_submodule Subalgebra.mem_toSubmoduleₓ'. -/
 /- TODO: bundle other forgetful maps between algebraic substructures, e.g.
   `to_subsemiring` and `to_subring` in this file. -/
@@ -653,7 +653,7 @@ theorem mem_toSubmodule {x} : x ∈ S.toSubmodule ↔ x ∈ S :=
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), Eq.{succ u2} (Set.{u2} A) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (coeFn.{succ u2, succ u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (fun (_x : RelEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) => (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) -> (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (RelEmbedding.hasCoeToFun.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) S)) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) S)
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), Eq.{succ u2} (Set.{u2} A) (SetLike.coe.{u2, u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (FunLike.coe.{succ u2, succ u2, succ u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (fun (_x : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) _x) (RelHomClass.toFunLike.{u2, u2, u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) S)) (SetLike.coe.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) S)
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), Eq.{succ u2} (Set.{u2} A) (SetLike.coe.{u2, u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (FunLike.coe.{succ u2, succ u2, succ u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (fun (_x : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) _x) (RelHomClass.toFunLike.{u2, u2, u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A 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(Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) S)) (SetLike.coe.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) S)
 Case conversion may be inaccurate. Consider using '#align subalgebra.coe_to_submodule Subalgebra.coe_toSubmoduleₓ'. -/
 @[simp]
 theorem coe_toSubmodule (S : Subalgebra R A) : (↑S.toSubmodule : Set A) = S :=
@@ -792,7 +792,7 @@ theorem coe_smul [Semiring R'] [SMul R' R] [Module R' A] [IsScalarTower R' R A]
 lean 3 declaration is
   forall {R' : Type.{u2}} {R : Type.{u1}} {A : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u3} A] [_inst_3 : Algebra.{u1, u3} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) [_inst_8 : CommSemiring.{u2} R'] [_inst_9 : SMul.{u2, u1} R' R] [_inst_10 : Algebra.{u2, u3} R' A _inst_8 _inst_2] [_inst_11 : IsScalarTower.{u2, u1, u3} R' R A _inst_9 (SMulZeroClass.toHasSmul.{u1, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u1, u3} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toHasSmul.{u2, u3} R' A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} R' A (MulZeroClass.toHasZero.{u2} R' (MulZeroOneClass.toMulZeroClass.{u2} R' (MonoidWithZero.toMulZeroOneClass.{u2} R' (Semiring.toMonoidWithZero.{u2} R' (CommSemiring.toSemiring.{u2} R' _inst_8))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} R' A (Semiring.toMonoidWithZero.{u2} R' (CommSemiring.toSemiring.{u2} R' _inst_8)) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2)))))) (Module.toMulActionWithZero.{u2, u3} R' A (CommSemiring.toSemiring.{u2} R' _inst_8) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R' A _inst_8 _inst_2 _inst_10)))))] (r : R'), Eq.{succ u3} A ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u3} R A _inst_1 _inst_2 _inst_3)) S) A (HasLiftT.mk.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u3} R A _inst_1 _inst_2 _inst_3)) S) A (CoeTCₓ.coe.{succ u3, 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 but is expected to have type
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_inst_3)) x S)) (Subalgebra.toSemiring.{u1, u3} R A _inst_1 _inst_2 _inst_3 S))) R' (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3)) x S)) (Semiring.toNonAssocSemiring.{u2} R' (CommSemiring.toSemiring.{u2} R' _inst_8)) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3)) x S)) (Subalgebra.toSemiring.{u1, u3} R A _inst_1 _inst_2 _inst_3 S)) (RingHom.instRingHomClassRingHom.{u2, u3} R' (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) 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(Subalgebra.algebra'.{u1, u2, u3} R' R A _inst_1 _inst_2 _inst_3 S _inst_8 _inst_9 _inst_10 _inst_11)) r)) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RingHom.{u2, u3} R' A (Semiring.toNonAssocSemiring.{u2} R' (CommSemiring.toSemiring.{u2} R' _inst_8)) (Semiring.toNonAssocSemiring.{u3} A _inst_2)) R' (fun (_x : R') => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R') => A) _x) (MulHomClass.toFunLike.{max u2 u3, u2, u3} (RingHom.{u2, u3} R' A (Semiring.toNonAssocSemiring.{u2} R' (CommSemiring.toSemiring.{u2} R' _inst_8)) (Semiring.toNonAssocSemiring.{u3} A _inst_2)) R' A (NonUnitalNonAssocSemiring.toMul.{u2} R' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R' (Semiring.toNonAssocSemiring.{u2} R' (CommSemiring.toSemiring.{u2} R' _inst_8)))) (NonUnitalNonAssocSemiring.toMul.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} R' A (Semiring.toNonAssocSemiring.{u2} R' (CommSemiring.toSemiring.{u2} R' _inst_8)) (Semiring.toNonAssocSemiring.{u3} A _inst_2)) R' A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R' (Semiring.toNonAssocSemiring.{u2} R' (CommSemiring.toSemiring.{u2} R' _inst_8))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} R' A (Semiring.toNonAssocSemiring.{u2} R' (CommSemiring.toSemiring.{u2} R' _inst_8)) (Semiring.toNonAssocSemiring.{u3} A _inst_2)) R' A (Semiring.toNonAssocSemiring.{u2} R' (CommSemiring.toSemiring.{u2} R' _inst_8)) (Semiring.toNonAssocSemiring.{u3} A _inst_2) (RingHom.instRingHomClassRingHom.{u2, u3} R' A (Semiring.toNonAssocSemiring.{u2} R' (CommSemiring.toSemiring.{u2} R' _inst_8)) (Semiring.toNonAssocSemiring.{u3} A _inst_2))))) (algebraMap.{u2, u3} R' A _inst_8 _inst_2 _inst_10) r)
+  forall {R' : Type.{u2}} {R : Type.{u1}} {A : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u3} A] [_inst_3 : Algebra.{u1, u3} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) [_inst_8 : CommSemiring.{u2} R'] [_inst_9 : SMul.{u2, u1} R' R] [_inst_10 : Algebra.{u2, u3} R' A _inst_8 _inst_2] [_inst_11 : IsScalarTower.{u2, u1, u3} R' R A _inst_9 (Algebra.toSMul.{u1, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.toSMul.{u2, u3} R' A _inst_8 _inst_2 _inst_10)] (r : R'), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R') => A) r) (Subtype.val.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Set.{u3} A) (Set.instMembershipSet.{u3} A) x (SetLike.coe.{u3, u3} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) S)) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RingHom.{u2, u3} R' (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3)) x S)) (Semiring.toNonAssocSemiring.{u2} R' (CommSemiring.toSemiring.{u2} R' _inst_8)) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3)) x S)) (Subalgebra.toSemiring.{u1, u3} R A _inst_1 _inst_2 _inst_3 S))) R' (fun (_x : R') => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R') => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3)) x S)) _x) (MulHomClass.toFunLike.{max u2 u3, u2, u3} (RingHom.{u2, u3} R' (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3)) x S)) (Semiring.toNonAssocSemiring.{u2} R' (CommSemiring.toSemiring.{u2} R' _inst_8)) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3)) x S)) (Subalgebra.toSemiring.{u1, u3} R A _inst_1 _inst_2 _inst_3 S))) R' (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3)) x S)) (NonUnitalNonAssocSemiring.toMul.{u2} R' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R' (Semiring.toNonAssocSemiring.{u2} R' (CommSemiring.toSemiring.{u2} R' _inst_8)))) (NonUnitalNonAssocSemiring.toMul.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3)) x S)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3)) x S)) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3)) x S)) (Subalgebra.toSemiring.{u1, u3} R A _inst_1 _inst_2 _inst_3 S)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} R' (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3)) x S)) (Semiring.toNonAssocSemiring.{u2} R' (CommSemiring.toSemiring.{u2} R' _inst_8)) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3)) x S)) (Subalgebra.toSemiring.{u1, u3} R A _inst_1 _inst_2 _inst_3 S))) R' (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3)) x S)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R' (Semiring.toNonAssocSemiring.{u2} R' (CommSemiring.toSemiring.{u2} R' _inst_8))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3)) x S)) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3)) x S)) (Subalgebra.toSemiring.{u1, u3} R A _inst_1 _inst_2 _inst_3 S))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} R' (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3)) x S)) (Semiring.toNonAssocSemiring.{u2} R' (CommSemiring.toSemiring.{u2} R' _inst_8)) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3)) x S)) (Subalgebra.toSemiring.{u1, u3} R A _inst_1 _inst_2 _inst_3 S))) R' (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3)) x S)) (Semiring.toNonAssocSemiring.{u2} R' (CommSemiring.toSemiring.{u2} R' _inst_8)) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3)) x S)) (Subalgebra.toSemiring.{u1, u3} R A _inst_1 _inst_2 _inst_3 S)) (RingHom.instRingHomClassRingHom.{u2, u3} R' (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3)) x S)) (Semiring.toNonAssocSemiring.{u2} R' (CommSemiring.toSemiring.{u2} R' _inst_8)) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3)) x S)) (Subalgebra.toSemiring.{u1, u3} R A _inst_1 _inst_2 _inst_3 S)))))) (algebraMap.{u2, u3} R' (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3)) x S)) _inst_8 (Subalgebra.toSemiring.{u1, u3} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.algebra'.{u1, u2, u3} R' R A _inst_1 _inst_2 _inst_3 S _inst_8 _inst_9 _inst_10 _inst_11)) r)) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RingHom.{u2, u3} R' A (Semiring.toNonAssocSemiring.{u2} R' (CommSemiring.toSemiring.{u2} R' _inst_8)) (Semiring.toNonAssocSemiring.{u3} A _inst_2)) R' (fun (_x : R') => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R') => A) _x) (MulHomClass.toFunLike.{max u2 u3, u2, u3} (RingHom.{u2, u3} R' A (Semiring.toNonAssocSemiring.{u2} R' (CommSemiring.toSemiring.{u2} R' _inst_8)) (Semiring.toNonAssocSemiring.{u3} A _inst_2)) R' A (NonUnitalNonAssocSemiring.toMul.{u2} R' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R' (Semiring.toNonAssocSemiring.{u2} R' (CommSemiring.toSemiring.{u2} R' _inst_8)))) (NonUnitalNonAssocSemiring.toMul.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} R' A (Semiring.toNonAssocSemiring.{u2} R' (CommSemiring.toSemiring.{u2} R' _inst_8)) (Semiring.toNonAssocSemiring.{u3} A _inst_2)) R' A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R' (Semiring.toNonAssocSemiring.{u2} R' (CommSemiring.toSemiring.{u2} R' _inst_8))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} R' A (Semiring.toNonAssocSemiring.{u2} R' (CommSemiring.toSemiring.{u2} R' _inst_8)) (Semiring.toNonAssocSemiring.{u3} A _inst_2)) R' A (Semiring.toNonAssocSemiring.{u2} R' (CommSemiring.toSemiring.{u2} R' _inst_8)) (Semiring.toNonAssocSemiring.{u3} A _inst_2) (RingHom.instRingHomClassRingHom.{u2, u3} R' A (Semiring.toNonAssocSemiring.{u2} R' (CommSemiring.toSemiring.{u2} R' _inst_8)) (Semiring.toNonAssocSemiring.{u3} A _inst_2))))) (algebraMap.{u2, u3} R' A _inst_8 _inst_2 _inst_10) r)
 Case conversion may be inaccurate. Consider using '#align subalgebra.coe_algebra_map Subalgebra.coe_algebraMapₓ'. -/
 @[simp, norm_cast]
 theorem coe_algebraMap [CommSemiring R'] [SMul R' R] [Algebra R' A] [IsScalarTower R' R A]
@@ -890,7 +890,7 @@ theorem toSubring_subtype {R A : Type _} [CommRing R] [Ring A] [Algebra R A] (S
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Subalgebra.toSubmoduleEquiv._proof_1.{u1} R _inst_1) (Subalgebra.toSubmoduleEquiv._proof_2.{u1} R _inst_1) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (coeFn.{succ u2, succ u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A 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R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A 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 but is expected to have type
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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A 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_inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) S)) (Subalgebra.instModuleSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToNonAssocSemiringToSubsemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S)
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) (SetLike.instMembership.{u2, u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (FunLike.coe.{succ u2, succ u2, succ u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (fun (a : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) a) (RelHomClass.toFunLike.{u2, u2, u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R 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(Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (fun (_x : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) _x) (RelHomClass.toFunLike.{u2, u2, u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) S)) (Subalgebra.instModuleSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToNonAssocSemiringToSubsemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S)
 Case conversion may be inaccurate. Consider using '#align subalgebra.to_submodule_equiv Subalgebra.toSubmoduleEquivₓ'. -/
 /-- Linear equivalence between `S : submodule R A` and `S`. Though these types are equal,
 we define it as a `linear_equiv` to avoid type equalities. -/
@@ -951,7 +951,7 @@ theorem mem_map {S : Subalgebra R A} {f : A →ₐ[R] B} {y : B} : y ∈ map f S
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3} {f : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5}, Eq.{succ u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (coeFn.{succ u3, succ u3} (OrderEmbedding.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (PartialOrder.toPreorder.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (CompleteSemilatticeInf.toPartialOrder.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B 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(Submodule.completeLattice.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)))))))) (Subalgebra.toSubmodule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Subalgebra.map.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 f S)) (Submodule.map.{u1, u1, u2, u3, max u2 u3} R R A B (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R A B (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A 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(Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) => (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) -> (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (RelEmbedding.hasCoeToFun.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) S))
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3} {f : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5}, Eq.{succ u3} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) => Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Subalgebra.map.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 f S)) (FunLike.coe.{succ u3, succ u3, succ u3} (OrderEmbedding.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Submodule.{u1, u3} R B 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(Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (fun (_x : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) _x) (RelHomClass.toFunLike.{u2, u2, u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) S))
+  forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3} {f : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5}, Eq.{succ u3} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) => Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Subalgebra.map.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 f S)) (FunLike.coe.{succ u3, succ u3, succ u3} (OrderEmbedding.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Preorder.toLE.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (PartialOrder.toPreorder.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instPartialOrder.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)))) (Preorder.toLE.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (PartialOrder.toPreorder.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Submodule.completeLattice.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5))))))) (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (fun (_x : Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) => Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) _x) (RelHomClass.toFunLike.{u3, u3, u3} (OrderEmbedding.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Preorder.toLE.{u3} 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(Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) S))
 Case conversion may be inaccurate. Consider using '#align subalgebra.map_to_submodule Subalgebra.map_toSubmoduleₓ'. -/
 theorem map_toSubmodule {S : Subalgebra R A} {f : A →ₐ[R] B} :
     (S.map f).toSubmodule = S.toSubmodule.map f.toLinearMap :=
@@ -1101,7 +1101,7 @@ theorem coe_toSubalgebra (p : Submodule R A) (h_one h_mul) :
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (s : Set.{u2} A) (h0 : Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) (OfNat.ofNat.{u2} A 0 (OfNat.mk.{u2} A 0 (Zero.zero.{u2} A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))))))) s) (hadd : forall {a : A} {b : A}, (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) a s) -> (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) b s) -> (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (AddZeroClass.toHasAdd.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))))) a b) s)) (hsmul : forall (c : R) {x : A}, (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) x s) -> (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) (SMul.smul.{u1, u2} R A (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) c x) s)) (h1 : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (OfNat.ofNat.{u2} A 1 (OfNat.mk.{u2} A 1 (One.one.{u2} A (AddMonoidWithOne.toOne.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))))) (Submodule.mk.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) s hadd h0 hsmul)) (hmul : forall (x : A) (y : A), (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (Submodule.mk.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) s hadd h0 hsmul)) -> (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) y (Submodule.mk.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) s hadd h0 hsmul)) -> (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y) (Submodule.mk.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R 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_inst_2)))))))) s) (id_tag Tactic.IdTag.rw (Eq.{1} Prop (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) s) (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) (SMul.smul.{u1, u2} R A (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A 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(OfNat.ofNat.{u2} A 1 (OfNat.mk.{u2} A 1 (One.one.{u2} A (AddMonoidWithOne.toOne.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))))) (Algebra.algebraMap_eq_smul_one.{u1, u2} R A _inst_1 _inst_2 _inst_3 r))) (hsmul r (OfNat.ofNat.{u2} A 1 (OfNat.mk.{u2} A 1 (One.one.{u2} A (AddMonoidWithOne.toOne.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))))) h1)))
 but is expected to have type
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(Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) (OfNat.ofNat.{u1} A 1 (One.toOfNat1.{u1} A (Semiring.toOne.{u1} A _inst_2))) s) (hadd : forall (a : A) (b : A), (Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) a s) -> (Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) s) hadd) h0) (fun {a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6476 : A} {b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6477 : A} => Submodule.add_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6476 b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6477) (Submodule.zero_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s))))))) (Eq.ndrec.{0, 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(CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2) (RingHom.instRingHomClassRingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2))))) (algebraMap.{u2, u1} R A _inst_1 _inst_2 _inst_3) r) (fun (_a : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) => Eq.{1} Prop (Membership.mem.{u1, u1} ((fun 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R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2) (RingHom.instRingHomClassRingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2))))) (algebraMap.{u2, u1} R A _inst_1 _inst_2 _inst_3) r) (Subsemigroup.carrier.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (Submonoid.toSubsemigroup.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemiring.toSubmonoid.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Subsemiring.mk.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Submonoid.mk.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemigroup.mk.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) s) hadd) h0) (fun {a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6476 : A} {b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6477 : A} => Submodule.add_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6476 b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6477) (Submodule.zero_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s)))))) (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) (Set.{u1} A) (Set.instMembershipSet.{u1} A) _a (Subsemigroup.carrier.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (Submonoid.toSubsemigroup.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemiring.toSubmonoid.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Subsemiring.mk.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Submonoid.mk.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemigroup.mk.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) s) hadd) h0) (fun {a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6476 : A} {b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6477 : A} => Submodule.add_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6476 b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6477) (Submodule.zero_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s))))))) (Eq.refl.{1} Prop (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) (Set.{u1} A) (Set.instMembershipSet.{u1} A) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2) (RingHom.instRingHomClassRingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2))))) (algebraMap.{u2, u1} R A _inst_1 _inst_2 _inst_3) r) (Subsemigroup.carrier.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (Submonoid.toSubsemigroup.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemiring.toSubmonoid.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Subsemiring.mk.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Submonoid.mk.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemigroup.mk.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) s) hadd) h0) (fun {a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6476 : A} {b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6477 : A} => Submodule.add_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6476 b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6477) (Submodule.zero_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s))))))) (HSMul.hSMul.{u2, u1, u1} R A A (instHSMul.{u2, u1} R A (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_2 _inst_3)) r (OfNat.ofNat.{u1} A 1 (One.toOfNat1.{u1} A (Semiring.toOne.{u1} A _inst_2)))) (Algebra.algebraMap_eq_smul_one.{u2, u1} R A _inst_1 _inst_2 _inst_3 r))) (Submodule.smul_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s (OfNat.ofNat.{u1} A 1 (One.toOfNat1.{u1} A (Semiring.toOne.{u1} A _inst_2))) r h0)))
+  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u1} A] [_inst_3 : Algebra.{u2, u1} R A _inst_1 _inst_2] (s : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (h0 : Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) (OfNat.ofNat.{u1} A 1 (One.toOfNat1.{u1} A (Semiring.toOne.{u1} A _inst_2))) s) (hadd : forall (a : A) (b : A), (Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) a s) -> (Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A 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(NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemiring.toSubmonoid.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Subsemiring.mk.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Submonoid.mk.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemigroup.mk.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) s) hadd) h0) (fun {a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6476 : A} {b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6477 : A} => Submodule.add_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6476 b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6477) (Submodule.zero_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s))))))) (Eq.ndrec.{0, succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) r) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2) (RingHom.instRingHomClassRingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2))))) (algebraMap.{u2, u1} R A _inst_1 _inst_2 _inst_3) r) (fun (_a : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) r) => Eq.{1} Prop (Membership.mem.{u1, u1} ((fun 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R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2) (RingHom.instRingHomClassRingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2))))) (algebraMap.{u2, u1} R A _inst_1 _inst_2 _inst_3) r) (Subsemigroup.carrier.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (Submonoid.toSubsemigroup.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemiring.toSubmonoid.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Subsemiring.mk.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Submonoid.mk.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemigroup.mk.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) s) hadd) h0) (fun {a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6476 : A} {b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6477 : A} => Submodule.add_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6476 b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6477) (Submodule.zero_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s)))))) (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) r) (Set.{u1} A) (Set.instMembershipSet.{u1} A) _a (Subsemigroup.carrier.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (Submonoid.toSubsemigroup.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemiring.toSubmonoid.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Subsemiring.mk.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Submonoid.mk.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemigroup.mk.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) s) hadd) h0) (fun {a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6476 : A} {b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6477 : A} => Submodule.add_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6476 b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6477) (Submodule.zero_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s))))))) (Eq.refl.{1} Prop (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) r) (Set.{u1} A) (Set.instMembershipSet.{u1} A) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) a) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2) (RingHom.instRingHomClassRingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2))))) (algebraMap.{u2, u1} R A _inst_1 _inst_2 _inst_3) r) (Subsemigroup.carrier.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (Submonoid.toSubsemigroup.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemiring.toSubmonoid.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Subsemiring.mk.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Submonoid.mk.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemigroup.mk.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) s) hadd) h0) (fun {a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6476 : A} {b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6477 : A} => Submodule.add_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6476 b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6477) (Submodule.zero_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s))))))) (HSMul.hSMul.{u2, u1, u1} R A A (instHSMul.{u2, u1} R A (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_2 _inst_3)) r (OfNat.ofNat.{u1} A 1 (One.toOfNat1.{u1} A (Semiring.toOne.{u1} A _inst_2)))) (Algebra.algebraMap_eq_smul_one.{u2, u1} R A _inst_1 _inst_2 _inst_3 r))) (Submodule.smul_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s (OfNat.ofNat.{u1} A 1 (One.toOfNat1.{u1} A (Semiring.toOne.{u1} A _inst_2))) r h0)))
 Case conversion may be inaccurate. Consider using '#align submodule.to_subalgebra_mk Submodule.toSubalgebra_mkₓ'. -/
 @[simp]
 theorem toSubalgebra_mk (s : Set A) (h0 hadd hsmul h1 hmul) :
@@ -1117,7 +1117,7 @@ theorem toSubalgebra_mk (s : Set A) (h0 hadd hsmul h1 hmul) :
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (p : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (h_one : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (OfNat.ofNat.{u2} A 1 (OfNat.mk.{u2} A 1 (One.one.{u2} A (AddMonoidWithOne.toOne.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))))) p) (h_mul : forall (x : A) (y : A), (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x p) -> (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) y p) -> (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y) p)), Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (coeFn.{succ u2, succ u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (fun (_x : RelEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) => (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) -> (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (RelEmbedding.hasCoeToFun.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 p h_one h_mul)) p
 but is expected to have type
-  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u1} A] [_inst_3 : Algebra.{u2, u1} R A _inst_1 _inst_2] (p : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (h_one : Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) (OfNat.ofNat.{u1} A 1 (One.toOfNat1.{u1} A (Semiring.toOne.{u1} A _inst_2))) p) (h_mul : forall (x : A) (y : A), (Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) x p) -> (Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) y p) -> (Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u1, u1, u1} A A A (instHMul.{u1} A (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) x y) p)), Eq.{succ u1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Submodule.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 p h_one h_mul)) (FunLike.coe.{succ u1, succ u1, succ u1} (OrderEmbedding.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A 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(Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => LE.le.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => LE.le.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Subalgebra.toSubmodule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 p h_one h_mul)) p
+  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u1} A] [_inst_3 : Algebra.{u2, u1} R A _inst_1 _inst_2] (p : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (h_one : Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) (OfNat.ofNat.{u1} A 1 (One.toOfNat1.{u1} A (Semiring.toOne.{u1} A _inst_2))) p) (h_mul : forall (x : A) (y : A), (Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) x p) -> (Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) y p) -> (Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u1, u1, u1} A A A (instHMul.{u1} A (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) x y) p)), Eq.{succ u1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Submodule.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 p h_one h_mul)) (FunLike.coe.{succ u1, succ u1, succ u1} (OrderEmbedding.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (fun (_x : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) _x) (RelHomClass.toFunLike.{u1, u1, u1} (OrderEmbedding.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => LE.le.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => LE.le.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Subalgebra.toSubmodule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 p h_one h_mul)) p
 Case conversion may be inaccurate. Consider using '#align submodule.to_subalgebra_to_submodule Submodule.toSubalgebra_toSubmoduleₓ'. -/
 @[simp]
 theorem toSubalgebra_toSubmodule (p : Submodule R A) (h_one h_mul) :
@@ -1129,7 +1129,7 @@ theorem toSubalgebra_toSubmodule (p : Submodule R A) (h_one h_mul) :
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), Eq.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (coeFn.{succ u2, succ u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (fun (_x : RelEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) => (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) -> (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (RelEmbedding.hasCoeToFun.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) S) (Subalgebra.one_mem.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (fun (_x : A) (_x_1 : A) => Subalgebra.mul_mem.{u1, u2} R A _inst_1 _inst_2 _inst_3 S _x _x_1)) S
 but is expected to have type
-  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u1} A] [_inst_3 : Algebra.{u2, u1} R A _inst_1 _inst_2] (S : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3), Eq.{succ u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 (FunLike.coe.{succ u1, succ u1, succ u1} (OrderEmbedding.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (fun (_x : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) _x) (RelHomClass.toFunLike.{u1, u1, u1} (OrderEmbedding.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => LE.le.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => LE.le.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Subalgebra.toSubmodule.{u2, u1} R A _inst_1 _inst_2 _inst_3) S) (Subalgebra.one_mem.{u2, u1} R A _inst_1 _inst_2 _inst_3 S) (fun (_x : A) (_x_1 : A) => Subalgebra.mul_mem.{u2, u1} R A _inst_1 _inst_2 _inst_3 S _x _x_1)) S
+  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u1} A] [_inst_3 : Algebra.{u2, u1} R A _inst_1 _inst_2] (S : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3), Eq.{succ u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 (FunLike.coe.{succ u1, succ u1, succ u1} (OrderEmbedding.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (fun (_x : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) _x) (RelHomClass.toFunLike.{u1, u1, u1} (OrderEmbedding.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => LE.le.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => LE.le.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Subalgebra.toSubmodule.{u2, u1} R A _inst_1 _inst_2 _inst_3) S) (Subalgebra.one_mem.{u2, u1} R A _inst_1 _inst_2 _inst_3 S) (fun (_x : A) (_x_1 : A) => Subalgebra.mul_mem.{u2, u1} R A _inst_1 _inst_2 _inst_3 S _x _x_1)) S
 Case conversion may be inaccurate. Consider using '#align subalgebra.to_submodule_to_subalgebra Subalgebra.toSubmodule_toSubalgebraₓ'. -/
 @[simp]
 theorem Subalgebra.toSubmodule_toSubalgebra (S : Subalgebra R A) :
@@ -1461,7 +1461,7 @@ theorem mem_top {x : A} : x ∈ (⊤ : Subalgebra R A) :=
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (coeFn.{succ u2, succ u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (fun (_x : RelEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) => (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) -> (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (RelEmbedding.hasCoeToFun.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Top.top.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toHasTop.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Top.top.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.hasTop.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], Eq.{succ u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Top.top.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toTop.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (FunLike.coe.{succ u2, succ u2, succ u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (fun (_x : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) _x) (RelHomClass.toFunLike.{u2, u2, u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Top.top.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toTop.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Top.top.{u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Top.top.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toTop.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Submodule.instTopSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], Eq.{succ u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Top.top.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toTop.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (FunLike.coe.{succ u2, succ u2, succ u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (fun (_x : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) _x) (RelHomClass.toFunLike.{u2, u2, u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Top.top.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toTop.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Top.top.{u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Top.top.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toTop.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Submodule.instTopSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))
 Case conversion may be inaccurate. Consider using '#align algebra.top_to_submodule Algebra.top_toSubmoduleₓ'. -/
 @[simp]
 theorem top_toSubmodule : (⊤ : Subalgebra R A).toSubmodule = ⊤ :=
@@ -1495,7 +1495,7 @@ theorem top_toSubring {R A : Type _} [CommRing R] [Ring A] [Algebra R A] :
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3}, Iff (Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (coeFn.{succ u2, succ u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (fun (_x : RelEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) => (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) -> (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (RelEmbedding.hasCoeToFun.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) S) (Top.top.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.hasTop.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Eq.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) S (Top.top.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toHasTop.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))))
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3}, Iff (Eq.{succ u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) (FunLike.coe.{succ u2, succ u2, succ u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (fun (_x : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) _x) (RelHomClass.toFunLike.{u2, u2, u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) S) (Top.top.{u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) (Submodule.instTopSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Eq.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) S (Top.top.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toTop.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))))
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3}, Iff (Eq.{succ u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) (FunLike.coe.{succ u2, succ u2, succ u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (fun (_x : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) _x) (RelHomClass.toFunLike.{u2, u2, u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) S) (Top.top.{u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) (Submodule.instTopSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Eq.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) S (Top.top.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toTop.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))))
 Case conversion may be inaccurate. Consider using '#align algebra.to_submodule_eq_top Algebra.toSubmodule_eq_topₓ'. -/
 @[simp]
 theorem toSubmodule_eq_top {S : Subalgebra R A} : S.toSubmodule = ⊤ ↔ S = ⊤ :=
@@ -1591,7 +1591,7 @@ theorem mem_inf {S T : Subalgebra R A} {x : A} : x ∈ S ⊓ T ↔ x ∈ S ∧ x
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (T : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (coeFn.{succ u2, succ u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) 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(CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) => (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) -> (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (RelEmbedding.hasCoeToFun.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) T))
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (T : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), Eq.{succ u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Inf.inf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Lattice.toInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) 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(Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (fun (_x : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) _x) (RelHomClass.toFunLike.{u2, u2, u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A 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(CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) S) (FunLike.coe.{succ u2, succ u2, succ u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A 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Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) _x) (RelHomClass.toFunLike.{u2, u2, u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) T))
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (T : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), Eq.{succ u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Inf.inf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Lattice.toInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) S T)) (FunLike.coe.{succ u2, succ u2, succ u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (fun (_x : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) _x) (RelHomClass.toFunLike.{u2, u2, u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A 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(Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : 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(Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Inf.inf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Lattice.toInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) S T)) (Inf.inf.{u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) 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(Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R 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_inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) T))
 Case conversion may be inaccurate. Consider using '#align algebra.inf_to_submodule Algebra.inf_toSubmoduleₓ'. -/
 @[simp]
 theorem inf_toSubmodule (S T : Subalgebra R A) :
@@ -1636,7 +1636,7 @@ theorem mem_sInf {S : Set (Subalgebra R A)} {x : A} : x ∈ sInf S ↔ ∀ p ∈
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Set.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)), Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (coeFn.{succ u2, succ u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (fun (_x : RelEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) => (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) -> (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (RelEmbedding.hasCoeToFun.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (InfSet.sInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))) S)) (InfSet.sInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.hasInf.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A 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(CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) => (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) -> (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (RelEmbedding.hasCoeToFun.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S))
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Set.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)), Eq.{succ u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (InfSet.sInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toInfSet.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))) S)) (FunLike.coe.{succ u2, succ u2, succ u2} 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R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (fun (_x : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) _x) (RelHomClass.toFunLike.{u2, u2, u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, u2} R A 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S))
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Set.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)), Eq.{succ u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (InfSet.sInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toInfSet.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))) S)) (FunLike.coe.{succ u2, succ u2, succ u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (fun (_x : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) _x) (RelHomClass.toFunLike.{u2, u2, u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) 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x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (InfSet.sInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toInfSet.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))) S)) (InfSet.sInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.instInfSetSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} 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(Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) 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A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) _x) (RelHomClass.toFunLike.{u2, u2, u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A 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(Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S))
 Case conversion may be inaccurate. Consider using '#align algebra.Inf_to_submodule Algebra.sInf_toSubmoduleₓ'. -/
 @[simp]
 theorem sInf_toSubmodule (S : Set (Subalgebra R A)) :
@@ -1681,7 +1681,7 @@ theorem mem_iInf {ι : Sort _} {S : ι → Subalgebra R A} {x : A} : (x ∈ ⨅
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {ι : Sort.{u3}} (S : ι -> (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)), Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (coeFn.{succ u2, succ u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 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(Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) => (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) -> (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (RelEmbedding.hasCoeToFun.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (iInf.{u2, u3} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => S i))) (iInf.{u2, u3} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.hasInf.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) ι (fun (i : ι) => coeFn.{succ u2, succ u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) 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_inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) 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(Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) -> (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (RelEmbedding.hasCoeToFun.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (S i)))
 but is expected to have type
-  forall {R : Type.{u2}} {A : Type.{u3}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u3} A] [_inst_3 : Algebra.{u2, u3} R A _inst_1 _inst_2] {ι : Sort.{u1}} (S : ι -> (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)), Eq.{succ u3} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (iInf.{u3, u1} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toInfSet.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => S i))) (FunLike.coe.{succ 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(PartialOrder.toPreorder.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (fun (_x : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) _x) (RelHomClass.toFunLike.{u3, u3, u3} (OrderEmbedding.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) => LE.le.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) => LE.le.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Subalgebra.toSubmodule.{u2, u3} R A _inst_1 _inst_2 _inst_3) (iInf.{u3, u1} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toInfSet.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => S i))) (iInf.{u3, u1} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.instInfSetSubmodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (fun (_x : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) _x) (RelHomClass.toFunLike.{u3, u3, u3} (OrderEmbedding.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) => LE.le.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) => LE.le.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Subalgebra.toSubmodule.{u2, u3} R A _inst_1 _inst_2 _inst_3) (S i)))
+  forall {R : Type.{u2}} {A : Type.{u3}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u3} A] [_inst_3 : Algebra.{u2, u3} R A _inst_1 _inst_2] {ι : Sort.{u1}} (S : ι -> (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)), Eq.{succ u3} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (iInf.{u3, u1} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toInfSet.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => S i))) (FunLike.coe.{succ u3, succ u3, succ u3} (OrderEmbedding.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (fun (_x : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) _x) (RelHomClass.toFunLike.{u3, u3, u3} (OrderEmbedding.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A 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_inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) => LE.le.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Subalgebra.toSubmodule.{u2, u3} R A _inst_1 _inst_2 _inst_3) (S i)))
 Case conversion may be inaccurate. Consider using '#align algebra.infi_to_submodule Algebra.iInf_toSubmoduleₓ'. -/
 @[simp]
 theorem iInf_toSubmodule {ι : Sort _} (S : ι → Subalgebra R A) :
@@ -1696,7 +1696,7 @@ instance : Inhabited (Subalgebra R A) :=
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {x : A}, Iff (Membership.Mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x (Bot.bot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toHasBot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) x (Set.range.{u2, succ u1} A R (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3))))
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {x : A}, Iff (Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x (Bot.bot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toBot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) x (Set.range.{u2, succ u1} A R (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3))))
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {x : A}, Iff (Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x (Bot.bot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toBot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) x (Set.range.{u2, succ u1} A R (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3))))
 Case conversion may be inaccurate. Consider using '#align algebra.mem_bot Algebra.mem_botₓ'. -/
 theorem mem_bot {x : A} : x ∈ (⊥ : Subalgebra R A) ↔ x ∈ Set.range (algebraMap R A) :=
   suffices (ofId R A).range = (⊥ : Subalgebra R A)
@@ -1710,7 +1710,7 @@ theorem mem_bot {x : A} : x ∈ (⊥ : Subalgebra R A) ↔ x ∈ Set.range (alge
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (coeFn.{succ u2, succ u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (fun (_x : RelEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) => (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) -> (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (RelEmbedding.hasCoeToFun.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Bot.bot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toHasBot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Submodule.span.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.hasSingleton.{u2} A) (OfNat.ofNat.{u2} A 1 (OfNat.mk.{u2} A 1 (One.one.{u2} A (AddMonoidWithOne.toOne.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))))))
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], Eq.{succ u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Bot.bot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toBot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (FunLike.coe.{succ u2, succ u2, succ u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (fun (_x : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) _x) (RelHomClass.toFunLike.{u2, u2, u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Bot.bot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toBot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Submodule.span.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) (OfNat.ofNat.{u2} A 1 (One.toOfNat1.{u2} A (Semiring.toOne.{u2} A _inst_2)))))
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], Eq.{succ u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Bot.bot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toBot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (FunLike.coe.{succ u2, succ u2, succ u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (fun (_x : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) _x) (RelHomClass.toFunLike.{u2, u2, u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A 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(Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Bot.bot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toBot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Submodule.span.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) (OfNat.ofNat.{u2} A 1 (One.toOfNat1.{u2} A (Semiring.toOne.{u2} A _inst_2)))))
 Case conversion may be inaccurate. Consider using '#align algebra.to_submodule_bot Algebra.toSubmodule_botₓ'. -/
 theorem toSubmodule_bot : (⊥ : Subalgebra R A).toSubmodule = R ∙ 1 :=
   by
@@ -1722,7 +1722,7 @@ theorem toSubmodule_bot : (⊥ : Subalgebra R A).toSubmodule = R ∙ 1 :=
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], Eq.{succ u2} (Set.{u2} A) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Bot.bot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toHasBot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Set.range.{u2, succ u1} A R (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3)))
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], Eq.{succ u2} (Set.{u2} A) (SetLike.coe.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Bot.bot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toBot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Set.range.{u2, succ u1} A R (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3)))
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], Eq.{succ u2} (Set.{u2} A) (SetLike.coe.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Bot.bot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toBot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Set.range.{u2, succ u1} A R (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3)))
 Case conversion may be inaccurate. Consider using '#align algebra.coe_bot Algebra.coe_botₓ'. -/
 @[simp]
 theorem coe_bot : ((⊥ : Subalgebra R A) : Set A) = Set.range (algebraMap R A) := by
@@ -1811,7 +1811,7 @@ def toTop : A →ₐ[R] (⊤ : Subalgebra R A) :=
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], Iff (Function.Surjective.{succ u1, succ u2} R A (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Eq.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Top.top.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toHasTop.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Bot.bot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toHasBot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))))
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], Iff (Function.Surjective.{succ u1, succ u2} R A (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Eq.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Top.top.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toTop.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Bot.bot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toBot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))))
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], Iff (Function.Surjective.{succ u1, succ u2} R A (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Eq.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Top.top.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toTop.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Bot.bot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toBot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))))
 Case conversion may be inaccurate. Consider using '#align algebra.surjective_algebra_map_iff Algebra.surjective_algebraMap_iffₓ'. -/
 theorem surjective_algebraMap_iff :
     Function.Surjective (algebraMap R A) ↔ (⊤ : Subalgebra R A) = ⊥ :=
@@ -1826,7 +1826,7 @@ theorem surjective_algebraMap_iff :
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_6 : Field.{u1} R] [_inst_7 : Semiring.{u2} A] [_inst_8 : Nontrivial.{u2} A] [_inst_9 : Algebra.{u1, u2} R A (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_6)) _inst_7], Iff (Function.Bijective.{succ u1, succ u2} R A (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_6)))) (Semiring.toNonAssocSemiring.{u2} A _inst_7)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_6)))) (Semiring.toNonAssocSemiring.{u2} A _inst_7)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_6)))) (Semiring.toNonAssocSemiring.{u2} A _inst_7)) (algebraMap.{u1, u2} R A (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_6)) _inst_7 _inst_9))) (Eq.{succ u2} (Subalgebra.{u1, u2} R A (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_6)) _inst_7 _inst_9) (Top.top.{u2} (Subalgebra.{u1, u2} R A (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_6)) _inst_7 _inst_9) (CompleteLattice.toHasTop.{u2} (Subalgebra.{u1, u2} R A (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_6)) _inst_7 _inst_9) (Algebra.Subalgebra.completeLattice.{u1, u2} R A (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_6)) _inst_7 _inst_9))) (Bot.bot.{u2} (Subalgebra.{u1, u2} R A (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_6)) _inst_7 _inst_9) (CompleteLattice.toHasBot.{u2} (Subalgebra.{u1, u2} R A (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_6)) _inst_7 _inst_9) (Algebra.Subalgebra.completeLattice.{u1, u2} R A (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_6)) _inst_7 _inst_9))))
 but is expected to have type
-  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_6 : Field.{u2} R] [_inst_7 : Semiring.{u1} A] [_inst_8 : Nontrivial.{u1} A] [_inst_9 : Algebra.{u2, u1} R A (Semifield.toCommSemiring.{u2} R (Field.toSemifield.{u2} R _inst_6)) _inst_7], Iff (Function.Bijective.{succ u2, succ u1} R A (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (Semifield.toCommSemiring.{u2} R (Field.toSemifield.{u2} R _inst_6)))) (Semiring.toNonAssocSemiring.{u1} A _inst_7)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (Semifield.toCommSemiring.{u2} R (Field.toSemifield.{u2} R _inst_6)))) (Semiring.toNonAssocSemiring.{u1} A _inst_7)) R A (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (Semifield.toCommSemiring.{u2} R (Field.toSemifield.{u2} R _inst_6)))))) (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_7))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (Semifield.toCommSemiring.{u2} R (Field.toSemifield.{u2} R _inst_6)))) (Semiring.toNonAssocSemiring.{u1} A _inst_7)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (Semifield.toCommSemiring.{u2} R (Field.toSemifield.{u2} R _inst_6))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_7)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (Semifield.toCommSemiring.{u2} R (Field.toSemifield.{u2} R _inst_6)))) (Semiring.toNonAssocSemiring.{u1} A _inst_7)) R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (Semifield.toCommSemiring.{u2} R (Field.toSemifield.{u2} R _inst_6)))) (Semiring.toNonAssocSemiring.{u1} A _inst_7) (RingHom.instRingHomClassRingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (Semifield.toCommSemiring.{u2} R (Field.toSemifield.{u2} R _inst_6)))) (Semiring.toNonAssocSemiring.{u1} A _inst_7))))) (algebraMap.{u2, u1} R A (Semifield.toCommSemiring.{u2} R (Field.toSemifield.{u2} R _inst_6)) _inst_7 _inst_9))) (Eq.{succ u1} (Subalgebra.{u2, u1} R A (Semifield.toCommSemiring.{u2} R (Field.toSemifield.{u2} R _inst_6)) _inst_7 _inst_9) (Top.top.{u1} (Subalgebra.{u2, u1} R A (Semifield.toCommSemiring.{u2} R (Field.toSemifield.{u2} R _inst_6)) _inst_7 _inst_9) (CompleteLattice.toTop.{u1} (Subalgebra.{u2, u1} R A (Semifield.toCommSemiring.{u2} R (Field.toSemifield.{u2} R _inst_6)) _inst_7 _inst_9) (Algebra.instCompleteLatticeSubalgebra.{u2, u1} R A (Semifield.toCommSemiring.{u2} R (Field.toSemifield.{u2} R _inst_6)) _inst_7 _inst_9))) (Bot.bot.{u1} (Subalgebra.{u2, u1} R A (Semifield.toCommSemiring.{u2} R (Field.toSemifield.{u2} R _inst_6)) _inst_7 _inst_9) (CompleteLattice.toBot.{u1} (Subalgebra.{u2, u1} R A (Semifield.toCommSemiring.{u2} R (Field.toSemifield.{u2} R _inst_6)) _inst_7 _inst_9) (Algebra.instCompleteLatticeSubalgebra.{u2, u1} R A (Semifield.toCommSemiring.{u2} R (Field.toSemifield.{u2} R _inst_6)) _inst_7 _inst_9))))
+  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_6 : Field.{u2} R] [_inst_7 : Semiring.{u1} A] [_inst_8 : Nontrivial.{u1} A] [_inst_9 : Algebra.{u2, u1} R A (Semifield.toCommSemiring.{u2} R (Field.toSemifield.{u2} R _inst_6)) _inst_7], Iff (Function.Bijective.{succ u2, succ u1} R A (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (Semifield.toCommSemiring.{u2} R (Field.toSemifield.{u2} R _inst_6)))) (Semiring.toNonAssocSemiring.{u1} A _inst_7)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (Semifield.toCommSemiring.{u2} R (Field.toSemifield.{u2} R _inst_6)))) (Semiring.toNonAssocSemiring.{u1} A _inst_7)) R A (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (Semifield.toCommSemiring.{u2} R (Field.toSemifield.{u2} R _inst_6)))))) (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_7))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (Semifield.toCommSemiring.{u2} R (Field.toSemifield.{u2} R _inst_6)))) (Semiring.toNonAssocSemiring.{u1} A _inst_7)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (Semifield.toCommSemiring.{u2} R (Field.toSemifield.{u2} R _inst_6))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_7)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (Semifield.toCommSemiring.{u2} R (Field.toSemifield.{u2} R _inst_6)))) (Semiring.toNonAssocSemiring.{u1} A _inst_7)) R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (Semifield.toCommSemiring.{u2} R (Field.toSemifield.{u2} R _inst_6)))) (Semiring.toNonAssocSemiring.{u1} A _inst_7) (RingHom.instRingHomClassRingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (Semifield.toCommSemiring.{u2} R (Field.toSemifield.{u2} R _inst_6)))) (Semiring.toNonAssocSemiring.{u1} A _inst_7))))) (algebraMap.{u2, u1} R A (Semifield.toCommSemiring.{u2} R (Field.toSemifield.{u2} R _inst_6)) _inst_7 _inst_9))) (Eq.{succ u1} (Subalgebra.{u2, u1} R A (Semifield.toCommSemiring.{u2} R (Field.toSemifield.{u2} R _inst_6)) _inst_7 _inst_9) (Top.top.{u1} (Subalgebra.{u2, u1} R A (Semifield.toCommSemiring.{u2} R (Field.toSemifield.{u2} R _inst_6)) _inst_7 _inst_9) (CompleteLattice.toTop.{u1} (Subalgebra.{u2, u1} R A (Semifield.toCommSemiring.{u2} R (Field.toSemifield.{u2} R _inst_6)) _inst_7 _inst_9) (Algebra.instCompleteLatticeSubalgebra.{u2, u1} R A (Semifield.toCommSemiring.{u2} R (Field.toSemifield.{u2} R _inst_6)) _inst_7 _inst_9))) (Bot.bot.{u1} (Subalgebra.{u2, u1} R A (Semifield.toCommSemiring.{u2} R (Field.toSemifield.{u2} R _inst_6)) _inst_7 _inst_9) (CompleteLattice.toBot.{u1} (Subalgebra.{u2, u1} R A (Semifield.toCommSemiring.{u2} R (Field.toSemifield.{u2} R _inst_6)) _inst_7 _inst_9) (Algebra.instCompleteLatticeSubalgebra.{u2, u1} R A (Semifield.toCommSemiring.{u2} R (Field.toSemifield.{u2} R _inst_6)) _inst_7 _inst_9))))
 Case conversion may be inaccurate. Consider using '#align algebra.bijective_algebra_map_iff Algebra.bijective_algebraMap_iffₓ'. -/
 theorem bijective_algebraMap_iff {R A : Type _} [Field R] [Semiring A] [Nontrivial A]
     [Algebra R A] : Function.Bijective (algebraMap R A) ↔ (⊤ : Subalgebra R A) = ⊥ :=
@@ -1838,7 +1838,7 @@ theorem bijective_algebraMap_iff {R A : Type _} [Field R] [Semiring A] [Nontrivi
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], (Function.Injective.{succ u1, succ u2} R A (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3))) -> (AlgEquiv.{u1, u2, u1} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Bot.bot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toHasBot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) R _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (Bot.bot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toHasBot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (CommSemiring.toSemiring.{u1} R _inst_1) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (Bot.bot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toHasBot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Algebra.id.{u1} R _inst_1))
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], (Function.Injective.{succ u1, succ u2} R A (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3))) -> (AlgEquiv.{u1, u2, u1} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x (Bot.bot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toBot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) R _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (Bot.bot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toBot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (CommSemiring.toSemiring.{u1} R _inst_1) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (Bot.bot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toBot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Algebra.id.{u1} R _inst_1))
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], (Function.Injective.{succ u1, succ u2} R A (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3))) -> (AlgEquiv.{u1, u2, u1} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x (Bot.bot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toBot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) R _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (Bot.bot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toBot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (CommSemiring.toSemiring.{u1} R _inst_1) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (Bot.bot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toBot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Algebra.id.{u1} R _inst_1))
 Case conversion may be inaccurate. Consider using '#align algebra.bot_equiv_of_injective Algebra.botEquivOfInjectiveₓ'. -/
 /-- The bottom subalgebra is isomorphic to the base ring. -/
 noncomputable def botEquivOfInjective (h : Function.Injective (algebraMap R A)) :
@@ -2108,7 +2108,7 @@ theorem coe_prod : (prod S S₁ : Set (A × B)) = S ×ˢ S₁ :=
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (S₁ : Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5), Eq.{succ (max u2 u3)} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.semiring.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (coeFn.{succ (max u2 u3), succ (max u2 u3)} (OrderEmbedding.{max u2 u3, max u2 u3} 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u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (SetLike.partialOrder.{max u2 u3, max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (Prod.{u2, u3} A B) (Subalgebra.setLike.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))))) (Preorder.toHasLe.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.semiring.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (PartialOrder.toPreorder.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.semiring.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (CompleteSemilatticeInf.toPartialOrder.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.semiring.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (CompleteLattice.toCompleteSemilatticeInf.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.semiring.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (Submodule.completeLattice.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.semiring.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)))))))) (fun (_x : RelEmbedding.{max u2 u3, max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.semiring.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (LE.le.{max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (Preorder.toHasLe.{max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (PartialOrder.toPreorder.{max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (SetLike.partialOrder.{max u2 u3, max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (Prod.{u2, u3} A B) (Subalgebra.setLike.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)))))) (LE.le.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.semiring.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (Preorder.toHasLe.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.semiring.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (PartialOrder.toPreorder.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.semiring.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) 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(CompleteSemilatticeInf.toPartialOrder.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Submodule.completeLattice.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)))))))) (Subalgebra.toSubmodule.{u1, u3} R B _inst_1 _inst_4 _inst_5) S₁))
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (S₁ : Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5), Eq.{max (succ u2) (succ u3)} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) => Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) 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_inst_2 _inst_3 _inst_4 _inst_5))))) (Preorder.toLE.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (PartialOrder.toPreorder.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (OmegaCompletePartialOrder.toPartialOrder.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (CompleteLattice.instOmegaCompletePartialOrder.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (Submodule.completeLattice.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)))))))) (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (fun (_x : Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) => Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) _x) (RelHomClass.toFunLike.{max u2 u3, max u2 u3, max u2 u3} (OrderEmbedding.{max u2 u3, max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (Preorder.toLE.{max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (PartialOrder.toPreorder.{max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (SetLike.instPartialOrder.{max u2 u3, max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (Prod.{u2, u3} A B) (Subalgebra.instSetLikeSubalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))))) (Preorder.toLE.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (PartialOrder.toPreorder.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (OmegaCompletePartialOrder.toPartialOrder.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (CompleteLattice.instOmegaCompletePartialOrder.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (Submodule.completeLattice.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)))))))) (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) => LE.le.{max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (Preorder.toLE.{max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (PartialOrder.toPreorder.{max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (SetLike.instPartialOrder.{max u2 u3, max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (Prod.{u2, u3} A B) (Subalgebra.instSetLikeSubalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) => LE.le.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (Preorder.toLE.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (PartialOrder.toPreorder.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (OmegaCompletePartialOrder.toPartialOrder.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (CompleteLattice.instOmegaCompletePartialOrder.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (Submodule.completeLattice.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{max u2 u3, max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) => LE.le.{max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (Preorder.toLE.{max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (PartialOrder.toPreorder.{max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (SetLike.instPartialOrder.{max u2 u3, max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (Prod.{u2, u3} A B) (Subalgebra.instSetLikeSubalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) => LE.le.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (Preorder.toLE.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (PartialOrder.toPreorder.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (OmegaCompletePartialOrder.toPartialOrder.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (CompleteLattice.instOmegaCompletePartialOrder.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (Submodule.completeLattice.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Subalgebra.toSubmodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (Subalgebra.prod.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 S S₁)) (Submodule.prod.{u1, u2, u3} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, 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(Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (fun (_x : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) _x) (RelHomClass.toFunLike.{u2, u2, u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) 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x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 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Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A 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(Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) S) B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (FunLike.coe.{succ u3, succ u3, succ u3} (OrderEmbedding.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Preorder.toLE.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (PartialOrder.toPreorder.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) _x) (RelHomClass.toFunLike.{u3, u3, u3} (OrderEmbedding.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Preorder.toLE.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (PartialOrder.toPreorder.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instPartialOrder.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)))) (Preorder.toLE.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) 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(Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) => LE.le.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Preorder.toLE.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (PartialOrder.toPreorder.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Submodule.completeLattice.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) => LE.le.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Preorder.toLE.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (PartialOrder.toPreorder.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instPartialOrder.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) => LE.le.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Preorder.toLE.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (PartialOrder.toPreorder.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Submodule.completeLattice.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Subalgebra.toSubmodule.{u1, u3} R B _inst_1 _inst_4 _inst_5) S₁))
+  forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (S₁ : Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5), Eq.{max (succ u2) (succ u3)} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) => Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (Subalgebra.prod.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 S S₁)) (FunLike.coe.{succ (max u2 u3), succ (max u2 u3), succ (max u2 u3)} (OrderEmbedding.{max u2 u3, max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 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_inst_2 _inst_3 _inst_4 _inst_5))))) (Preorder.toLE.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (PartialOrder.toPreorder.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (OmegaCompletePartialOrder.toPartialOrder.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (CompleteLattice.instOmegaCompletePartialOrder.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (Submodule.completeLattice.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)))))))) (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (fun (_x : Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) => Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) _x) (RelHomClass.toFunLike.{max u2 u3, max u2 u3, max u2 u3} (OrderEmbedding.{max u2 u3, max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (Preorder.toLE.{max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (PartialOrder.toPreorder.{max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (SetLike.instPartialOrder.{max u2 u3, max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (Prod.{u2, u3} A B) (Subalgebra.instSetLikeSubalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))))) (Preorder.toLE.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (PartialOrder.toPreorder.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (OmegaCompletePartialOrder.toPartialOrder.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (CompleteLattice.instOmegaCompletePartialOrder.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (Submodule.completeLattice.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)))))))) (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) => LE.le.{max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (Preorder.toLE.{max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (PartialOrder.toPreorder.{max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (SetLike.instPartialOrder.{max u2 u3, max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (Prod.{u2, u3} A B) (Subalgebra.instSetLikeSubalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))))) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) => LE.le.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (Preorder.toLE.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (PartialOrder.toPreorder.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (OmegaCompletePartialOrder.toPartialOrder.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (CompleteLattice.instOmegaCompletePartialOrder.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (Submodule.completeLattice.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))))))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{max u2 u3, max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) => LE.le.{max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (Preorder.toLE.{max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (PartialOrder.toPreorder.{max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (SetLike.instPartialOrder.{max u2 u3, max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (Prod.{u2, u3} A B) (Subalgebra.instSetLikeSubalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))))) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) => LE.le.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (Preorder.toLE.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) 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_inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (CompleteLattice.instOmegaCompletePartialOrder.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (Submodule.completeLattice.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) 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x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 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(CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A 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(Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) S) B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (FunLike.coe.{succ u3, succ u3, succ u3} (OrderEmbedding.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Preorder.toLE.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (PartialOrder.toPreorder.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instPartialOrder.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)))) (Preorder.toLE.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (PartialOrder.toPreorder.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Submodule.completeLattice.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5))))))) (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (fun (_x : Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) => Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) _x) (RelHomClass.toFunLike.{u3, u3, u3} (OrderEmbedding.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Preorder.toLE.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (PartialOrder.toPreorder.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instPartialOrder.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)))) (Preorder.toLE.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (PartialOrder.toPreorder.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B 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_inst_1 _inst_4 _inst_5) (Preorder.toLE.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (PartialOrder.toPreorder.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instPartialOrder.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)))) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) => LE.le.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Preorder.toLE.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (PartialOrder.toPreorder.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Submodule.completeLattice.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)))))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) => LE.le.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Preorder.toLE.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (PartialOrder.toPreorder.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instPartialOrder.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)))) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) => LE.le.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Preorder.toLE.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (PartialOrder.toPreorder.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Submodule.completeLattice.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)))))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Subalgebra.toSubmodule.{u1, u3} R B _inst_1 _inst_4 _inst_5) S₁))
 Case conversion may be inaccurate. Consider using '#align subalgebra.prod_to_submodule Subalgebra.prod_toSubmoduleₓ'. -/
 theorem prod_toSubmodule : (S.Prod S₁).toSubmodule = S.toSubmodule.Prod S₁.toSubmodule :=
   rfl
@@ -2447,7 +2447,7 @@ section Center
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (r : R), Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) (Set.center.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (r : R), Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) (Set.{u2} A) (Set.instMembershipSet.{u2} A) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) (Set.center.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (r : R), Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) r) (Set.{u2} A) (Set.instMembershipSet.{u2} A) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) (Set.center.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))
 Case conversion may be inaccurate. Consider using '#align set.algebra_map_mem_center Set.algebraMap_mem_centerₓ'. -/
 theorem Set.algebraMap_mem_center (r : R) : algebraMap R A r ∈ Set.center A := by
   simp [Algebra.commutes, Set.mem_center_iff]
@@ -2529,7 +2529,7 @@ section Centralizer
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {s : Set.{u2} A} (r : R), Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) (Set.centralizer.{u2} A s (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {s : Set.{u2} A} (r : R), Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) (Set.{u2} A) (Set.instMembershipSet.{u2} A) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) (Set.centralizer.{u2} A s (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {s : Set.{u2} A} (r : R), Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) r) (Set.{u2} A) (Set.instMembershipSet.{u2} A) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) (Set.centralizer.{u2} A s (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))
 Case conversion may be inaccurate. Consider using '#align set.algebra_map_mem_centralizer Set.algebraMap_mem_centralizerₓ'. -/
 @[simp]
 theorem Set.algebraMap_mem_centralizer {s : Set A} (r : R) : algebraMap R A r ∈ s.centralizer :=

bump to nightly-2023-05-18-03

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

b46e9d53

Diff

@@ -951,7 +951,7 @@ theorem mem_map {S : Subalgebra R A} {f : A →ₐ[R] B} {y : B} : y ∈ map f S
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3} {f : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5}, Eq.{succ u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (coeFn.{succ u3, succ u3} (OrderEmbedding.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Preorder.toHasLe.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (PartialOrder.toPreorder.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.partialOrder.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.setLike.{u1, u3} R B _inst_1 _inst_4 _inst_5)))) (Preorder.toHasLe.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (PartialOrder.toPreorder.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (CompleteSemilatticeInf.toPartialOrder.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Submodule.completeLattice.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5))))))) (fun (_x : RelEmbedding.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (LE.le.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Preorder.toHasLe.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (PartialOrder.toPreorder.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.partialOrder.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.setLike.{u1, u3} R B _inst_1 _inst_4 _inst_5))))) (LE.le.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Preorder.toHasLe.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (PartialOrder.toPreorder.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (CompleteSemilatticeInf.toPartialOrder.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B 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(Submodule.completeLattice.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)))))))) (Subalgebra.toSubmodule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Subalgebra.map.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 f S)) (Submodule.map.{u1, u1, u2, u3, max u2 u3} R R A B (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R A B (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A 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(Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) => (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) -> (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (RelEmbedding.hasCoeToFun.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) S))
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3} {f : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5}, Eq.{succ u3} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) => Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Subalgebra.map.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 f S)) (FunLike.coe.{succ u3, succ u3, succ u3} (OrderEmbedding.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Submodule.{u1, u3} R B 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(Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (fun (_x : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) _x) (RelHomClass.toFunLike.{u2, u2, u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) S))
+  forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3} {f : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5}, Eq.{succ u3} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) => Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Subalgebra.map.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 f S)) (FunLike.coe.{succ u3, succ u3, succ u3} (OrderEmbedding.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Preorder.toLE.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (PartialOrder.toPreorder.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instPartialOrder.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)))) (Preorder.toLE.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (PartialOrder.toPreorder.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Submodule.completeLattice.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5))))))) (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (fun (_x : Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) => Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) _x) (RelHomClass.toFunLike.{u3, u3, u3} (OrderEmbedding.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Preorder.toLE.{u3} 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(Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) 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(Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) S))
 Case conversion may be inaccurate. Consider using '#align subalgebra.map_to_submodule Subalgebra.map_toSubmoduleₓ'. -/
 theorem map_toSubmodule {S : Subalgebra R A} {f : A →ₐ[R] B} :
     (S.map f).toSubmodule = S.toSubmodule.map f.toLinearMap :=
@@ -2630,7 +2630,7 @@ theorem mem_of_finset_sum_eq_one_of_pow_smul_mem {S : Type _} [CommRing S] [Alge
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {S : Type.{u2}} [_inst_6 : CommRing.{u2} S] [_inst_7 : Algebra.{u1, u2} R S _inst_1 (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6))] (S' : Subalgebra.{u1, u2} R S _inst_1 (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_7) (s : Set.{u2} S) (l : Finsupp.{u2, u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} S) Type.{u2} (Set.hasCoeToSort.{u2} S) s) S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} S (NonAssocRing.toNonUnitalNonAssocRing.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_6))))))), (Eq.{succ u2} S (coeFn.{succ u2, succ u2} (LinearMap.{u2, u2, u2, u2} S S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)))) 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 but is expected to have type
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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6))))) (Semiring.toModule.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)))) (Semiring.toModule.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6))) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6))))) (Finsupp.total.{u1, u1, u1} (Set.Elem.{u1} S s) S S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_6))))) (Semiring.toModule.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6))) (Subtype.val.{succ u1} S (fun (x : S) => Membership.mem.{u1, u1} S (Set.{u1} S) (Set.instMembershipSet.{u1} S) x s))) l) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6))))) => S) l) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6))))) => S) l) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6))))) => S) l) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6))))) => S) l) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6))))) => S) l) _inst_6)))))) -> (HasSubset.Subset.{u1} (Set.{u1} S) (Set.instHasSubsetSet.{u1} S) s (SetLike.coe.{u1, u1} (Subalgebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)) _inst_7) S (Subalgebra.instSetLikeSubalgebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)) _inst_7) S')) -> (forall (i : Set.Elem.{u1} S s), Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : 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Exists.{1} Nat (fun (n : Nat) => Membership.mem.{u1, u1} S (Subalgebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)) _inst_7) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)) _inst_7) S (Subalgebra.instSetLikeSubalgebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)) _inst_7)) (HSMul.hSMul.{u1, u1, u1} S S S (instHSMul.{u1, u1} S S (Algebra.toSMul.{u1, u1} S S (CommRing.toCommSemiring.{u1} S _inst_6) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)) (Algebra.id.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)))) (HPow.hPow.{u1, 0, u1} S Nat S (instHPow.{u1, 0} S Nat (Monoid.Pow.{u1} S (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)))))) (Subtype.val.{succ u1} S (fun (x : S) => Membership.mem.{u1, u1} S (Set.{u1} S) (Set.instMembershipSet.{u1} S) x s) r) n) x) S')) -> (Membership.mem.{u1, u1} S (Subalgebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)) _inst_7) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)) _inst_7) S (Subalgebra.instSetLikeSubalgebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)) _inst_7)) x S'))
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {S : Type.{u1}} [_inst_6 : CommRing.{u1} S] [_inst_7 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6))] (S' : Subalgebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)) _inst_7) (s : Set.{u1} S) (l : Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (CommMonoidWithZero.toZero.{u1} S (CommSemiring.toCommMonoidWithZero.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)))), (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6))))) => S) l) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} S S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)))) (Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6))))) S (Finsupp.addCommMonoid.{u1, u1} (Set.Elem.{u1} S s) S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_6))))) (Finsupp.module.{u1, u1, u1} (Set.Elem.{u1} S s) S S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6))))) (Semiring.toModule.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)))) (Semiring.toModule.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)))) (Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6))))) (fun (_x : Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6))))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6))))) => S) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} S S (Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6))))) S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)) (Finsupp.addCommMonoid.{u1, u1} (Set.Elem.{u1} S s) S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_6))))) (Finsupp.module.{u1, u1, u1} (Set.Elem.{u1} S s) S S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6))))) (Semiring.toModule.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)))) (Semiring.toModule.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6))) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6))))) (Finsupp.total.{u1, u1, u1} (Set.Elem.{u1} S s) S S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_6))))) (Semiring.toModule.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6))) (Subtype.val.{succ u1} S (fun (x : S) => Membership.mem.{u1, u1} S (Set.{u1} S) (Set.instMembershipSet.{u1} S) x s))) l) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6))))) => S) l) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6))))) => S) l) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6))))) => S) l) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6))))) => S) l) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6))))) => S) l) _inst_6)))))) -> (HasSubset.Subset.{u1} (Set.{u1} S) (Set.instHasSubsetSet.{u1} S) s (SetLike.coe.{u1, u1} (Subalgebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)) _inst_7) S (Subalgebra.instSetLikeSubalgebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)) _inst_7) S')) -> (forall (i : Set.Elem.{u1} S s), Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : Set.Elem.{u1} S s) => S) i) (Subalgebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)) _inst_7) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)) _inst_7) S (Subalgebra.instSetLikeSubalgebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)) _inst_7)) (FunLike.coe.{succ u1, succ u1, succ u1} (Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (CommMonoidWithZero.toZero.{u1} S (CommSemiring.toCommMonoidWithZero.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)))) (Set.Elem.{u1} S s) (fun (_x : Set.Elem.{u1} S s) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : Set.Elem.{u1} S s) => S) _x) (Finsupp.funLike.{u1, u1} (Set.Elem.{u1} S s) S (CommMonoidWithZero.toZero.{u1} S (CommSemiring.toCommMonoidWithZero.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)))) l i) S') -> (forall (x : S), (forall (r : Set.Elem.{u1} S s), Exists.{1} Nat (fun (n : Nat) => Membership.mem.{u1, u1} S (Subalgebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)) _inst_7) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)) _inst_7) S (Subalgebra.instSetLikeSubalgebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)) _inst_7)) (HSMul.hSMul.{u1, u1, u1} S S S (instHSMul.{u1, u1} S S (Algebra.toSMul.{u1, u1} S S (CommRing.toCommSemiring.{u1} S _inst_6) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)) (Algebra.id.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)))) (HPow.hPow.{u1, 0, u1} S Nat S (instHPow.{u1, 0} S Nat (Monoid.Pow.{u1} S (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)))))) (Subtype.val.{succ u1} S (fun (x : S) => Membership.mem.{u1, u1} S (Set.{u1} S) (Set.instMembershipSet.{u1} S) x s) r) n) x) S')) -> (Membership.mem.{u1, u1} S (Subalgebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)) _inst_7) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)) _inst_7) S (Subalgebra.instSetLikeSubalgebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)) _inst_7)) x S'))
 Case conversion may be inaccurate. Consider using '#align subalgebra.mem_of_span_eq_top_of_smul_pow_mem Subalgebra.mem_of_span_eq_top_of_smul_pow_memₓ'. -/
 theorem mem_of_span_eq_top_of_smul_pow_mem {S : Type _} [CommRing S] [Algebra R S]
     (S' : Subalgebra R S) (s : Set S) (l : s →₀ S) (hs : Finsupp.total s S S coe l = 1)

bump to nightly-2023-05-16-22

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

00d01a10

Diff

@@ -1101,7 +1101,7 @@ theorem coe_toSubalgebra (p : Submodule R A) (h_one h_mul) :
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (s : Set.{u2} A) (h0 : Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) (OfNat.ofNat.{u2} A 0 (OfNat.mk.{u2} A 0 (Zero.zero.{u2} A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))))))) s) (hadd : forall {a : A} {b : A}, (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) a s) -> (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) b s) -> (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (AddZeroClass.toHasAdd.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))))) a b) s)) (hsmul : forall (c : R) {x : A}, (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) x s) -> (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) (SMul.smul.{u1, u2} R A (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) c x) s)) (h1 : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (OfNat.ofNat.{u2} A 1 (OfNat.mk.{u2} A 1 (One.one.{u2} A (AddMonoidWithOne.toOne.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))))) (Submodule.mk.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) s hadd h0 hsmul)) (hmul : forall (x : A) (y : A), (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A 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(RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) s) (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) (SMul.smul.{u1, u2} R A (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A 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_inst_2)))))))) s) (id_tag Tactic.IdTag.rw (Eq.{1} Prop (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) s) (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) (SMul.smul.{u1, u2} R A (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A 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(OfNat.ofNat.{u2} A 1 (OfNat.mk.{u2} A 1 (One.one.{u2} A (AddMonoidWithOne.toOne.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))))) (Algebra.algebraMap_eq_smul_one.{u1, u2} R A _inst_1 _inst_2 _inst_3 r))) (hsmul r (OfNat.ofNat.{u2} A 1 (OfNat.mk.{u2} A 1 (One.one.{u2} A (AddMonoidWithOne.toOne.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))))) h1)))
 but is expected to have type
-  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u1} A] [_inst_3 : Algebra.{u2, u1} R A _inst_1 _inst_2] (s : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (h0 : Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) 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{b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6478 : A} => Submodule.add_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6477 b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6478) (Submodule.zero_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s))))))) (HSMul.hSMul.{u2, u1, u1} R A A (instHSMul.{u2, u1} R A (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_2 _inst_3)) r (OfNat.ofNat.{u1} A 1 (One.toOfNat1.{u1} A (Semiring.toOne.{u1} A _inst_2)))) (Algebra.algebraMap_eq_smul_one.{u2, u1} R A _inst_1 _inst_2 _inst_3 r))) (Submodule.smul_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s (OfNat.ofNat.{u1} A 1 (One.toOfNat1.{u1} A (Semiring.toOne.{u1} A _inst_2))) r h0)))
+  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u1} A] [_inst_3 : Algebra.{u2, u1} R A _inst_1 _inst_2] (s : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (h0 : Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) (OfNat.ofNat.{u1} A 1 (One.toOfNat1.{u1} A (Semiring.toOne.{u1} A _inst_2))) s) (hadd : forall (a : A) (b : A), (Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) a s) -> (Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) b s) -> (Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u1, u1, u1} A A A (instHMul.{u1} A (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) a b) s)), Eq.{succ u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 s h0 hadd) (Subalgebra.mk.{u2, u1} R A _inst_1 _inst_2 _inst_3 (Subsemiring.mk.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Submonoid.mk.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemigroup.mk.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) s) hadd) h0) (fun {a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6476 : A} {b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6477 : A} => Submodule.add_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6476 b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6477) (Submodule.zero_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s)) (fun (r : R) => Eq.mpr.{0} (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) (Set.{u1} A) (Set.instMembershipSet.{u1} A) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2) (RingHom.instRingHomClassRingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2))))) (algebraMap.{u2, u1} R A _inst_1 _inst_2 _inst_3) r) (Subsemigroup.carrier.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (Submonoid.toSubsemigroup.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemiring.toSubmonoid.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Subsemiring.mk.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Submonoid.mk.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemigroup.mk.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) s) hadd) h0) (fun {a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6476 : A} {b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6477 : A} => Submodule.add_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6476 b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6477) (Submodule.zero_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s)))))) (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) (Set.{u1} A) (Set.instMembershipSet.{u1} A) (HSMul.hSMul.{u2, u1, u1} R A A (instHSMul.{u2, u1} R A (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_2 _inst_3)) r (OfNat.ofNat.{u1} A 1 (One.toOfNat1.{u1} A (Semiring.toOne.{u1} A _inst_2)))) (Subsemigroup.carrier.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (Submonoid.toSubsemigroup.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemiring.toSubmonoid.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Subsemiring.mk.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Submonoid.mk.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemigroup.mk.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) s) hadd) h0) (fun {a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6476 : A} {b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6477 : A} => Submodule.add_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6476 b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6477) (Submodule.zero_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s)))))) (id.{0} (Eq.{1} Prop (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) (Set.{u1} A) (Set.instMembershipSet.{u1} A) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) 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(MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2) (RingHom.instRingHomClassRingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2))))) (algebraMap.{u2, u1} R A _inst_1 _inst_2 _inst_3) r) (Subsemigroup.carrier.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (Submonoid.toSubsemigroup.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemiring.toSubmonoid.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Subsemiring.mk.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Submonoid.mk.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemigroup.mk.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) s) hadd) h0) (fun {a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6476 : A} {b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6477 : A} => Submodule.add_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6476 b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6477) (Submodule.zero_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s))))))) (HSMul.hSMul.{u2, u1, u1} R A A (instHSMul.{u2, u1} R A (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_2 _inst_3)) r (OfNat.ofNat.{u1} A 1 (One.toOfNat1.{u1} A (Semiring.toOne.{u1} A _inst_2)))) (Algebra.algebraMap_eq_smul_one.{u2, u1} R A _inst_1 _inst_2 _inst_3 r))) (Submodule.smul_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s (OfNat.ofNat.{u1} A 1 (One.toOfNat1.{u1} A (Semiring.toOne.{u1} A _inst_2))) r h0)))
 Case conversion may be inaccurate. Consider using '#align submodule.to_subalgebra_mk Submodule.toSubalgebra_mkₓ'. -/
 @[simp]
 theorem toSubalgebra_mk (s : Set A) (h0 hadd hsmul h1 hmul) :
@@ -2169,7 +2169,7 @@ variable {ι : Type _}
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {ι : Type.{u3}} [_inst_6 : Nonempty.{succ u3} ι] {S : ι -> (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)}, (Directed.{u2, succ u3} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) ι (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) S) -> (Eq.{succ u2} (Set.{u2} A) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (iSup.{u2, succ u3} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))) ι S)) (Set.iUnion.{u2, succ u3} A ι (fun (i : ι) => (fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (S i))))
 but is expected to have type
-  forall {R : Type.{u2}} {A : Type.{u3}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u3} A] [_inst_3 : Algebra.{u2, u3} R A _inst_1 _inst_2] {ι : Type.{u1}} [_inst_6 : Nonempty.{succ u1} ι] {S : ι -> (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)}, (Directed.{u3, succ u1} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) ι (fun (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.12747 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.12749 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) => LE.le.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3))))) x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.12747 x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.12749) S) -> (Eq.{succ u3} (Set.{u3} A) (SetLike.coe.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (iSup.{u3, succ u1} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3))) ι S)) (Set.iUnion.{u3, succ u1} A ι (fun (i : ι) => SetLike.coe.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (S i))))
+  forall {R : Type.{u2}} {A : Type.{u3}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u3} A] [_inst_3 : Algebra.{u2, u3} R A _inst_1 _inst_2] {ι : Type.{u1}} [_inst_6 : Nonempty.{succ u1} ι] {S : ι -> (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)}, (Directed.{u3, succ u1} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) ι (fun (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.12746 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.12748 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) => LE.le.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3))))) x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.12746 x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.12748) S) -> (Eq.{succ u3} (Set.{u3} A) (SetLike.coe.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (iSup.{u3, succ u1} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3))) ι S)) (Set.iUnion.{u3, succ u1} A ι (fun (i : ι) => SetLike.coe.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (S i))))
 Case conversion may be inaccurate. Consider using '#align subalgebra.coe_supr_of_directed Subalgebra.coe_iSup_of_directedₓ'. -/
 theorem coe_iSup_of_directed [Nonempty ι] {S : ι → Subalgebra R A} (dir : Directed (· ≤ ·) S) :
     ↑(iSup S) = ⋃ i, (S i : Set A) :=
@@ -2198,7 +2198,7 @@ theorem coe_iSup_of_directed [Nonempty ι] {S : ι → Subalgebra R A} (dir : Di
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {ι : Type.{u4}} [_inst_6 : Nonempty.{succ u4} ι] (K : ι -> (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)), (Directed.{u2, succ u4} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) ι (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) K) -> (forall (f : forall (i : ι), AlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K i)) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5), (forall (i : ι) (j : ι) (h : LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (K i) (K j)), Eq.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K i)) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) (f i) (AlgHom.comp.{u1, u2, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K i)) (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K j)) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K j)) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K j)) _inst_5 (f j) (Subalgebra.inclusion.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i) (K j) h))) -> (forall (T : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), (Eq.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) T (iSup.{u2, succ u4} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))) ι K)) -> (AlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) _inst_5)))
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {ι : Type.{u4}} [_inst_6 : Nonempty.{succ u4} ι] (K : ι -> (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)), (Directed.{u2, succ u4} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) ι (fun (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13130 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13132 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13130 x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13132) K) -> (forall (f : forall (i : ι), AlgHom.{u1, u2, u3} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5), (forall (i : ι) (j : ι) (h : LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (K i) (K j)), Eq.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) (f i) (AlgHom.comp.{u1, u2, u2, u3} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x (K j))) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K j)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K j)) _inst_5 (f j) (Subalgebra.inclusion.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i) (K j) h))) -> (forall (T : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), (Eq.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) T (iSup.{u2, succ u4} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))) ι K)) -> (AlgHom.{u1, u2, u3} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T)) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) _inst_5)))
+  forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {ι : Type.{u4}} [_inst_6 : Nonempty.{succ u4} ι] (K : ι -> (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)), (Directed.{u2, succ u4} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) ι (fun (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13129 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13131 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13129 x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13131) K) -> (forall (f : forall (i : ι), AlgHom.{u1, u2, u3} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5), (forall (i : ι) (j : ι) (h : LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (K i) (K j)), Eq.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) (f i) (AlgHom.comp.{u1, u2, u2, u3} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x (K j))) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K j)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K j)) _inst_5 (f j) (Subalgebra.inclusion.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i) (K j) h))) -> (forall (T : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), (Eq.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) T (iSup.{u2, succ u4} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))) ι K)) -> (AlgHom.{u1, u2, u3} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T)) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) _inst_5)))
 Case conversion may be inaccurate. Consider using '#align subalgebra.supr_lift Subalgebra.iSupLiftₓ'. -/
 /-- Define an algebra homomorphism on a directed supremum of subalgebras by defining
 it on each subalgebra, and proving that it agrees on the intersection of subalgebras. -/
@@ -2235,7 +2235,7 @@ variable [Nonempty ι] {K : ι → Subalgebra R A} {dir : Directed (· ≤ ·) K
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {ι : Type.{u4}} [_inst_6 : Nonempty.{succ u4} ι] {K : ι -> (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {dir : Directed.{u2, succ u4} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) ι (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) K} {f : forall (i : ι), AlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ 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u2} R A _inst_1 _inst_2 _inst_3 (K j)) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K j)) _inst_5 (f j) (Subalgebra.inclusion.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i) (K j) h))} {T : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3} {hT : Eq.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) T (iSup.{u2, succ u4} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))) ι K)} {i : ι} (x : coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K i)) (h : 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u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))) (Module.toDistribMulAction.{u2, u3} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i))))) (Algebra.toModule.{u2, u3} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) 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_inst_2 _inst_3 (K i)) _inst_5) R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)) (Module.toDistribMulAction.{u2, u3} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i))))) (Algebra.toModule.{u2, u3} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)))) (Module.toDistribMulAction.{u2, u4} R B (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u2, u4} R B _inst_1 _inst_4 _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u3, u4, max u3 u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5 (AlgHom.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) (AlgHom.algHomClass.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5))))) (f i) x)
+  forall {R : Type.{u2}} {A : Type.{u3}} {B : Type.{u4}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u3} A] [_inst_3 : Algebra.{u2, u3} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u4} B] [_inst_5 : Algebra.{u2, u4} R B _inst_1 _inst_4] {ι : Type.{u1}} [_inst_6 : Nonempty.{succ u1} ι] {K : ι -> (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)} {dir : Directed.{u3, succ u1} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) ι (fun (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13717 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13719 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) => LE.le.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3))))) x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13717 x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13719) K} {f : forall (i : ι), AlgHom.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5} {hf : forall (i : ι) (j : ι) (h : LE.le.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3))))) (K i) (K j)), Eq.{max (succ u3) (succ u4)} (AlgHom.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) (f i) (AlgHom.comp.{u2, u3, u3, u4} R 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u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))) (Module.toDistribMulAction.{u2, u3} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 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_inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5 (AlgHom.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) (AlgHom.algHomClass.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5))))) (f i) x)
 Case conversion may be inaccurate. Consider using '#align subalgebra.supr_lift_inclusion Subalgebra.iSupLift_inclusionₓ'. -/
 @[simp]
 theorem iSupLift_inclusion {i : ι} (x : K i) (h : K i ≤ T) :
@@ -2247,7 +2247,7 @@ theorem iSupLift_inclusion {i : ι} (x : K i) (h : K i ≤ T) :
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {ι : Type.{u4}} [_inst_6 : Nonempty.{succ u4} ι] {K : ι -> (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {dir : Directed.{u2, succ u4} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) ι (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) K} {f : forall (i : ι), AlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K i)) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5} {hf : forall (i : ι) (j : ι) (h : LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (K i) (K j)), Eq.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K i)) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) (f i) (AlgHom.comp.{u1, u2, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K i)) (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K j)) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K j)) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K j)) _inst_5 (f j) (Subalgebra.inclusion.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i) (K j) h))} {T : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3} {hT : Eq.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) T (iSup.{u2, succ u4} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))) ι K)} {i : ι} (h : LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (K i) T), Eq.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K i)) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) (AlgHom.comp.{u1, u2, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K i)) (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) _inst_5 (Subalgebra.iSupLift.{u1, u2, u3, u4} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 ι _inst_6 K dir f hf T hT) (Subalgebra.inclusion.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i) T h)) (f i)
 but is expected to have type
-  forall {R : Type.{u2}} {A : Type.{u3}} {B : Type.{u4}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u3} A] [_inst_3 : Algebra.{u2, u3} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u4} B] [_inst_5 : Algebra.{u2, u4} R B _inst_1 _inst_4] {ι : Type.{u1}} [_inst_6 : Nonempty.{succ u1} ι] {K : ι -> (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)} {dir : Directed.{u3, succ u1} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) ι (fun (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13873 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13875 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) => LE.le.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3))))) x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13873 x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13875) K} {f : forall (i : ι), AlgHom.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5} {hf : forall (i : ι) (j : ι) (h : LE.le.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 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(Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K j))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K j)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K j)) _inst_5 (f j) (Subalgebra.inclusion.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i) (K j) h))} {T : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3} {hT : Eq.{succ u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) T (iSup.{u3, succ u1} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3))) ι K)} {i : ι} (h : LE.le.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3))))) (K i) T), Eq.{max (succ u3) (succ u4)} (AlgHom.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) (AlgHom.comp.{u2, u3, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subtype.{succ u3} A (fun (x : A) => 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+  forall {R : Type.{u2}} {A : Type.{u3}} {B : Type.{u4}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u3} A] [_inst_3 : Algebra.{u2, u3} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u4} B] [_inst_5 : Algebra.{u2, u4} R B _inst_1 _inst_4] {ι : Type.{u1}} [_inst_6 : Nonempty.{succ u1} ι] {K : ι -> (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)} {dir : Directed.{u3, succ u1} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) ι (fun (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13872 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13874 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) => LE.le.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3))))) x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13872 x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13874) K} {f : forall (i : ι), AlgHom.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5} {hf : forall (i : ι) (j : ι) (h : LE.le.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 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(Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K j))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K j)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K j)) _inst_5 (f j) (Subalgebra.inclusion.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i) (K j) h))} {T : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3} {hT : Eq.{succ u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) T (iSup.{u3, succ u1} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3))) ι K)} {i : ι} (h : LE.le.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) 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 Case conversion may be inaccurate. Consider using '#align subalgebra.supr_lift_comp_inclusion Subalgebra.iSupLift_comp_inclusionₓ'. -/
 @[simp]
 theorem iSupLift_comp_inclusion {i : ι} (h : K i ≤ T) :
@@ -2258,7 +2258,7 @@ theorem iSupLift_comp_inclusion {i : ι} (h : K i ≤ T) :
 lean 3 declaration is
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 but is expected to have type
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+  forall {R : Type.{u2}} {A : Type.{u3}} {B : Type.{u4}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u3} A] [_inst_3 : Algebra.{u2, u3} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u4} B] [_inst_5 : Algebra.{u2, u4} R B _inst_1 _inst_4] {ι : Type.{u1}} [_inst_6 : Nonempty.{succ u1} ι] {K : ι -> (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)} {dir : Directed.{u3, succ u1} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) ι (fun (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13999 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.14001 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) => LE.le.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) 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(Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)))))) (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))) (Module.toDistribMulAction.{u2, u3} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i))))) (Algebra.toModule.{u2, u3} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)))) (Module.toDistribMulAction.{u2, u4} R B (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u2, u4} R B _inst_1 _inst_4 _inst_5)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u3 u4, u2, u3, u4} (AlgHom.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)) (Module.toDistribMulAction.{u2, u3} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i))))) (Algebra.toModule.{u2, u3} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)))) (Module.toDistribMulAction.{u2, u4} R B (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u2, u4} R B _inst_1 _inst_4 _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u3, u4, max u3 u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5 (AlgHom.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) (AlgHom.algHomClass.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5))))) (f i) x)
 Case conversion may be inaccurate. Consider using '#align subalgebra.supr_lift_mk Subalgebra.iSupLift_mkₓ'. -/
 @[simp]
 theorem iSupLift_mk {i : ι} (x : K i) (hx : (x : A) ∈ T) :
@@ -2269,7 +2269,7 @@ theorem iSupLift_mk {i : ι} (x : K i) (hx : (x : A) ∈ T) :
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {ι : Type.{u4}} [_inst_6 : Nonempty.{succ u4} ι] {K : ι -> (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {dir : Directed.{u2, succ u4} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) ι (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) K} {f : forall (i : ι), AlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K i)) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5} {hf : forall (i : ι) (j : ι) (h : LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (K i) (K j)), Eq.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} 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(AddMonoid.toAddZeroClass.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))))) (DistribMulAction.toDistribSMul.{u2, u4} R B (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))) (Module.toDistribMulAction.{u2, u4} R B (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u2, u4} R B _inst_1 _inst_4 _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u4, u2, u3, u4} (AlgHom.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) 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(SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)))))) (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))) (Module.toDistribMulAction.{u2, u3} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i))))) (Algebra.toModule.{u2, u3} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)))) (Module.toDistribMulAction.{u2, u4} R B (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u2, u4} R B _inst_1 _inst_4 _inst_5)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u3 u4, u2, u3, u4} (AlgHom.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)) (Module.toDistribMulAction.{u2, u3} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i))))) (Algebra.toModule.{u2, u3} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)))) (Module.toDistribMulAction.{u2, u4} R B (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u2, u4} R B _inst_1 _inst_4 _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u3, u4, max u3 u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5 (AlgHom.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) (AlgHom.algHomClass.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5))))) (f i) (Subtype.mk.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i)) (Subtype.val.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Set.{u3} A) (Set.instMembershipSet.{u3} A) x (SetLike.coe.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) T)) x) hx))
+  forall {R : Type.{u2}} {A : Type.{u3}} {B : Type.{u4}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u3} A] [_inst_3 : Algebra.{u2, u3} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u4} B] [_inst_5 : Algebra.{u2, u4} R B _inst_1 _inst_4] {ι : Type.{u1}} [_inst_6 : Nonempty.{succ u1} ι] {K : ι -> (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)} {dir : Directed.{u3, succ u1} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) ι (fun (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.14154 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.14156 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) => LE.le.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) 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_inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i))))) (Algebra.toModule.{u2, u3} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)))) (Module.toDistribMulAction.{u2, u4} R B (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u2, u4} R B _inst_1 _inst_4 _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u3, u4, max u3 u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5 (AlgHom.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) (AlgHom.algHomClass.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5))))) (f i) (Subtype.mk.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i)) (Subtype.val.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Set.{u3} A) (Set.instMembershipSet.{u3} A) x (SetLike.coe.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) T)) x) hx))
 Case conversion may be inaccurate. Consider using '#align subalgebra.supr_lift_of_mem Subalgebra.iSupLift_of_memₓ'. -/
 theorem iSupLift_of_mem {i : ι} (x : T) (hx : (x : A) ∈ K i) :
     iSupLift K dir f hf T hT x = f i ⟨x, hx⟩ := by subst hT <;> exact Set.iUnionLift_of_mem x hx

bump to nightly-2023-05-16-16

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

9cb92e8c

Diff

@@ -172,7 +172,7 @@ theorem algebraMap_mem (r : R) : algebraMap R A r ∈ S :=
 
 /- warning: subalgebra.srange_le -> Subalgebra.rangeS_le is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), LE.le.{u2} (Subsemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (Preorder.toLE.{u2} (Subsemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (PartialOrder.toPreorder.{u2} (Subsemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subsemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subsemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (Subsemiring.completeLattice.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (RingHom.rangeS.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Subalgebra.toSubsemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S)
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), LE.le.{u2} (Subsemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (Preorder.toHasLe.{u2} (Subsemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (PartialOrder.toPreorder.{u2} (Subsemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subsemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subsemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (Subsemiring.completeLattice.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (RingHom.rangeS.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Subalgebra.toSubsemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S)
 but is expected to have type
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), LE.le.{u2} (Subsemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (Preorder.toLE.{u2} (Subsemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (PartialOrder.toPreorder.{u2} (Subsemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Subsemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Subsemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (Subsemiring.instCompleteLatticeSubsemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (RingHom.rangeS.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Subalgebra.toSubsemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S)
 Case conversion may be inaccurate. Consider using '#align subalgebra.srange_le Subalgebra.rangeS_leₓ'. -/
@@ -617,7 +617,7 @@ end
 
 /- warning: subalgebra.to_submodule -> Subalgebra.toSubmodule is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))
 but is expected to have type
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))
 Case conversion may be inaccurate. Consider using '#align subalgebra.to_submodule Subalgebra.toSubmoduleₓ'. -/
@@ -638,7 +638,7 @@ def toSubmodule : Subalgebra R A ↪o Submodule R A
 
 /- warning: subalgebra.mem_to_submodule -> Subalgebra.mem_toSubmodule is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) {x : A}, Iff (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (coeFn.{succ u2, succ u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (fun (_x : RelEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (RelEmbedding.hasCoeToFun.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) S)) (Membership.Mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) {x : A}, Iff (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (coeFn.{succ u2, succ u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (fun (_x : RelEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) => (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) -> (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (RelEmbedding.hasCoeToFun.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) S)) (Membership.Mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)
 but is expected to have type
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) {x : A}, Iff (Membership.mem.{u2, u2} A ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) (SetLike.instMembership.{u2, u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (FunLike.coe.{succ u2, succ u2, succ u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (fun (_x : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) _x) (RelHomClass.toFunLike.{u2, u2, u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) S)) (Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)
 Case conversion may be inaccurate. Consider using '#align subalgebra.mem_to_submodule Subalgebra.mem_toSubmoduleₓ'. -/
@@ -651,7 +651,7 @@ theorem mem_toSubmodule {x} : x ∈ S.toSubmodule ↔ x ∈ S :=
 
 /- warning: subalgebra.coe_to_submodule -> Subalgebra.coe_toSubmodule is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), Eq.{succ u2} (Set.{u2} A) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R A 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(Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) S)
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), Eq.{succ u2} (Set.{u2} A) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R A 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) => (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) -> (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (RelEmbedding.hasCoeToFun.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) S)) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) S)
 but is expected to have type
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), Eq.{succ u2} (Set.{u2} A) (SetLike.coe.{u2, u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (FunLike.coe.{succ u2, succ u2, succ u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (fun (_x : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) _x) (RelHomClass.toFunLike.{u2, u2, u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) S)) (SetLike.coe.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) S)
 Case conversion may be inaccurate. Consider using '#align subalgebra.coe_to_submodule Subalgebra.coe_toSubmoduleₓ'. -/
@@ -888,7 +888,7 @@ theorem toSubring_subtype {R A : Type _} [CommRing R] [Ring A] [Algebra R A] (S
 
 /- warning: subalgebra.to_submodule_equiv -> Subalgebra.toSubmoduleEquiv is a dubious translation:
 lean 3 declaration is
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+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Subalgebra.toSubmoduleEquiv._proof_1.{u1} R _inst_1) (Subalgebra.toSubmoduleEquiv._proof_2.{u1} R _inst_1) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R A 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 but is expected to have type
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_inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A 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_inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) S)) (Subalgebra.instModuleSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToNonAssocSemiringToSubsemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S)
 Case conversion may be inaccurate. Consider using '#align subalgebra.to_submodule_equiv Subalgebra.toSubmoduleEquivₓ'. -/
@@ -908,7 +908,7 @@ def map (f : A →ₐ[R] B) (S : Subalgebra R A) : Subalgebra R B :=
 
 /- warning: subalgebra.map_mono -> Subalgebra.map_mono is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {S₁ : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3} {S₂ : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3} {f : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5}, (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) S₁ S₂) -> (LE.le.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Preorder.toLE.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (PartialOrder.toPreorder.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.partialOrder.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.setLike.{u1, u3} R B _inst_1 _inst_4 _inst_5)))) (Subalgebra.map.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 f S₁) (Subalgebra.map.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 f S₂))
+  forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {S₁ : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3} {S₂ : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3} {f : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5}, (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) S₁ S₂) -> (LE.le.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Preorder.toHasLe.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (PartialOrder.toPreorder.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.partialOrder.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.setLike.{u1, u3} R B _inst_1 _inst_4 _inst_5)))) (Subalgebra.map.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 f S₁) (Subalgebra.map.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 f S₂))
 but is expected to have type
   forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {S₁ : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3} {S₂ : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3} {f : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5}, (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) S₁ S₂) -> (LE.le.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Preorder.toLE.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (PartialOrder.toPreorder.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instPartialOrder.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)))) (Subalgebra.map.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 f S₁) (Subalgebra.map.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 f S₂))
 Case conversion may be inaccurate. Consider using '#align subalgebra.map_mono Subalgebra.map_monoₓ'. -/
@@ -949,7 +949,7 @@ theorem mem_map {S : Subalgebra R A} {f : A →ₐ[R] B} {y : B} : y ∈ map f S
 
 /- warning: subalgebra.map_to_submodule -> Subalgebra.map_toSubmodule is a dubious translation:
 lean 3 declaration is
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(Submodule.completeLattice.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)))))))) (Subalgebra.toSubmodule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Subalgebra.map.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 f S)) (Submodule.map.{u1, u1, u2, u3, max u2 u3} R R A B (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R A B (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AlgHom.toLinearMap.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 f) (coeFn.{succ u2, succ u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) 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(Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) S))
+  forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3} {f : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5}, Eq.{succ u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (coeFn.{succ u3, succ u3} (OrderEmbedding.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R 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(Submodule.completeLattice.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)))))))) (Subalgebra.toSubmodule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Subalgebra.map.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 f S)) (Submodule.map.{u1, u1, u2, u3, max u2 u3} R R A B (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R A B (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A 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(Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) S))
 but is expected to have type
   forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3} {f : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5}, Eq.{succ u3} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) => Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Subalgebra.map.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 f S)) (FunLike.coe.{succ u3, succ u3, succ u3} (OrderEmbedding.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Submodule.{u1, u3} R B 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_inst_5)) (Submodule.completeLattice.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) => LE.le.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) 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_inst_4 _inst_5)) => LE.le.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Preorder.toLE.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (PartialOrder.toPreorder.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R 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(Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (fun (_x : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) _x) (RelHomClass.toFunLike.{u2, u2, u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) S))
 Case conversion may be inaccurate. Consider using '#align subalgebra.map_to_submodule Subalgebra.map_toSubmoduleₓ'. -/
@@ -987,7 +987,7 @@ def comap (f : A →ₐ[R] B) (S : Subalgebra R B) : Subalgebra R A :=
 
 /- warning: subalgebra.map_le -> Subalgebra.map_le is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3} {f : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5} {U : Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5}, Iff (LE.le.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Preorder.toLE.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (PartialOrder.toPreorder.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.partialOrder.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.setLike.{u1, u3} R B _inst_1 _inst_4 _inst_5)))) (Subalgebra.map.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 f S) U) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) S (Subalgebra.comap.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 f U))
+  forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3} {f : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5} {U : Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5}, Iff (LE.le.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Preorder.toHasLe.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (PartialOrder.toPreorder.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.partialOrder.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.setLike.{u1, u3} R B _inst_1 _inst_4 _inst_5)))) (Subalgebra.map.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 f S) U) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) S (Subalgebra.comap.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 f U))
 but is expected to have type
   forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3} {f : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5} {U : Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5}, Iff (LE.le.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Preorder.toLE.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (PartialOrder.toPreorder.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instPartialOrder.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)))) (Subalgebra.map.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 f S) U) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) S (Subalgebra.comap.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 f U))
 Case conversion may be inaccurate. Consider using '#align subalgebra.map_le Subalgebra.map_leₓ'. -/
@@ -1115,7 +1115,7 @@ theorem toSubalgebra_mk (s : Set A) (h0 hadd hsmul h1 hmul) :
 
 /- warning: submodule.to_subalgebra_to_submodule -> Submodule.toSubalgebra_toSubmodule is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (p : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (h_one : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (OfNat.ofNat.{u2} A 1 (OfNat.mk.{u2} A 1 (One.one.{u2} A (AddMonoidWithOne.toOne.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))))) p) (h_mul : forall (x : A) (y : A), (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x p) -> (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) y p) -> (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y) p)), Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (coeFn.{succ u2, succ u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (fun (_x : RelEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) => (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) -> (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (RelEmbedding.hasCoeToFun.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 p h_one h_mul)) p
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (p : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (h_one : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (OfNat.ofNat.{u2} A 1 (OfNat.mk.{u2} A 1 (One.one.{u2} A (AddMonoidWithOne.toOne.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))))) p) (h_mul : forall (x : A) (y : A), (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x p) -> (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) y p) -> (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y) p)), Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (coeFn.{succ u2, succ u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A 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_inst_1 _inst_2 _inst_3))))))) (fun (_x : RelEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} 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R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 p h_one h_mul)) p
 but is expected to have type
   forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u1} A] [_inst_3 : Algebra.{u2, u1} R A _inst_1 _inst_2] (p : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (h_one : Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) (OfNat.ofNat.{u1} A 1 (One.toOfNat1.{u1} A (Semiring.toOne.{u1} A _inst_2))) p) (h_mul : forall (x : A) (y : A), (Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) x p) -> (Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) y p) -> (Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u1, u1, u1} A A A (instHMul.{u1} A (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) x y) p)), Eq.{succ u1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Submodule.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 p h_one h_mul)) (FunLike.coe.{succ u1, succ u1, succ u1} (OrderEmbedding.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A 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(Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => LE.le.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) 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_inst_3)) (Submodule.completeLattice.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => LE.le.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R 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(Submodule.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 p h_one h_mul)) p
 Case conversion may be inaccurate. Consider using '#align submodule.to_subalgebra_to_submodule Submodule.toSubalgebra_toSubmoduleₓ'. -/
@@ -1127,7 +1127,7 @@ theorem toSubalgebra_toSubmodule (p : Submodule R A) (h_one h_mul) :
 
 /- warning: subalgebra.to_submodule_to_subalgebra -> Subalgebra.toSubmodule_toSubalgebra is a dubious translation:
 lean 3 declaration is
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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) => (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) -> (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (RelEmbedding.hasCoeToFun.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) S) (Subalgebra.one_mem.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (fun (_x : A) (_x_1 : A) => Subalgebra.mul_mem.{u1, u2} R A _inst_1 _inst_2 _inst_3 S _x _x_1)) S
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), Eq.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (coeFn.{succ u2, succ u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (fun (_x : RelEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) => (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) -> (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (RelEmbedding.hasCoeToFun.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) S) (Subalgebra.one_mem.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (fun (_x : A) (_x_1 : A) => Subalgebra.mul_mem.{u1, u2} R A _inst_1 _inst_2 _inst_3 S _x _x_1)) S
 but is expected to have type
   forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u1} A] [_inst_3 : Algebra.{u2, u1} R A _inst_1 _inst_2] (S : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3), Eq.{succ u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 (FunLike.coe.{succ u1, succ u1, succ u1} (OrderEmbedding.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (fun (_x : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) _x) (RelHomClass.toFunLike.{u1, u1, u1} (OrderEmbedding.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => LE.le.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => LE.le.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Subalgebra.toSubmodule.{u2, u1} R A _inst_1 _inst_2 _inst_3) S) (Subalgebra.one_mem.{u2, u1} R A _inst_1 _inst_2 _inst_3 S) (fun (_x : A) (_x_1 : A) => Subalgebra.mul_mem.{u2, u1} R A _inst_1 _inst_2 _inst_3 S _x _x_1)) S
 Case conversion may be inaccurate. Consider using '#align subalgebra.to_submodule_to_subalgebra Subalgebra.toSubmodule_toSubalgebraₓ'. -/
@@ -1199,7 +1199,7 @@ theorem range_comp (f : A →ₐ[R] B) (g : B →ₐ[R] C) : (g.comp f).range =
 
 /- warning: alg_hom.range_comp_le_range -> AlgHom.range_comp_le_range is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} {C : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] [_inst_6 : Semiring.{u4} C] [_inst_7 : Algebra.{u1, u4} R C _inst_1 _inst_6] (f : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (g : AlgHom.{u1, u3, u4} R B C _inst_1 _inst_4 _inst_6 _inst_5 _inst_7), LE.le.{u4} (Subalgebra.{u1, u4} R C _inst_1 _inst_6 _inst_7) (Preorder.toLE.{u4} (Subalgebra.{u1, u4} R C _inst_1 _inst_6 _inst_7) (PartialOrder.toPreorder.{u4} (Subalgebra.{u1, u4} R C _inst_1 _inst_6 _inst_7) (SetLike.partialOrder.{u4, u4} (Subalgebra.{u1, u4} R C _inst_1 _inst_6 _inst_7) C (Subalgebra.setLike.{u1, u4} R C _inst_1 _inst_6 _inst_7)))) (AlgHom.range.{u1, u2, u4} R A C _inst_1 _inst_2 _inst_3 _inst_6 _inst_7 (AlgHom.comp.{u1, u2, u3, u4} R A B C _inst_1 _inst_2 _inst_4 _inst_6 _inst_3 _inst_5 _inst_7 g f)) (AlgHom.range.{u1, u3, u4} R B C _inst_1 _inst_4 _inst_5 _inst_6 _inst_7 g)
+  forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} {C : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] [_inst_6 : Semiring.{u4} C] [_inst_7 : Algebra.{u1, u4} R C _inst_1 _inst_6] (f : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (g : AlgHom.{u1, u3, u4} R B C _inst_1 _inst_4 _inst_6 _inst_5 _inst_7), LE.le.{u4} (Subalgebra.{u1, u4} R C _inst_1 _inst_6 _inst_7) (Preorder.toHasLe.{u4} (Subalgebra.{u1, u4} R C _inst_1 _inst_6 _inst_7) (PartialOrder.toPreorder.{u4} (Subalgebra.{u1, u4} R C _inst_1 _inst_6 _inst_7) (SetLike.partialOrder.{u4, u4} (Subalgebra.{u1, u4} R C _inst_1 _inst_6 _inst_7) C (Subalgebra.setLike.{u1, u4} R C _inst_1 _inst_6 _inst_7)))) (AlgHom.range.{u1, u2, u4} R A C _inst_1 _inst_2 _inst_3 _inst_6 _inst_7 (AlgHom.comp.{u1, u2, u3, u4} R A B C _inst_1 _inst_2 _inst_4 _inst_6 _inst_3 _inst_5 _inst_7 g f)) (AlgHom.range.{u1, u3, u4} R B C _inst_1 _inst_4 _inst_5 _inst_6 _inst_7 g)
 but is expected to have type
   forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} {C : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] [_inst_6 : Semiring.{u4} C] [_inst_7 : Algebra.{u1, u4} R C _inst_1 _inst_6] (f : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (g : AlgHom.{u1, u3, u4} R B C _inst_1 _inst_4 _inst_6 _inst_5 _inst_7), LE.le.{u4} (Subalgebra.{u1, u4} R C _inst_1 _inst_6 _inst_7) (Preorder.toLE.{u4} (Subalgebra.{u1, u4} R C _inst_1 _inst_6 _inst_7) (PartialOrder.toPreorder.{u4} (Subalgebra.{u1, u4} R C _inst_1 _inst_6 _inst_7) (SetLike.instPartialOrder.{u4, u4} (Subalgebra.{u1, u4} R C _inst_1 _inst_6 _inst_7) C (Subalgebra.instSetLikeSubalgebra.{u1, u4} R C _inst_1 _inst_6 _inst_7)))) (AlgHom.range.{u1, u2, u4} R A C _inst_1 _inst_2 _inst_3 _inst_6 _inst_7 (AlgHom.comp.{u1, u2, u3, u4} R A B C _inst_1 _inst_2 _inst_4 _inst_6 _inst_3 _inst_5 _inst_7 g f)) (AlgHom.range.{u1, u3, u4} R B C _inst_1 _inst_4 _inst_5 _inst_6 _inst_7 g)
 Case conversion may be inaccurate. Consider using '#align alg_hom.range_comp_le_range AlgHom.range_comp_le_rangeₓ'. -/
@@ -1459,7 +1459,7 @@ theorem mem_top {x : A} : x ∈ (⊤ : Subalgebra R A) :=
 
 /- warning: algebra.top_to_submodule -> Algebra.top_toSubmodule is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (coeFn.{succ u2, succ u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (fun (_x : RelEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) => (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) -> (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (RelEmbedding.hasCoeToFun.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Top.top.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toHasTop.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Top.top.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.hasTop.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (coeFn.{succ u2, succ u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (fun (_x : RelEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 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(Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Top.top.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toHasTop.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Top.top.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.hasTop.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))
 but is expected to have type
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], Eq.{succ u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Top.top.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toTop.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (FunLike.coe.{succ u2, succ u2, succ u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (fun (_x : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) _x) (RelHomClass.toFunLike.{u2, u2, u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Top.top.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toTop.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Top.top.{u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Top.top.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toTop.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Submodule.instTopSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))
 Case conversion may be inaccurate. Consider using '#align algebra.top_to_submodule Algebra.top_toSubmoduleₓ'. -/
@@ -1493,7 +1493,7 @@ theorem top_toSubring {R A : Type _} [CommRing R] [Ring A] [Algebra R A] :
 
 /- warning: algebra.to_submodule_eq_top -> Algebra.toSubmodule_eq_top is a dubious translation:
 lean 3 declaration is
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_inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (fun (_x : RelEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) => (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) -> (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (RelEmbedding.hasCoeToFun.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) S) (Top.top.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.hasTop.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Eq.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) S (Top.top.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toHasTop.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))))
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3}, Iff (Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (coeFn.{succ u2, succ u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (fun (_x : RelEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 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(CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) => (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) -> (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (RelEmbedding.hasCoeToFun.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) S) (Top.top.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.hasTop.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Eq.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) S (Top.top.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toHasTop.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))))
 but is expected to have type
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3}, Iff (Eq.{succ u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) (FunLike.coe.{succ u2, succ u2, succ u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (fun (_x : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) _x) (RelHomClass.toFunLike.{u2, u2, u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) S) (Top.top.{u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) (Submodule.instTopSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Eq.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) S (Top.top.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toTop.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))))
 Case conversion may be inaccurate. Consider using '#align algebra.to_submodule_eq_top Algebra.toSubmodule_eq_topₓ'. -/
@@ -1589,7 +1589,7 @@ theorem mem_inf {S T : Subalgebra R A} {x : A} : x ∈ S ⊓ T ↔ x ∈ S ∧ x
 
 /- warning: algebra.inf_to_submodule -> Algebra.inf_toSubmodule is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (T : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (coeFn.{succ u2, succ u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) 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(Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) S) (coeFn.{succ u2, succ u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A 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u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (RelEmbedding.hasCoeToFun.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) T))
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (T : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (coeFn.{succ u2, succ u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) 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(Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) T))
 but is expected to have type
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (T : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), Eq.{succ u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Inf.inf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Lattice.toInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) S T)) (FunLike.coe.{succ u2, succ u2, succ u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (fun (_x : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) _x) (RelHomClass.toFunLike.{u2, u2, u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A 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_inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A 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x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) T))
 Case conversion may be inaccurate. Consider using '#align algebra.inf_to_submodule Algebra.inf_toSubmoduleₓ'. -/
@@ -1634,7 +1634,7 @@ theorem mem_sInf {S : Set (Subalgebra R A)} {x : A} : x ∈ sInf S ↔ ∀ p ∈
 
 /- warning: algebra.Inf_to_submodule -> Algebra.sInf_toSubmodule is a dubious translation:
 lean 3 declaration is
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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (InfSet.sInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))) S)) (InfSet.sInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.hasInf.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.image.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (coeFn.{succ u2, succ u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A 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(CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) => (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) -> (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (RelEmbedding.hasCoeToFun.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S))
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Set.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)), Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (coeFn.{succ u2, succ u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R 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(CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) => (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) -> (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (RelEmbedding.hasCoeToFun.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S))
 but is expected to have type
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Set.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)), Eq.{succ u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (InfSet.sInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toInfSet.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))) S)) (FunLike.coe.{succ u2, succ u2, succ u2} 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(Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A 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x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (InfSet.sInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toInfSet.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))) S)) (InfSet.sInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.instInfSetSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} 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(CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S))
 Case conversion may be inaccurate. Consider using '#align algebra.Inf_to_submodule Algebra.sInf_toSubmoduleₓ'. -/
@@ -1679,7 +1679,7 @@ theorem mem_iInf {ι : Sort _} {S : ι → Subalgebra R A} {x : A} : (x ∈ ⨅
 
 /- warning: algebra.infi_to_submodule -> Algebra.iInf_toSubmodule is a dubious translation:
 lean 3 declaration is
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_inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) => (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) -> (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (RelEmbedding.hasCoeToFun.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (iInf.{u2, u3} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => S i))) (iInf.{u2, u3} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.hasInf.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) ι (fun (i : ι) => coeFn.{succ u2, succ u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (fun (_x : RelEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} 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(CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) => (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) -> (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (RelEmbedding.hasCoeToFun.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (S i)))
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {ι : Sort.{u3}} (S : ι -> (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)), Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (coeFn.{succ u2, succ u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (fun (_x : RelEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) 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(Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) => (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) -> (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (RelEmbedding.hasCoeToFun.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (iInf.{u2, u3} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => S i))) (iInf.{u2, u3} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.hasInf.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) ι (fun (i : ι) => coeFn.{succ u2, succ u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (fun (_x : RelEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) => (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) -> (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (RelEmbedding.hasCoeToFun.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (S i)))
 but is expected to have type
   forall {R : Type.{u2}} {A : Type.{u3}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u3} A] [_inst_3 : Algebra.{u2, u3} R A _inst_1 _inst_2] {ι : Sort.{u1}} (S : ι -> (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)), Eq.{succ u3} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (iInf.{u3, u1} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toInfSet.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => S i))) (FunLike.coe.{succ 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_inst_3))))))) (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) => LE.le.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun 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_inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A 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_inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Subalgebra.toSubmodule.{u2, u3} R A _inst_1 _inst_2 _inst_3) (S i)))
 Case conversion may be inaccurate. Consider using '#align algebra.infi_to_submodule Algebra.iInf_toSubmoduleₓ'. -/
@@ -1708,7 +1708,7 @@ theorem mem_bot {x : A} : x ∈ (⊥ : Subalgebra R A) ↔ x ∈ Set.range (alge
 
 /- warning: algebra.to_submodule_bot -> Algebra.toSubmodule_bot is a dubious translation:
 lean 3 declaration is
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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) => (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) -> (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (RelEmbedding.hasCoeToFun.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Bot.bot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toHasBot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Submodule.span.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.hasSingleton.{u2} A) (OfNat.ofNat.{u2} A 1 (OfNat.mk.{u2} A 1 (One.one.{u2} A (AddMonoidWithOne.toOne.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))))))
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (coeFn.{succ u2, succ u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (fun (_x : RelEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) => (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) -> (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (RelEmbedding.hasCoeToFun.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Bot.bot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toHasBot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Submodule.span.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.hasSingleton.{u2} A) (OfNat.ofNat.{u2} A 1 (OfNat.mk.{u2} A 1 (One.one.{u2} A (AddMonoidWithOne.toOne.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))))))
 but is expected to have type
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], Eq.{succ u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Bot.bot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toBot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (FunLike.coe.{succ u2, succ u2, succ u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (fun (_x : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) _x) (RelHomClass.toFunLike.{u2, u2, u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Bot.bot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toBot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Submodule.span.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) (OfNat.ofNat.{u2} A 1 (One.toOfNat1.{u2} A (Semiring.toOne.{u2} A _inst_2)))))
 Case conversion may be inaccurate. Consider using '#align algebra.to_submodule_bot Algebra.toSubmodule_botₓ'. -/
@@ -1932,7 +1932,7 @@ instance : Unique (Subalgebra R R) :=
 
 /- warning: subalgebra.inclusion -> Subalgebra.inclusion is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3} {T : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3}, (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) S T) -> (AlgHom.{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 T))
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3} {T : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3}, (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) S T) -> (AlgHom.{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 T))
 but is expected to have type
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3} {T : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3}, (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) S T) -> (AlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T)) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T))
 Case conversion may be inaccurate. Consider using '#align subalgebra.inclusion Subalgebra.inclusionₓ'. -/
@@ -1951,7 +1951,7 @@ def inclusion {S T : Subalgebra R A} (h : S ≤ T) : S →ₐ[R] T
 
 /- warning: subalgebra.inclusion_injective -> Subalgebra.inclusion_injective is a dubious translation:
 lean 3 declaration is
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+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3} {T : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3} (h : LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) S T), Function.Injective.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T) (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 T)) (fun (_x : AlgHom.{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 T)) => (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) -> (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T)) ([anonymous].{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 T)) (Subalgebra.inclusion.{u1, u2} R A _inst_1 _inst_2 _inst_3 S T h))
 but is expected to have type
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(Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T)) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T)))))) (Subalgebra.inclusion.{u1, u2} R A _inst_1 _inst_2 _inst_3 S T h))
 Case conversion may be inaccurate. Consider using '#align subalgebra.inclusion_injective Subalgebra.inclusion_injectiveₓ'. -/
@@ -1972,7 +1972,7 @@ theorem inclusion_self {S : Subalgebra R A} : inclusion (le_refl S) = AlgHom.id
 
 /- warning: subalgebra.inclusion_mk -> Subalgebra.inclusion_mk is a dubious translation:
 lean 3 declaration is
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 but is expected to have type
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(SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S))) (Module.toDistribMulAction.{u1, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T)) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T)) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T)) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T)))) (Algebra.toModule.{u1, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T)) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u2, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T)) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) (AlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T)) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T)) (AlgHom.algHomClass.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T)) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T)))))) (Subalgebra.inclusion.{u1, u2} R A _inst_1 _inst_2 _inst_3 S T h) (Subtype.mk.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S) x hx)) (Subtype.mk.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T) x (h x hx))
 Case conversion may be inaccurate. Consider using '#align subalgebra.inclusion_mk Subalgebra.inclusion_mkₓ'. -/
@@ -1984,7 +1984,7 @@ theorem inclusion_mk {S T : Subalgebra R A} (h : S ≤ T) (x : A) (hx : x ∈ S)
 
 /- warning: subalgebra.inclusion_right -> Subalgebra.inclusion_right is a dubious translation:
 lean 3 declaration is
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 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align subalgebra.inclusion_right Subalgebra.inclusion_rightₓ'. -/
@@ -1995,7 +1995,7 @@ theorem inclusion_right {S T : Subalgebra R A} (h : S ≤ T) (x : T) (m : (x : A
 
 /- warning: subalgebra.inclusion_inclusion -> Subalgebra.inclusion_inclusion is a dubious translation:
 lean 3 declaration is
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 but is expected to have type
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(Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 U) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 U)))))) (Subalgebra.inclusion.{u1, u2} R A _inst_1 _inst_2 _inst_3 S U (le_trans.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) S T U hst htu)) x)
 Case conversion may be inaccurate. Consider using '#align subalgebra.inclusion_inclusion Subalgebra.inclusion_inclusionₓ'. -/
@@ -2007,7 +2007,7 @@ theorem inclusion_inclusion {S T U : Subalgebra R A} (hst : S ≤ T) (htu : T 
 
 /- warning: subalgebra.coe_inclusion -> Subalgebra.coe_inclusion is a dubious translation:
 lean 3 declaration is
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 but is expected to have type
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_inst_1 _inst_2 _inst_3 T)))) (Algebra.toModule.{u1, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T)) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u2, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A 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(Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T)) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T)) (AlgHom.algHomClass.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T)) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T)))))) (Subalgebra.inclusion.{u1, u2} R A _inst_1 _inst_2 _inst_3 S T h) s)) (Subtype.val.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) x (SetLike.coe.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) S)) s)
 Case conversion may be inaccurate. Consider using '#align subalgebra.coe_inclusion Subalgebra.coe_inclusionₓ'. -/
@@ -2106,7 +2106,7 @@ theorem coe_prod : (prod S S₁ : Set (A × B)) = S ×ˢ S₁ :=
 
 /- warning: subalgebra.prod_to_submodule -> Subalgebra.prod_toSubmodule is a dubious translation:
 lean 3 declaration is
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u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (LE.le.{max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (Preorder.toLE.{max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (PartialOrder.toPreorder.{max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (SetLike.partialOrder.{max u2 u3, max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (Prod.{u2, u3} A B) (Subalgebra.setLike.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)))))) (LE.le.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.semiring.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (Preorder.toLE.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.semiring.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (PartialOrder.toPreorder.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.semiring.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (CompleteSemilatticeInf.toPartialOrder.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.semiring.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (CompleteLattice.toCompleteSemilatticeInf.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.semiring.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (Submodule.completeLattice.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.semiring.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))))))))) => (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) -> (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) 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u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (LE.le.{max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (Preorder.toLE.{max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (PartialOrder.toPreorder.{max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (SetLike.partialOrder.{max u2 u3, max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (Prod.{u2, u3} A B) (Subalgebra.setLike.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)))))) (LE.le.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.semiring.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (Preorder.toLE.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, 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A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (Submodule.completeLattice.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.semiring.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))))))))) (Subalgebra.toSubmodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (Subalgebra.prod.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 S S₁)) (Submodule.prod.{u1, u2, u3} R A 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u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5))) (RelEmbedding.hasCoeToFun.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (LE.le.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Preorder.toLE.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (PartialOrder.toPreorder.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.partialOrder.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.setLike.{u1, u3} R B _inst_1 _inst_4 _inst_5))))) (LE.le.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Preorder.toLE.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (PartialOrder.toPreorder.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (CompleteSemilatticeInf.toPartialOrder.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Submodule.completeLattice.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)))))))) (Subalgebra.toSubmodule.{u1, u3} R B _inst_1 _inst_4 _inst_5) S₁))
+  forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (S₁ : Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5), Eq.{succ (max u2 u3)} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.semiring.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (coeFn.{succ (max u2 u3), succ (max u2 u3)} (OrderEmbedding.{max u2 u3, max u2 u3} 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u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (SetLike.partialOrder.{max u2 u3, max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (Prod.{u2, u3} A B) (Subalgebra.setLike.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))))) (Preorder.toHasLe.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.semiring.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (PartialOrder.toPreorder.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.semiring.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (CompleteSemilatticeInf.toPartialOrder.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.semiring.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (CompleteLattice.toCompleteSemilatticeInf.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.semiring.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (Submodule.completeLattice.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.semiring.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)))))))) (fun (_x : RelEmbedding.{max u2 u3, max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.semiring.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (LE.le.{max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (Preorder.toHasLe.{max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (PartialOrder.toPreorder.{max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (SetLike.partialOrder.{max u2 u3, max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (Prod.{u2, u3} A B) (Subalgebra.setLike.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)))))) (LE.le.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.semiring.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (Preorder.toHasLe.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.semiring.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (PartialOrder.toPreorder.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.semiring.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (CompleteSemilatticeInf.toPartialOrder.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.semiring.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (CompleteLattice.toCompleteSemilatticeInf.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.semiring.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (Submodule.completeLattice.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.semiring.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))))))))) => (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) -> (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.semiring.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)))) (RelEmbedding.hasCoeToFun.{max u2 u3, max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.semiring.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (LE.le.{max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (Preorder.toHasLe.{max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (PartialOrder.toPreorder.{max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (SetLike.partialOrder.{max u2 u3, max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (Prod.{u2, u3} A B) (Subalgebra.setLike.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)))))) (LE.le.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.semiring.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (Preorder.toHasLe.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) 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B _inst_1 _inst_4 _inst_5)))))))) => (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) -> (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5))) (RelEmbedding.hasCoeToFun.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (LE.le.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Preorder.toHasLe.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (PartialOrder.toPreorder.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.partialOrder.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.setLike.{u1, u3} R B _inst_1 _inst_4 _inst_5))))) (LE.le.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Preorder.toHasLe.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (PartialOrder.toPreorder.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (CompleteSemilatticeInf.toPartialOrder.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Submodule.completeLattice.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)))))))) (Subalgebra.toSubmodule.{u1, u3} R B _inst_1 _inst_4 _inst_5) S₁))
 but is expected to have type
   forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (S₁ : Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5), Eq.{max (succ u2) (succ u3)} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) => Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (Subalgebra.prod.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 S S₁)) (FunLike.coe.{succ (max u2 u3), succ (max u2 u3), succ (max u2 u3)} (OrderEmbedding.{max u2 u3, max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (Preorder.toLE.{max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (PartialOrder.toPreorder.{max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (SetLike.instPartialOrder.{max u2 u3, max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (Prod.{u2, u3} A B) (Subalgebra.instSetLikeSubalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))))) (Preorder.toLE.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (PartialOrder.toPreorder.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (OmegaCompletePartialOrder.toPartialOrder.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (CompleteLattice.instOmegaCompletePartialOrder.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (Submodule.completeLattice.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)))))))) (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (fun (_x : Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) => Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) _x) (RelHomClass.toFunLike.{max u2 u3, max u2 u3, max u2 u3} (OrderEmbedding.{max u2 u3, max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (Preorder.toLE.{max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (PartialOrder.toPreorder.{max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (SetLike.instPartialOrder.{max u2 u3, max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (Prod.{u2, u3} A B) (Subalgebra.instSetLikeSubalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))))) (Preorder.toLE.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (PartialOrder.toPreorder.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (OmegaCompletePartialOrder.toPartialOrder.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (CompleteLattice.instOmegaCompletePartialOrder.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (Submodule.completeLattice.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)))))))) (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) => LE.le.{max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (Preorder.toLE.{max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (PartialOrder.toPreorder.{max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (SetLike.instPartialOrder.{max u2 u3, max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (Prod.{u2, u3} A B) (Subalgebra.instSetLikeSubalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) => LE.le.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (Preorder.toLE.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (PartialOrder.toPreorder.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (OmegaCompletePartialOrder.toPartialOrder.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (CompleteLattice.instOmegaCompletePartialOrder.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (Submodule.completeLattice.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{max u2 u3, max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) => LE.le.{max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (Preorder.toLE.{max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (PartialOrder.toPreorder.{max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (SetLike.instPartialOrder.{max u2 u3, max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (Prod.{u2, u3} A B) (Subalgebra.instSetLikeSubalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) => LE.le.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (Preorder.toLE.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (PartialOrder.toPreorder.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (OmegaCompletePartialOrder.toPartialOrder.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) _x) (RelHomClass.toFunLike.{u3, u3, u3} (OrderEmbedding.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Preorder.toLE.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (PartialOrder.toPreorder.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instPartialOrder.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)))) (Preorder.toLE.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (PartialOrder.toPreorder.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B 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_inst_1 _inst_4 _inst_5) (Preorder.toLE.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (PartialOrder.toPreorder.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instPartialOrder.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) => LE.le.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Preorder.toLE.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (PartialOrder.toPreorder.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Submodule.completeLattice.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) => LE.le.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Preorder.toLE.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (PartialOrder.toPreorder.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instPartialOrder.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) => LE.le.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Preorder.toLE.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (PartialOrder.toPreorder.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Submodule.completeLattice.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Subalgebra.toSubmodule.{u1, u3} R B _inst_1 _inst_4 _inst_5) S₁))
 Case conversion may be inaccurate. Consider using '#align subalgebra.prod_to_submodule Subalgebra.prod_toSubmoduleₓ'. -/
@@ -2138,7 +2138,7 @@ theorem prod_top : (prod ⊤ ⊤ : Subalgebra R (A × B)) = ⊤ := by ext <;> si
 
 /- warning: subalgebra.prod_mono -> Subalgebra.prod_mono is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3} {T : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3} {S₁ : Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5} {T₁ : Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5}, (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) S T) -> (LE.le.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Preorder.toLE.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (PartialOrder.toPreorder.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (CompleteSemilatticeInf.toPartialOrder.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.Subalgebra.completeLattice.{u1, u3} R B _inst_1 _inst_4 _inst_5))))) S₁ T₁) -> (LE.le.{max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (Preorder.toLE.{max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (PartialOrder.toPreorder.{max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (CompleteSemilatticeInf.toPartialOrder.{max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (CompleteLattice.toCompleteSemilatticeInf.{max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (Algebra.Subalgebra.completeLattice.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)))))) (Subalgebra.prod.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 S S₁) (Subalgebra.prod.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 T T₁))
+  forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3} {T : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3} {S₁ : Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5} {T₁ : Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5}, (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) S T) -> (LE.le.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Preorder.toHasLe.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (PartialOrder.toPreorder.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (CompleteSemilatticeInf.toPartialOrder.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.Subalgebra.completeLattice.{u1, u3} R B _inst_1 _inst_4 _inst_5))))) S₁ T₁) -> (LE.le.{max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (Preorder.toHasLe.{max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (PartialOrder.toPreorder.{max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (CompleteSemilatticeInf.toPartialOrder.{max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (CompleteLattice.toCompleteSemilatticeInf.{max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (Algebra.Subalgebra.completeLattice.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)))))) (Subalgebra.prod.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 S S₁) (Subalgebra.prod.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 T T₁))
 but is expected to have type
   forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3} {T : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3} {S₁ : Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5} {T₁ : Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5}, (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) S T) -> (LE.le.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Preorder.toLE.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (PartialOrder.toPreorder.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Algebra.instCompleteLatticeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5))))) S₁ T₁) -> (LE.le.{max u2 u3} (Subalgebra.{u1, max u3 u2} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (Preorder.toLE.{max u2 u3} (Subalgebra.{u1, max u3 u2} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (PartialOrder.toPreorder.{max u2 u3} (Subalgebra.{u1, max u3 u2} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (OmegaCompletePartialOrder.toPartialOrder.{max u2 u3} (Subalgebra.{u1, max u3 u2} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (CompleteLattice.instOmegaCompletePartialOrder.{max u2 u3} (Subalgebra.{u1, max u3 u2} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (Algebra.instCompleteLatticeSubalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)))))) (Subalgebra.prod.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 S S₁) (Subalgebra.prod.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 T T₁))
 Case conversion may be inaccurate. Consider using '#align subalgebra.prod_mono Subalgebra.prod_monoₓ'. -/
@@ -2167,7 +2167,7 @@ variable {ι : Type _}
 
 /- warning: subalgebra.coe_supr_of_directed -> Subalgebra.coe_iSup_of_directed is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {ι : Type.{u3}} [_inst_6 : Nonempty.{succ u3} ι] {S : ι -> (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)}, (Directed.{u2, succ u3} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) ι (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) S) -> (Eq.{succ u2} (Set.{u2} A) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (iSup.{u2, succ u3} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))) ι S)) (Set.iUnion.{u2, succ u3} A ι (fun (i : ι) => (fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (S i))))
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {ι : Type.{u3}} [_inst_6 : Nonempty.{succ u3} ι] {S : ι -> (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)}, (Directed.{u2, succ u3} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) ι (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) S) -> (Eq.{succ u2} (Set.{u2} A) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (iSup.{u2, succ u3} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))) ι S)) (Set.iUnion.{u2, succ u3} A ι (fun (i : ι) => (fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (S i))))
 but is expected to have type
   forall {R : Type.{u2}} {A : Type.{u3}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u3} A] [_inst_3 : Algebra.{u2, u3} R A _inst_1 _inst_2] {ι : Type.{u1}} [_inst_6 : Nonempty.{succ u1} ι] {S : ι -> (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)}, (Directed.{u3, succ u1} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) ι (fun (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.12747 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.12749 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) => LE.le.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3))))) x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.12747 x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.12749) S) -> (Eq.{succ u3} (Set.{u3} A) (SetLike.coe.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (iSup.{u3, succ u1} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3))) ι S)) (Set.iUnion.{u3, succ u1} A ι (fun (i : ι) => SetLike.coe.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (S i))))
 Case conversion may be inaccurate. Consider using '#align subalgebra.coe_supr_of_directed Subalgebra.coe_iSup_of_directedₓ'. -/
@@ -2196,7 +2196,7 @@ theorem coe_iSup_of_directed [Nonempty ι] {S : ι → Subalgebra R A} (dir : Di
 
 /- warning: subalgebra.supr_lift -> Subalgebra.iSupLift is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {ι : Type.{u4}} [_inst_6 : Nonempty.{succ u4} ι] (K : ι -> (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)), (Directed.{u2, succ u4} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) ι (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) K) -> (forall (f : forall (i : ι), AlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K i)) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5), (forall (i : ι) (j : ι) (h : LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (K i) (K j)), Eq.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K i)) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) (f i) (AlgHom.comp.{u1, u2, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K i)) (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K j)) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K j)) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K j)) _inst_5 (f j) (Subalgebra.inclusion.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i) (K j) h))) -> (forall (T : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), (Eq.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) T (iSup.{u2, succ u4} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))) ι K)) -> (AlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) _inst_5)))
+  forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {ι : Type.{u4}} [_inst_6 : Nonempty.{succ u4} ι] (K : ι -> (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)), (Directed.{u2, succ u4} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) ι (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) K) -> (forall (f : forall (i : ι), AlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K i)) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5), (forall (i : ι) (j : ι) (h : LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (K i) (K j)), Eq.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K i)) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) (f i) (AlgHom.comp.{u1, u2, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K i)) (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K j)) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K j)) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K j)) _inst_5 (f j) (Subalgebra.inclusion.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i) (K j) h))) -> (forall (T : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), (Eq.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) T (iSup.{u2, succ u4} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))) ι K)) -> (AlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) _inst_5)))
 but is expected to have type
   forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {ι : Type.{u4}} [_inst_6 : Nonempty.{succ u4} ι] (K : ι -> (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)), (Directed.{u2, succ u4} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) ι (fun (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13130 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13132 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13130 x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13132) K) -> (forall (f : forall (i : ι), AlgHom.{u1, u2, u3} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5), (forall (i : ι) (j : ι) (h : LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (K i) (K j)), Eq.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) (f i) (AlgHom.comp.{u1, u2, u2, u3} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x (K j))) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K j)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K j)) _inst_5 (f j) (Subalgebra.inclusion.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i) (K j) h))) -> (forall (T : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), (Eq.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) T (iSup.{u2, succ u4} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))) ι K)) -> (AlgHom.{u1, u2, u3} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T)) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) _inst_5)))
 Case conversion may be inaccurate. Consider using '#align subalgebra.supr_lift Subalgebra.iSupLiftₓ'. -/
@@ -2233,7 +2233,7 @@ variable [Nonempty ι] {K : ι → Subalgebra R A} {dir : Directed (· ≤ ·) K
 
 /- warning: subalgebra.supr_lift_inclusion -> Subalgebra.iSupLift_inclusion is a dubious translation:
 lean 3 declaration is
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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))) (Module.toDistribMulAction.{u2, u3} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 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_inst_2 _inst_3 (K i)) _inst_5) R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A 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(Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)))) (Module.toDistribMulAction.{u2, u4} R B (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u2, u4} R B _inst_1 _inst_4 _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u3, u4, max u3 u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5 (AlgHom.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) (AlgHom.algHomClass.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5))))) (f i) x)
 Case conversion may be inaccurate. Consider using '#align subalgebra.supr_lift_inclusion Subalgebra.iSupLift_inclusionₓ'. -/
@@ -2245,7 +2245,7 @@ theorem iSupLift_inclusion {i : ι} (x : K i) (h : K i ≤ T) :
 
 /- warning: subalgebra.supr_lift_comp_inclusion -> Subalgebra.iSupLift_comp_inclusion is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {ι : Type.{u4}} [_inst_6 : Nonempty.{succ u4} ι] {K : ι -> (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {dir : Directed.{u2, succ u4} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) ι (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) K} {f : forall (i : ι), AlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K i)) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5} {hf : forall (i : ι) (j : ι) (h : LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (K i) (K j)), Eq.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, 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_inst_2 _inst_3 (K j)) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K j)) _inst_5 (f j) (Subalgebra.inclusion.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i) (K j) h))} {T : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3} {hT : Eq.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) T (iSup.{u2, succ u4} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))) ι K)} {i : ι} (h : LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} 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+  forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {ι : Type.{u4}} [_inst_6 : Nonempty.{succ u4} ι] {K : ι -> (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {dir : Directed.{u2, succ u4} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) ι (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) K} {f : forall (i : ι), AlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ 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 but is expected to have type
   forall {R : Type.{u2}} {A : Type.{u3}} {B : Type.{u4}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u3} A] [_inst_3 : Algebra.{u2, u3} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u4} B] [_inst_5 : Algebra.{u2, u4} R B _inst_1 _inst_4] {ι : Type.{u1}} [_inst_6 : Nonempty.{succ u1} ι] {K : ι -> (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)} {dir : Directed.{u3, succ u1} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) ι (fun (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13873 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13875 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) => LE.le.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3))))) x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13873 x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13875) K} {f : forall (i : ι), AlgHom.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5} {hf : forall (i : ι) (j : ι) (h : LE.le.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 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(Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K j))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K j)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K j)) _inst_5 (f j) (Subalgebra.inclusion.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i) (K j) h))} {T : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3} {hT : Eq.{succ u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) T (iSup.{u3, succ u1} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3))) ι K)} {i : ι} (h : LE.le.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3))))) (K i) T), Eq.{max (succ u3) (succ u4)} (AlgHom.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) (AlgHom.comp.{u2, u3, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subtype.{succ u3} A (fun (x : A) => 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 Case conversion may be inaccurate. Consider using '#align subalgebra.supr_lift_comp_inclusion Subalgebra.iSupLift_comp_inclusionₓ'. -/
@@ -2256,7 +2256,7 @@ theorem iSupLift_comp_inclusion {i : ι} (h : K i ≤ T) :
 
 /- warning: subalgebra.supr_lift_mk -> Subalgebra.iSupLift_mk is a dubious translation:
 lean 3 declaration is
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_inst_4))))) (DistribSMul.toSMulZeroClass.{u2, u4} R B (AddMonoid.toAddZeroClass.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))))) (DistribMulAction.toDistribSMul.{u2, u4} R B (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))) (Module.toDistribMulAction.{u2, u4} R B (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u2, u4} R B _inst_1 _inst_4 _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u4, u2, u3, u4} (AlgHom.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A 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_inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)))))) (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))) (Module.toDistribMulAction.{u2, u3} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i))))) (Algebra.toModule.{u2, u3} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) 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u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)) (Module.toDistribMulAction.{u2, u3} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i))))) (Algebra.toModule.{u2, u3} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)))) (Module.toDistribMulAction.{u2, u4} R B (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u2, u4} R B _inst_1 _inst_4 _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u3, u4, max u3 u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5 (AlgHom.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) (AlgHom.algHomClass.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5))))) (f i) x)
 Case conversion may be inaccurate. Consider using '#align subalgebra.supr_lift_mk Subalgebra.iSupLift_mkₓ'. -/
@@ -2267,7 +2267,7 @@ theorem iSupLift_mk {i : ι} (x : K i) (hx : (x : A) ∈ T) :
 
 /- warning: subalgebra.supr_lift_of_mem -> Subalgebra.iSupLift_of_mem is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {ι : Type.{u4}} [_inst_6 : Nonempty.{succ u4} ι] {K : ι -> (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {dir : Directed.{u2, succ u4} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) ι (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) K} {f : forall (i : ι), AlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} 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(SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)))))) (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))) (Module.toDistribMulAction.{u2, u3} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i))))) (Algebra.toModule.{u2, u3} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)))) (Module.toDistribMulAction.{u2, u4} R B (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u2, u4} R B _inst_1 _inst_4 _inst_5)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u3 u4, u2, u3, u4} (AlgHom.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)) (Module.toDistribMulAction.{u2, u3} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i))))) (Algebra.toModule.{u2, u3} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)))) (Module.toDistribMulAction.{u2, u4} R B (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u2, u4} R B _inst_1 _inst_4 _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u3, u4, max u3 u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5 (AlgHom.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) (AlgHom.algHomClass.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5))))) (f i) (Subtype.mk.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i)) (Subtype.val.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Set.{u3} A) (Set.instMembershipSet.{u3} A) x (SetLike.coe.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) T)) x) hx))
 Case conversion may be inaccurate. Consider using '#align subalgebra.supr_lift_of_mem Subalgebra.iSupLift_of_memₓ'. -/
@@ -2568,7 +2568,7 @@ theorem mem_centralizer_iff {s : Set A} {z : A} : z ∈ centralizer R s ↔ ∀
 
 /- warning: subalgebra.centralizer_le -> Subalgebra.centralizer_le is a dubious translation:
 lean 3 declaration is
-  forall (R : Type.{u1}) {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (s : Set.{u2} A) (t : Set.{u2} A), (HasSubset.Subset.{u2} (Set.{u2} A) (Set.hasSubset.{u2} A) s t) -> (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (Subalgebra.centralizer.{u1, u2} R A _inst_1 _inst_2 _inst_3 t) (Subalgebra.centralizer.{u1, u2} R A _inst_1 _inst_2 _inst_3 s))
+  forall (R : Type.{u1}) {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (s : Set.{u2} A) (t : Set.{u2} A), (HasSubset.Subset.{u2} (Set.{u2} A) (Set.hasSubset.{u2} A) s t) -> (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (Subalgebra.centralizer.{u1, u2} R A _inst_1 _inst_2 _inst_3 t) (Subalgebra.centralizer.{u1, u2} R A _inst_1 _inst_2 _inst_3 s))
 but is expected to have type
   forall (R : Type.{u1}) {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (s : Set.{u2} A) (t : Set.{u2} A), (HasSubset.Subset.{u2} (Set.{u2} A) (Set.instHasSubsetSet.{u2} A) s t) -> (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (Subalgebra.centralizer.{u1, u2} R A _inst_1 _inst_2 _inst_3 t) (Subalgebra.centralizer.{u1, u2} R A _inst_1 _inst_2 _inst_3 s))
 Case conversion may be inaccurate. Consider using '#align subalgebra.centralizer_le Subalgebra.centralizer_leₓ'. -/

bump to nightly-2023-05-16-14

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

b356e20f

Diff

@@ -1101,7 +1101,7 @@ theorem coe_toSubalgebra (p : Submodule R A) (h_one h_mul) :
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (s : Set.{u2} A) (h0 : Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) (OfNat.ofNat.{u2} A 0 (OfNat.mk.{u2} A 0 (Zero.zero.{u2} A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))))))) s) (hadd : forall {a : A} {b : A}, (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) a s) -> (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) b s) -> (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (AddZeroClass.toHasAdd.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))))) a b) s)) (hsmul : forall (c : R) {x : A}, (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) x s) -> (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) (SMul.smul.{u1, u2} R A (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) c x) s)) (h1 : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A 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R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) s)) (SMul.smul.{u1, u2} R A (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R 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(OfNat.ofNat.{u2} A 1 (OfNat.mk.{u2} A 1 (One.one.{u2} A (AddMonoidWithOne.toOne.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))))) (Algebra.algebraMap_eq_smul_one.{u1, u2} R A _inst_1 _inst_2 _inst_3 r))) (hsmul r (OfNat.ofNat.{u2} A 1 (OfNat.mk.{u2} A 1 (One.one.{u2} A (AddMonoidWithOne.toOne.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))))) h1)))
 but is expected to have type
-  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u1} A] [_inst_3 : Algebra.{u2, u1} R A _inst_1 _inst_2] (s : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (h0 : Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) (OfNat.ofNat.{u1} A 1 (One.toOfNat1.{u1} A (Semiring.toOne.{u1} A _inst_2))) s) (hadd : forall (a : A) (b : A), (Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) a s) -> (Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) b s) -> (Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u1, u1, u1} A A A (instHMul.{u1} A (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) a b) s)), Eq.{succ u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 s h0 hadd) (Subalgebra.mk.{u2, u1} R A _inst_1 _inst_2 _inst_3 (Subsemiring.mk.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Submonoid.mk.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemigroup.mk.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) s) hadd) h0) (fun {a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6483 : A} {b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6484 : A} => Submodule.add_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6483 b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6484) (Submodule.zero_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s)) (fun (r : R) => Eq.mpr.{0} (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) (Set.{u1} A) (Set.instMembershipSet.{u1} A) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2) (RingHom.instRingHomClassRingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2))))) (algebraMap.{u2, u1} R A _inst_1 _inst_2 _inst_3) r) (Subsemigroup.carrier.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (Submonoid.toSubsemigroup.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemiring.toSubmonoid.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Subsemiring.mk.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Submonoid.mk.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemigroup.mk.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) s) hadd) h0) (fun {a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6483 : A} {b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6484 : A} => Submodule.add_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6483 b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6484) (Submodule.zero_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s)))))) (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) (Set.{u1} A) (Set.instMembershipSet.{u1} A) (HSMul.hSMul.{u2, u1, u1} R A A (instHSMul.{u2, u1} R A (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_2 _inst_3)) r (OfNat.ofNat.{u1} A 1 (One.toOfNat1.{u1} A (Semiring.toOne.{u1} A _inst_2)))) (Subsemigroup.carrier.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (Submonoid.toSubsemigroup.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemiring.toSubmonoid.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Subsemiring.mk.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Submonoid.mk.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemigroup.mk.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) s) hadd) h0) (fun {a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6483 : A} {b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6484 : A} => Submodule.add_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6483 b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6484) (Submodule.zero_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6483 b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6484) (Submodule.zero_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s))))))) (Eq.refl.{1} Prop (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) (Set.{u1} A) (Set.instMembershipSet.{u1} A) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) 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u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2) (RingHom.instRingHomClassRingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2))))) (algebraMap.{u2, u1} R A _inst_1 _inst_2 _inst_3) r) (Subsemigroup.carrier.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (Submonoid.toSubsemigroup.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemiring.toSubmonoid.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Subsemiring.mk.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Submonoid.mk.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemigroup.mk.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) s) hadd) h0) (fun {a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6483 : A} {b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6484 : A} => Submodule.add_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6483 b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6484) (Submodule.zero_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s))))))) (HSMul.hSMul.{u2, u1, u1} R A A (instHSMul.{u2, u1} R A (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_2 _inst_3)) r (OfNat.ofNat.{u1} A 1 (One.toOfNat1.{u1} A (Semiring.toOne.{u1} A _inst_2)))) (Algebra.algebraMap_eq_smul_one.{u2, u1} R A _inst_1 _inst_2 _inst_3 r))) (Submodule.smul_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s (OfNat.ofNat.{u1} A 1 (One.toOfNat1.{u1} A (Semiring.toOne.{u1} A _inst_2))) r h0)))
+  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u1} A] [_inst_3 : Algebra.{u2, u1} R A _inst_1 _inst_2] (s : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (h0 : Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) (OfNat.ofNat.{u1} A 1 (One.toOfNat1.{u1} A (Semiring.toOne.{u1} A _inst_2))) s) (hadd : forall (a : A) (b : A), (Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) a s) -> (Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) b s) -> (Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u1, u1, u1} A A A (instHMul.{u1} A (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) a b) s)), Eq.{succ u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 s h0 hadd) (Subalgebra.mk.{u2, u1} R A _inst_1 _inst_2 _inst_3 (Subsemiring.mk.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Submonoid.mk.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemigroup.mk.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) s) hadd) h0) (fun {a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6477 : A} {b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6478 : A} => Submodule.add_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6477 b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6478) (Submodule.zero_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s)) (fun (r : R) => Eq.mpr.{0} (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) (Set.{u1} A) (Set.instMembershipSet.{u1} A) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2) (RingHom.instRingHomClassRingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2))))) (algebraMap.{u2, u1} R A _inst_1 _inst_2 _inst_3) r) (Subsemigroup.carrier.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (Submonoid.toSubsemigroup.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemiring.toSubmonoid.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Subsemiring.mk.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Submonoid.mk.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemigroup.mk.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) s) hadd) h0) (fun {a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6477 : A} {b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6478 : A} => Submodule.add_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6477 b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6478) (Submodule.zero_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s)))))) (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) (Set.{u1} A) (Set.instMembershipSet.{u1} A) (HSMul.hSMul.{u2, u1, u1} R A A (instHSMul.{u2, u1} R A (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_2 _inst_3)) r (OfNat.ofNat.{u1} A 1 (One.toOfNat1.{u1} A (Semiring.toOne.{u1} A _inst_2)))) (Subsemigroup.carrier.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (Submonoid.toSubsemigroup.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemiring.toSubmonoid.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Subsemiring.mk.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Submonoid.mk.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemigroup.mk.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) 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_inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) s) hadd) h0) (fun {a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6477 : A} {b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6478 : A} => Submodule.add_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6477 b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6478) (Submodule.zero_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s)))))) (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) (Set.{u1} A) (Set.instMembershipSet.{u1} A) _a (Subsemigroup.carrier.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (Submonoid.toSubsemigroup.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemiring.toSubmonoid.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Subsemiring.mk.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Submonoid.mk.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemigroup.mk.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) s) hadd) h0) (fun {a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6477 : A} {b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6478 : A} => Submodule.add_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6477 b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6478) (Submodule.zero_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s))))))) (Eq.refl.{1} Prop (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) (Set.{u1} A) (Set.instMembershipSet.{u1} A) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2) (RingHom.instRingHomClassRingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2))))) (algebraMap.{u2, u1} R A _inst_1 _inst_2 _inst_3) r) (Subsemigroup.carrier.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (Submonoid.toSubsemigroup.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemiring.toSubmonoid.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Subsemiring.mk.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Submonoid.mk.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemigroup.mk.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) s) hadd) h0) (fun {a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6477 : A} {b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6478 : A} => Submodule.add_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6477 b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6478) (Submodule.zero_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s))))))) (HSMul.hSMul.{u2, u1, u1} R A A (instHSMul.{u2, u1} R A (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_2 _inst_3)) r (OfNat.ofNat.{u1} A 1 (One.toOfNat1.{u1} A (Semiring.toOne.{u1} A _inst_2)))) (Algebra.algebraMap_eq_smul_one.{u2, u1} R A _inst_1 _inst_2 _inst_3 r))) (Submodule.smul_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s (OfNat.ofNat.{u1} A 1 (One.toOfNat1.{u1} A (Semiring.toOne.{u1} A _inst_2))) r h0)))
 Case conversion may be inaccurate. Consider using '#align submodule.to_subalgebra_mk Submodule.toSubalgebra_mkₓ'. -/
 @[simp]
 theorem toSubalgebra_mk (s : Set A) (h0 hadd hsmul h1 hmul) :
@@ -2169,7 +2169,7 @@ variable {ι : Type _}
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {ι : Type.{u3}} [_inst_6 : Nonempty.{succ u3} ι] {S : ι -> (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)}, (Directed.{u2, succ u3} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) ι (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) S) -> (Eq.{succ u2} (Set.{u2} A) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (iSup.{u2, succ u3} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))) ι S)) (Set.iUnion.{u2, succ u3} A ι (fun (i : ι) => (fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (S i))))
 but is expected to have type
-  forall {R : Type.{u2}} {A : Type.{u3}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u3} A] [_inst_3 : Algebra.{u2, u3} R A _inst_1 _inst_2] {ι : Type.{u1}} [_inst_6 : Nonempty.{succ u1} ι] {S : ι -> (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)}, (Directed.{u3, succ u1} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) ι (fun (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.12753 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.12755 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) => LE.le.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3))))) x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.12753 x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.12755) S) -> (Eq.{succ u3} (Set.{u3} A) (SetLike.coe.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (iSup.{u3, succ u1} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3))) ι S)) (Set.iUnion.{u3, succ u1} A ι (fun (i : ι) => SetLike.coe.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (S i))))
+  forall {R : Type.{u2}} {A : Type.{u3}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u3} A] [_inst_3 : Algebra.{u2, u3} R A _inst_1 _inst_2] {ι : Type.{u1}} [_inst_6 : Nonempty.{succ u1} ι] {S : ι -> (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)}, (Directed.{u3, succ u1} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) ι (fun (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.12747 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.12749 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) => LE.le.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3))))) x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.12747 x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.12749) S) -> (Eq.{succ u3} (Set.{u3} A) (SetLike.coe.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (iSup.{u3, succ u1} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3))) ι S)) (Set.iUnion.{u3, succ u1} A ι (fun (i : ι) => SetLike.coe.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (S i))))
 Case conversion may be inaccurate. Consider using '#align subalgebra.coe_supr_of_directed Subalgebra.coe_iSup_of_directedₓ'. -/
 theorem coe_iSup_of_directed [Nonempty ι] {S : ι → Subalgebra R A} (dir : Directed (· ≤ ·) S) :
     ↑(iSup S) = ⋃ i, (S i : Set A) :=
@@ -2198,7 +2198,7 @@ theorem coe_iSup_of_directed [Nonempty ι] {S : ι → Subalgebra R A} (dir : Di
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {ι : Type.{u4}} [_inst_6 : Nonempty.{succ u4} ι] (K : ι -> (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)), (Directed.{u2, succ u4} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) ι (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) K) -> (forall (f : forall (i : ι), AlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K i)) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5), (forall (i : ι) (j : ι) (h : LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (K i) (K j)), Eq.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K i)) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) (f i) (AlgHom.comp.{u1, u2, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K i)) (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K j)) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K j)) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K j)) _inst_5 (f j) (Subalgebra.inclusion.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i) (K j) h))) -> (forall (T : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), (Eq.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) T (iSup.{u2, succ u4} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))) ι K)) -> (AlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) _inst_5)))
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {ι : Type.{u4}} [_inst_6 : Nonempty.{succ u4} ι] (K : ι -> (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)), (Directed.{u2, succ u4} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) ι (fun (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13136 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13138 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13136 x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13138) K) -> (forall (f : forall (i : ι), AlgHom.{u1, u2, u3} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5), (forall (i : ι) (j : ι) (h : LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (K i) (K j)), Eq.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) (f i) (AlgHom.comp.{u1, u2, u2, u3} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x (K j))) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K j)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K j)) _inst_5 (f j) (Subalgebra.inclusion.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i) (K j) h))) -> (forall (T : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), (Eq.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) T (iSup.{u2, succ u4} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))) ι K)) -> (AlgHom.{u1, u2, u3} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T)) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) _inst_5)))
+  forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {ι : Type.{u4}} [_inst_6 : Nonempty.{succ u4} ι] (K : ι -> (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)), (Directed.{u2, succ u4} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) ι (fun (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13130 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13132 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13130 x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13132) K) -> (forall (f : forall (i : ι), AlgHom.{u1, u2, u3} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5), (forall (i : ι) (j : ι) (h : LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (K i) (K j)), Eq.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) (f i) (AlgHom.comp.{u1, u2, u2, u3} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x (K j))) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K j)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K j)) _inst_5 (f j) (Subalgebra.inclusion.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i) (K j) h))) -> (forall (T : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), (Eq.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) T (iSup.{u2, succ u4} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))) ι K)) -> (AlgHom.{u1, u2, u3} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T)) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) _inst_5)))
 Case conversion may be inaccurate. Consider using '#align subalgebra.supr_lift Subalgebra.iSupLiftₓ'. -/
 /-- Define an algebra homomorphism on a directed supremum of subalgebras by defining
 it on each subalgebra, and proving that it agrees on the intersection of subalgebras. -/
@@ -2235,7 +2235,7 @@ variable [Nonempty ι] {K : ι → Subalgebra R A} {dir : Directed (· ≤ ·) K
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {ι : Type.{u4}} [_inst_6 : Nonempty.{succ u4} ι] {K : ι -> (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {dir : Directed.{u2, succ u4} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) ι (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) K} {f : forall (i : ι), AlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K i)) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5} {hf : forall (i : ι) (j : ι) (h : LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (K i) (K j)), Eq.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, 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 but is expected to have type
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+  forall {R : Type.{u2}} {A : Type.{u3}} {B : Type.{u4}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u3} A] [_inst_3 : Algebra.{u2, u3} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u4} B] [_inst_5 : Algebra.{u2, u4} R B _inst_1 _inst_4] {ι : Type.{u1}} [_inst_6 : Nonempty.{succ u1} ι] {K : ι -> (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)} {dir : Directed.{u3, succ u1} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) ι (fun (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13718 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13720 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) => LE.le.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) 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(Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)) (Module.toDistribMulAction.{u2, u3} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i))))) (Algebra.toModule.{u2, u3} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)))) (Module.toDistribMulAction.{u2, u4} R B (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u2, u4} R B _inst_1 _inst_4 _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u3, u4, max u3 u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5 (AlgHom.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) (AlgHom.algHomClass.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5))))) (f i) x)
 Case conversion may be inaccurate. Consider using '#align subalgebra.supr_lift_inclusion Subalgebra.iSupLift_inclusionₓ'. -/
 @[simp]
 theorem iSupLift_inclusion {i : ι} (x : K i) (h : K i ≤ T) :
@@ -2247,7 +2247,7 @@ theorem iSupLift_inclusion {i : ι} (x : K i) (h : K i ≤ T) :
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {ι : Type.{u4}} [_inst_6 : Nonempty.{succ u4} ι] {K : ι -> (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {dir : Directed.{u2, succ u4} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) ι (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) K} {f : forall (i : ι), AlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K i)) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5} {hf : forall (i : ι) (j : ι) (h : LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (K i) (K j)), Eq.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K i)) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) (f i) (AlgHom.comp.{u1, u2, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K i)) (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K j)) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K j)) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K j)) _inst_5 (f j) (Subalgebra.inclusion.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i) (K j) h))} {T : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3} {hT : Eq.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) T (iSup.{u2, succ u4} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))) ι K)} {i : ι} (h : LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (K i) T), Eq.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K i)) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) (AlgHom.comp.{u1, u2, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K i)) (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) _inst_5 (Subalgebra.iSupLift.{u1, u2, u3, u4} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 ι _inst_6 K dir f hf T hT) (Subalgebra.inclusion.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i) T h)) (f i)
 but is expected to have type
-  forall {R : Type.{u2}} {A : Type.{u3}} {B : Type.{u4}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u3} A] [_inst_3 : Algebra.{u2, u3} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u4} B] [_inst_5 : Algebra.{u2, u4} R B _inst_1 _inst_4] {ι : Type.{u1}} [_inst_6 : Nonempty.{succ u1} ι] {K : ι -> (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)} {dir : Directed.{u3, succ u1} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) ι (fun (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13879 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13881 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) => LE.le.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3))))) x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13879 x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13881) K} {f : forall (i : ι), AlgHom.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5} {hf : forall (i : ι) (j : ι) (h : LE.le.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3))))) (K i) (K j)), Eq.{max (succ u3) (succ u4)} (AlgHom.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) (f i) (AlgHom.comp.{u2, u3, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K j))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K j)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K j)) _inst_5 (f j) (Subalgebra.inclusion.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i) (K j) h))} {T : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3} {hT : Eq.{succ u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) T (iSup.{u3, succ u1} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3))) ι K)} {i : ι} (h : LE.le.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3))))) (K i) T), Eq.{max (succ u3) (succ u4)} (AlgHom.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) (AlgHom.comp.{u2, u3, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x T)) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 T) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 T) _inst_5 (Subalgebra.iSupLift.{u2, u3, u4, u1} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 ι _inst_6 K dir f hf T hT) (Subalgebra.inclusion.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i) T h)) (f i)
+  forall {R : Type.{u2}} {A : Type.{u3}} {B : Type.{u4}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u3} A] [_inst_3 : Algebra.{u2, u3} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u4} B] [_inst_5 : Algebra.{u2, u4} R B _inst_1 _inst_4] {ι : Type.{u1}} [_inst_6 : Nonempty.{succ u1} ι] {K : ι -> (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)} {dir : Directed.{u3, succ u1} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) ι (fun (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13873 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13875 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) => LE.le.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3))))) x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13873 x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13875) K} {f : forall (i : ι), AlgHom.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5} {hf : forall (i : ι) (j : ι) (h : LE.le.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3))))) (K i) (K j)), Eq.{max (succ u3) (succ u4)} (AlgHom.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) (f i) (AlgHom.comp.{u2, u3, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K j))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K j)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K j)) _inst_5 (f j) (Subalgebra.inclusion.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i) (K j) h))} {T : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3} {hT : Eq.{succ u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) T (iSup.{u3, succ u1} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3))) ι K)} {i : ι} (h : LE.le.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3))))) (K i) T), Eq.{max (succ u3) (succ u4)} (AlgHom.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) (AlgHom.comp.{u2, u3, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x T)) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 T) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 T) _inst_5 (Subalgebra.iSupLift.{u2, u3, u4, u1} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 ι _inst_6 K dir f hf T hT) (Subalgebra.inclusion.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i) T h)) (f i)
 Case conversion may be inaccurate. Consider using '#align subalgebra.supr_lift_comp_inclusion Subalgebra.iSupLift_comp_inclusionₓ'. -/
 @[simp]
 theorem iSupLift_comp_inclusion {i : ι} (h : K i ≤ T) :
@@ -2258,7 +2258,7 @@ theorem iSupLift_comp_inclusion {i : ι} (h : K i ≤ T) :
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {ι : Type.{u4}} [_inst_6 : Nonempty.{succ u4} ι] {K : ι -> (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {dir : Directed.{u2, succ u4} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) ι (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) K} {f : forall (i : ι), AlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K i)) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5} {hf : forall (i : ι) (j : ι) (h : LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (K i) (K j)), Eq.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K i)) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) (f i) (AlgHom.comp.{u1, u2, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K i)) (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K j)) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 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_inst_4))))) (DistribSMul.toSMulZeroClass.{u2, u4} R B (AddMonoid.toAddZeroClass.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))))) (DistribMulAction.toDistribSMul.{u2, u4} R B (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))) (Module.toDistribMulAction.{u2, u4} R B (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u2, u4} R B _inst_1 _inst_4 _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u4, u2, u3, u4} (AlgHom.{u2, u3, u4} R 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_inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)))))) (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))) (Module.toDistribMulAction.{u2, u3} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i))))) (Algebra.toModule.{u2, u3} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) 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u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)) (Module.toDistribMulAction.{u2, u3} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i))))) (Algebra.toModule.{u2, u3} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)))) (Module.toDistribMulAction.{u2, u4} R B (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u2, u4} R B _inst_1 _inst_4 _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u3, u4, max u3 u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5 (AlgHom.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) (AlgHom.algHomClass.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5))))) (f i) x)
+  forall {R : Type.{u2}} {A : Type.{u3}} {B : Type.{u4}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u3} A] [_inst_3 : Algebra.{u2, u3} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u4} B] [_inst_5 : Algebra.{u2, u4} R B _inst_1 _inst_4] {ι : Type.{u1}} [_inst_6 : Nonempty.{succ u1} ι] {K : ι -> (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)} {dir : Directed.{u3, succ u1} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) ι (fun (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.14000 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.14002 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) => LE.le.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3))))) x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.14000 x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.14002) K} {f : forall (i : ι), AlgHom.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5} {hf : forall (i : ι) (j : ι) (h : LE.le.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 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A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5 (AlgHom.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) (AlgHom.algHomClass.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5))))) (f i) x)
 Case conversion may be inaccurate. Consider using '#align subalgebra.supr_lift_mk Subalgebra.iSupLift_mkₓ'. -/
 @[simp]
 theorem iSupLift_mk {i : ι} (x : K i) (hx : (x : A) ∈ T) :
@@ -2269,7 +2269,7 @@ theorem iSupLift_mk {i : ι} (x : K i) (hx : (x : A) ∈ T) :
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {ι : Type.{u4}} [_inst_6 : Nonempty.{succ u4} ι] {K : ι -> (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {dir : Directed.{u2, succ u4} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) ι (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) K} {f : forall (i : ι), AlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K i)) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5} {hf : forall (i : ι) (j : ι) (h : LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (K i) (K j)), Eq.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, 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_inst_2 _inst_3 (K j)) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K j)) _inst_5 (f j) (Subalgebra.inclusion.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i) (K j) h))} {T : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3} {hT : Eq.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) T (iSup.{u2, succ u4} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))) ι K)} {i : ι} (x : coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T) (hx : Membership.Mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T) A (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T) A (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 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_inst_1 _inst_2 _inst_3 T) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) _inst_5) (fun (_x : AlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) _inst_5) => (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T) -> B) ([anonymous].{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) _inst_5) (Subalgebra.iSupLift.{u1, u2, u3, u4} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 ι _inst_6 K dir f hf T hT) x) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K i)) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) (fun (_x : AlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 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(Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x (K i)) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T) A (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T) A (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 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 but is expected to have type
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+  forall {R : Type.{u2}} {A : Type.{u3}} {B : Type.{u4}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u3} A] [_inst_3 : Algebra.{u2, u3} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u4} B] [_inst_5 : Algebra.{u2, u4} R B _inst_1 _inst_4] {ι : Type.{u1}} [_inst_6 : Nonempty.{succ u1} ι] {K : ι -> (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)} {dir : Directed.{u3, succ u1} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) ι (fun (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.14155 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.14157 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) => LE.le.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) 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A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i))))) (Algebra.toModule.{u2, u3} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)))) (Module.toDistribMulAction.{u2, u4} R B (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u2, u4} R B _inst_1 _inst_4 _inst_5)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u3 u4, u2, u3, u4} (AlgHom.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)) (Module.toDistribMulAction.{u2, u3} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i))))) (Algebra.toModule.{u2, u3} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)))) (Module.toDistribMulAction.{u2, u4} R B (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u2, u4} R B _inst_1 _inst_4 _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u3, u4, max u3 u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5 (AlgHom.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) (AlgHom.algHomClass.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5))))) (f i) (Subtype.mk.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i)) (Subtype.val.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Set.{u3} A) (Set.instMembershipSet.{u3} A) x (SetLike.coe.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) T)) x) hx))
 Case conversion may be inaccurate. Consider using '#align subalgebra.supr_lift_of_mem Subalgebra.iSupLift_of_memₓ'. -/
 theorem iSupLift_of_mem {i : ι} (x : T) (hx : (x : A) ∈ K i) :
     iSupLift K dir f hf T hT x = f i ⟨x, hx⟩ := by subst hT <;> exact Set.iUnionLift_of_mem x hx

bump to nightly-2023-05-14-08

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

d31da313

Diff

@@ -1611,83 +1611,83 @@ theorem inf_toSubsemiring (S T : Subalgebra R A) :
   rfl
 #align algebra.inf_to_subsemiring Algebra.inf_toSubsemiring
 
-/- warning: algebra.coe_Inf -> Algebra.coe_infₛ is a dubious translation:
+/- warning: algebra.coe_Inf -> Algebra.coe_sInf is a dubious translation:
 lean 3 declaration is
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+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Set.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)), Eq.{succ u2} (Set.{u2} A) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (InfSet.sInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))) S)) (Set.iInter.{u2, succ u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (fun (s : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Set.iInter.{u2, 0} A (Membership.Mem.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.hasMem.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) s S) (fun (H : Membership.Mem.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.hasMem.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) s S) => (fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) s)))
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Set.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)), Eq.{succ u2} (Set.{u2} A) (SetLike.coe.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (InfSet.infₛ.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toInfSet.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))) S)) (Set.interᵢ.{u2, succ u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (fun (s : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Set.interᵢ.{u2, 0} A (Membership.mem.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.instMembershipSet.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) s S) (fun (H : Membership.mem.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.instMembershipSet.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) s S) => SetLike.coe.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) s)))
-Case conversion may be inaccurate. Consider using '#align algebra.coe_Inf Algebra.coe_infₛₓ'. -/
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Set.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)), Eq.{succ u2} (Set.{u2} A) (SetLike.coe.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (InfSet.sInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toInfSet.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))) S)) (Set.iInter.{u2, succ u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (fun (s : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Set.iInter.{u2, 0} A (Membership.mem.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.instMembershipSet.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) s S) (fun (H : Membership.mem.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.instMembershipSet.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) s S) => SetLike.coe.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) s)))
+Case conversion may be inaccurate. Consider using '#align algebra.coe_Inf Algebra.coe_sInfₓ'. -/
 @[simp, norm_cast]
-theorem coe_infₛ (S : Set (Subalgebra R A)) : (↑(infₛ S) : Set A) = ⋂ s ∈ S, ↑s :=
-  infₛ_image
-#align algebra.coe_Inf Algebra.coe_infₛ
+theorem coe_sInf (S : Set (Subalgebra R A)) : (↑(sInf S) : Set A) = ⋂ s ∈ S, ↑s :=
+  sInf_image
+#align algebra.coe_Inf Algebra.coe_sInf
 
-/- warning: algebra.mem_Inf -> Algebra.mem_infₛ is a dubious translation:
+/- warning: algebra.mem_Inf -> Algebra.mem_sInf is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {S : Set.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {x : A}, Iff (Membership.Mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x (InfSet.infₛ.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))) S)) (forall (p : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), (Membership.Mem.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.hasMem.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) p S) -> (Membership.Mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x p))
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {S : Set.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {x : A}, Iff (Membership.Mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x (InfSet.sInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))) S)) (forall (p : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), (Membership.Mem.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.hasMem.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) p S) -> (Membership.Mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x p))
 but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align algebra.mem_Inf Algebra.mem_infₛₓ'. -/
-theorem mem_infₛ {S : Set (Subalgebra R A)} {x : A} : x ∈ infₛ S ↔ ∀ p ∈ S, x ∈ p := by
-  simp only [← SetLike.mem_coe, coe_Inf, Set.mem_interᵢ₂]
-#align algebra.mem_Inf Algebra.mem_infₛ
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {S : Set.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {x : A}, Iff (Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x (InfSet.sInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toInfSet.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))) S)) (forall (p : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), (Membership.mem.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.instMembershipSet.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) p S) -> (Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x p))
+Case conversion may be inaccurate. Consider using '#align algebra.mem_Inf Algebra.mem_sInfₓ'. -/
+theorem mem_sInf {S : Set (Subalgebra R A)} {x : A} : x ∈ sInf S ↔ ∀ p ∈ S, x ∈ p := by
+  simp only [← SetLike.mem_coe, coe_Inf, Set.mem_iInter₂]
+#align algebra.mem_Inf Algebra.mem_sInf
 
-/- warning: algebra.Inf_to_submodule -> Algebra.infₛ_toSubmodule is a dubious translation:
+/- warning: algebra.Inf_to_submodule -> Algebra.sInf_toSubmodule is a dubious translation:
 lean 3 declaration is
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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (InfSet.infₛ.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))) S)) (InfSet.infₛ.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.hasInf.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.image.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (coeFn.{succ u2, succ u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A 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(Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (fun (_x : RelEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} 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(CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) => (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) -> (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (RelEmbedding.hasCoeToFun.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S))
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Set.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)), Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (coeFn.{succ u2, succ u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A 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(CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) => (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) -> (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (RelEmbedding.hasCoeToFun.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S))
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Set.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)), Eq.{succ u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (InfSet.infₛ.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toInfSet.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))) S)) (FunLike.coe.{succ u2, succ u2, succ u2} 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(Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S))
-Case conversion may be inaccurate. Consider using '#align algebra.Inf_to_submodule Algebra.infₛ_toSubmoduleₓ'. -/
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Set.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)), Eq.{succ u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (InfSet.sInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toInfSet.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))) S)) (FunLike.coe.{succ u2, succ u2, succ u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (fun (_x : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) _x) (RelHomClass.toFunLike.{u2, u2, u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, u2} R A 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LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S))
+Case conversion may be inaccurate. Consider using '#align algebra.Inf_to_submodule Algebra.sInf_toSubmoduleₓ'. -/
 @[simp]
-theorem infₛ_toSubmodule (S : Set (Subalgebra R A)) :
-    (infₛ S).toSubmodule = infₛ (Subalgebra.toSubmodule '' S) :=
+theorem sInf_toSubmodule (S : Set (Subalgebra R A)) :
+    (sInf S).toSubmodule = sInf (Subalgebra.toSubmodule '' S) :=
   SetLike.coe_injective <| by simp
-#align algebra.Inf_to_submodule Algebra.infₛ_toSubmodule
+#align algebra.Inf_to_submodule Algebra.sInf_toSubmodule
 
-/- warning: algebra.Inf_to_subsemiring -> Algebra.infₛ_toSubsemiring is a dubious translation:
+/- warning: algebra.Inf_to_subsemiring -> Algebra.sInf_toSubsemiring is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Set.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)), Eq.{succ u2} (Subsemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (Subalgebra.toSubsemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (InfSet.infₛ.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))) S)) (InfSet.infₛ.{u2} (Subsemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (Subsemiring.hasInf.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (Set.image.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Subsemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (Subalgebra.toSubsemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3) S))
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Set.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)), Eq.{succ u2} (Subsemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (Subalgebra.toSubsemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (InfSet.sInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))) S)) (InfSet.sInf.{u2} (Subsemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (Subsemiring.hasInf.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (Set.image.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Subsemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (Subalgebra.toSubsemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3) S))
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Set.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)), Eq.{succ u2} (Subsemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (Subalgebra.toSubsemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (InfSet.infₛ.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toInfSet.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))) S)) (InfSet.infₛ.{u2} (Subsemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (Subsemiring.instInfSetSubsemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (Set.image.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Subsemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (Subalgebra.toSubsemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3) S))
-Case conversion may be inaccurate. Consider using '#align algebra.Inf_to_subsemiring Algebra.infₛ_toSubsemiringₓ'. -/
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Set.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)), Eq.{succ u2} (Subsemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (Subalgebra.toSubsemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (InfSet.sInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toInfSet.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))) S)) (InfSet.sInf.{u2} (Subsemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (Subsemiring.instInfSetSubsemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (Set.image.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Subsemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (Subalgebra.toSubsemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3) S))
+Case conversion may be inaccurate. Consider using '#align algebra.Inf_to_subsemiring Algebra.sInf_toSubsemiringₓ'. -/
 @[simp]
-theorem infₛ_toSubsemiring (S : Set (Subalgebra R A)) :
-    (infₛ S).toSubsemiring = infₛ (Subalgebra.toSubsemiring '' S) :=
+theorem sInf_toSubsemiring (S : Set (Subalgebra R A)) :
+    (sInf S).toSubsemiring = sInf (Subalgebra.toSubsemiring '' S) :=
   SetLike.coe_injective <| by simp
-#align algebra.Inf_to_subsemiring Algebra.infₛ_toSubsemiring
+#align algebra.Inf_to_subsemiring Algebra.sInf_toSubsemiring
 
-/- warning: algebra.coe_infi -> Algebra.coe_infᵢ is a dubious translation:
+/- warning: algebra.coe_infi -> Algebra.coe_iInf is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {ι : Sort.{u3}} {S : ι -> (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)}, Eq.{succ u2} (Set.{u2} A) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (infᵢ.{u2, u3} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => S i))) (Set.interᵢ.{u2, u3} A ι (fun (i : ι) => (fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (S i)))
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {ι : Sort.{u3}} {S : ι -> (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)}, Eq.{succ u2} (Set.{u2} A) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (iInf.{u2, u3} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => S i))) (Set.iInter.{u2, u3} A ι (fun (i : ι) => (fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (S i)))
 but is expected to have type
-  forall {R : Type.{u2}} {A : Type.{u3}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u3} A] [_inst_3 : Algebra.{u2, u3} R A _inst_1 _inst_2] {ι : Sort.{u1}} {S : ι -> (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)}, Eq.{succ u3} (Set.{u3} A) (SetLike.coe.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (infᵢ.{u3, u1} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toInfSet.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => S i))) (Set.interᵢ.{u3, u1} A ι (fun (i : ι) => SetLike.coe.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (S i)))
-Case conversion may be inaccurate. Consider using '#align algebra.coe_infi Algebra.coe_infᵢₓ'. -/
+  forall {R : Type.{u2}} {A : Type.{u3}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u3} A] [_inst_3 : Algebra.{u2, u3} R A _inst_1 _inst_2] {ι : Sort.{u1}} {S : ι -> (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)}, Eq.{succ u3} (Set.{u3} A) (SetLike.coe.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (iInf.{u3, u1} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toInfSet.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => S i))) (Set.iInter.{u3, u1} A ι (fun (i : ι) => SetLike.coe.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (S i)))
+Case conversion may be inaccurate. Consider using '#align algebra.coe_infi Algebra.coe_iInfₓ'. -/
 @[simp, norm_cast]
-theorem coe_infᵢ {ι : Sort _} {S : ι → Subalgebra R A} : (↑(⨅ i, S i) : Set A) = ⋂ i, S i := by
-  simp [infᵢ]
-#align algebra.coe_infi Algebra.coe_infᵢ
+theorem coe_iInf {ι : Sort _} {S : ι → Subalgebra R A} : (↑(⨅ i, S i) : Set A) = ⋂ i, S i := by
+  simp [iInf]
+#align algebra.coe_infi Algebra.coe_iInf
 
-/- warning: algebra.mem_infi -> Algebra.mem_infᵢ is a dubious translation:
+/- warning: algebra.mem_infi -> Algebra.mem_iInf is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {ι : Sort.{u3}} {S : ι -> (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {x : A}, Iff (Membership.Mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x (infᵢ.{u2, u3} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => S i))) (forall (i : ι), Membership.Mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x (S i))
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {ι : Sort.{u3}} {S : ι -> (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {x : A}, Iff (Membership.Mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x (iInf.{u2, u3} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => S i))) (forall (i : ι), Membership.Mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x (S i))
 but is expected to have type
-  forall {R : Type.{u2}} {A : Type.{u3}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u3} A] [_inst_3 : Algebra.{u2, u3} R A _inst_1 _inst_2] {ι : Sort.{u1}} {S : ι -> (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)} {x : A}, Iff (Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (infᵢ.{u3, u1} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toInfSet.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => S i))) (forall (i : ι), Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (S i))
-Case conversion may be inaccurate. Consider using '#align algebra.mem_infi Algebra.mem_infᵢₓ'. -/
-theorem mem_infᵢ {ι : Sort _} {S : ι → Subalgebra R A} {x : A} : (x ∈ ⨅ i, S i) ↔ ∀ i, x ∈ S i := by
-  simp only [infᵢ, mem_Inf, Set.forall_range_iff]
-#align algebra.mem_infi Algebra.mem_infᵢ
+  forall {R : Type.{u2}} {A : Type.{u3}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u3} A] [_inst_3 : Algebra.{u2, u3} R A _inst_1 _inst_2] {ι : Sort.{u1}} {S : ι -> (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)} {x : A}, Iff (Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (iInf.{u3, u1} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toInfSet.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => S i))) (forall (i : ι), Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (S i))
+Case conversion may be inaccurate. Consider using '#align algebra.mem_infi Algebra.mem_iInfₓ'. -/
+theorem mem_iInf {ι : Sort _} {S : ι → Subalgebra R A} {x : A} : (x ∈ ⨅ i, S i) ↔ ∀ i, x ∈ S i := by
+  simp only [iInf, mem_Inf, Set.forall_range_iff]
+#align algebra.mem_infi Algebra.mem_iInf
 
-/- warning: algebra.infi_to_submodule -> Algebra.infᵢ_toSubmodule is a dubious translation:
+/- warning: algebra.infi_to_submodule -> Algebra.iInf_toSubmodule is a dubious translation:
 lean 3 declaration is
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(Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) => (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) -> (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (RelEmbedding.hasCoeToFun.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (S i)))
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {ι : Sort.{u3}} (S : ι -> (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)), Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (coeFn.{succ u2, succ u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} 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(Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (fun (_x : RelEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 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(CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) => (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) -> (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (RelEmbedding.hasCoeToFun.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (iInf.{u2, u3} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => S i))) (iInf.{u2, u3} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.hasInf.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) ι (fun (i : ι) => coeFn.{succ u2, succ u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (fun (_x : RelEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) => (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) -> (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (RelEmbedding.hasCoeToFun.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (S i)))
 but is expected to have type
-  forall {R : Type.{u2}} {A : Type.{u3}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u3} A] [_inst_3 : Algebra.{u2, u3} R A _inst_1 _inst_2] {ι : Sort.{u1}} (S : ι -> (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)), Eq.{succ u3} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (infᵢ.{u3, u1} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toInfSet.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => S i))) (FunLike.coe.{succ 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(PartialOrder.toPreorder.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (fun (_x : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) _x) (RelHomClass.toFunLike.{u3, u3, u3} (OrderEmbedding.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) => LE.le.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) 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_inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) => LE.le.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Subalgebra.toSubmodule.{u2, u3} R A _inst_1 _inst_2 _inst_3) (S i)))
-Case conversion may be inaccurate. Consider using '#align algebra.infi_to_submodule Algebra.infᵢ_toSubmoduleₓ'. -/
+  forall {R : Type.{u2}} {A : Type.{u3}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u3} A] [_inst_3 : Algebra.{u2, u3} R A _inst_1 _inst_2] {ι : Sort.{u1}} (S : ι -> (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)), Eq.{succ u3} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (iInf.{u3, u1} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toInfSet.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => S i))) (FunLike.coe.{succ u3, succ u3, succ u3} (OrderEmbedding.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (fun (_x : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) _x) (RelHomClass.toFunLike.{u3, u3, u3} (OrderEmbedding.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) => LE.le.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) => LE.le.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) 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+Case conversion may be inaccurate. Consider using '#align algebra.infi_to_submodule Algebra.iInf_toSubmoduleₓ'. -/
 @[simp]
-theorem infᵢ_toSubmodule {ι : Sort _} (S : ι → Subalgebra R A) :
+theorem iInf_toSubmodule {ι : Sort _} (S : ι → Subalgebra R A) :
     (⨅ i, S i).toSubmodule = ⨅ i, (S i).toSubmodule :=
   SetLike.coe_injective <| by simp
-#align algebra.infi_to_submodule Algebra.infᵢ_toSubmodule
+#align algebra.infi_to_submodule Algebra.iInf_toSubmodule
 
 instance : Inhabited (Subalgebra R A) :=
   ⟨⊥⟩
@@ -2165,115 +2165,115 @@ section SuprLift
 
 variable {ι : Type _}
 
-/- warning: subalgebra.coe_supr_of_directed -> Subalgebra.coe_supᵢ_of_directed is a dubious translation:
+/- warning: subalgebra.coe_supr_of_directed -> Subalgebra.coe_iSup_of_directed is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {ι : Type.{u3}} [_inst_6 : Nonempty.{succ u3} ι] {S : ι -> (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)}, (Directed.{u2, succ u3} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) ι (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) S) -> (Eq.{succ u2} (Set.{u2} A) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (supᵢ.{u2, succ u3} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))) ι S)) (Set.unionᵢ.{u2, succ u3} A ι (fun (i : ι) => (fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (S i))))
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {ι : Type.{u3}} [_inst_6 : Nonempty.{succ u3} ι] {S : ι -> (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)}, (Directed.{u2, succ u3} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) ι (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) S) -> (Eq.{succ u2} (Set.{u2} A) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (iSup.{u2, succ u3} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))) ι S)) (Set.iUnion.{u2, succ u3} A ι (fun (i : ι) => (fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (S i))))
 but is expected to have type
-  forall {R : Type.{u2}} {A : Type.{u3}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u3} A] [_inst_3 : Algebra.{u2, u3} R A _inst_1 _inst_2] {ι : Type.{u1}} [_inst_6 : Nonempty.{succ u1} ι] {S : ι -> (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)}, (Directed.{u3, succ u1} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) ι (fun (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.12753 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.12755 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) => LE.le.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3))))) x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.12753 x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.12755) S) -> (Eq.{succ u3} (Set.{u3} A) (SetLike.coe.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (supᵢ.{u3, succ u1} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3))) ι S)) (Set.unionᵢ.{u3, succ u1} A ι (fun (i : ι) => SetLike.coe.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (S i))))
-Case conversion may be inaccurate. Consider using '#align subalgebra.coe_supr_of_directed Subalgebra.coe_supᵢ_of_directedₓ'. -/
-theorem coe_supᵢ_of_directed [Nonempty ι] {S : ι → Subalgebra R A} (dir : Directed (· ≤ ·) S) :
-    ↑(supᵢ S) = ⋃ i, (S i : Set A) :=
+  forall {R : Type.{u2}} {A : Type.{u3}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u3} A] [_inst_3 : Algebra.{u2, u3} R A _inst_1 _inst_2] {ι : Type.{u1}} [_inst_6 : Nonempty.{succ u1} ι] {S : ι -> (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)}, (Directed.{u3, succ u1} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) ι (fun (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.12753 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.12755 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) => LE.le.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3))))) x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.12753 x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.12755) S) -> (Eq.{succ u3} (Set.{u3} A) (SetLike.coe.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (iSup.{u3, succ u1} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3))) ι S)) (Set.iUnion.{u3, succ u1} A ι (fun (i : ι) => SetLike.coe.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (S i))))
+Case conversion may be inaccurate. Consider using '#align subalgebra.coe_supr_of_directed Subalgebra.coe_iSup_of_directedₓ'. -/
+theorem coe_iSup_of_directed [Nonempty ι] {S : ι → Subalgebra R A} (dir : Directed (· ≤ ·) S) :
+    ↑(iSup S) = ⋃ i, (S i : Set A) :=
   let K : Subalgebra R A :=
     { carrier := ⋃ i, S i
       mul_mem' := fun x y hx hy =>
-        let ⟨i, hi⟩ := Set.mem_unionᵢ.1 hx
-        let ⟨j, hj⟩ := Set.mem_unionᵢ.1 hy
+        let ⟨i, hi⟩ := Set.mem_iUnion.1 hx
+        let ⟨j, hj⟩ := Set.mem_iUnion.1 hy
         let ⟨k, hik, hjk⟩ := dir i j
-        Set.mem_unionᵢ.2 ⟨k, Subalgebra.mul_mem (S k) (hik hi) (hjk hj)⟩
+        Set.mem_iUnion.2 ⟨k, Subalgebra.mul_mem (S k) (hik hi) (hjk hj)⟩
       add_mem' := fun x y hx hy =>
-        let ⟨i, hi⟩ := Set.mem_unionᵢ.1 hx
-        let ⟨j, hj⟩ := Set.mem_unionᵢ.1 hy
+        let ⟨i, hi⟩ := Set.mem_iUnion.1 hx
+        let ⟨j, hj⟩ := Set.mem_iUnion.1 hy
         let ⟨k, hik, hjk⟩ := dir i j
-        Set.mem_unionᵢ.2 ⟨k, Subalgebra.add_mem (S k) (hik hi) (hjk hj)⟩
+        Set.mem_iUnion.2 ⟨k, Subalgebra.add_mem (S k) (hik hi) (hjk hj)⟩
       algebraMap_mem' := fun r =>
         let i := @Nonempty.some ι inferInstance
-        Set.mem_unionᵢ.2 ⟨i, Subalgebra.algebraMap_mem _ _⟩ }
-  have : supᵢ S = K :=
-    le_antisymm (supᵢ_le fun i => Set.subset_unionᵢ (fun i => ↑(S i)) i)
-      (SetLike.coe_subset_coe.1 (Set.unionᵢ_subset fun i => SetLike.coe_subset_coe.2 (le_supᵢ _ _)))
+        Set.mem_iUnion.2 ⟨i, Subalgebra.algebraMap_mem _ _⟩ }
+  have : iSup S = K :=
+    le_antisymm (iSup_le fun i => Set.subset_iUnion (fun i => ↑(S i)) i)
+      (SetLike.coe_subset_coe.1 (Set.iUnion_subset fun i => SetLike.coe_subset_coe.2 (le_iSup _ _)))
   this.symm ▸ rfl
-#align subalgebra.coe_supr_of_directed Subalgebra.coe_supᵢ_of_directed
+#align subalgebra.coe_supr_of_directed Subalgebra.coe_iSup_of_directed
 
-/- warning: subalgebra.supr_lift -> Subalgebra.supᵢLift is a dubious translation:
+/- warning: subalgebra.supr_lift -> Subalgebra.iSupLift is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {ι : Type.{u4}} [_inst_6 : Nonempty.{succ u4} ι] (K : ι -> (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)), (Directed.{u2, succ u4} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) ι (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) K) -> (forall (f : forall (i : ι), AlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K i)) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5), (forall (i : ι) (j : ι) (h : LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (K i) (K j)), Eq.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K i)) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) (f i) (AlgHom.comp.{u1, u2, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K i)) (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K j)) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K j)) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K j)) _inst_5 (f j) (Subalgebra.inclusion.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i) (K j) h))) -> (forall (T : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), (Eq.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) T (supᵢ.{u2, succ u4} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))) ι K)) -> (AlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) _inst_5)))
+  forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {ι : Type.{u4}} [_inst_6 : Nonempty.{succ u4} ι] (K : ι -> (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)), (Directed.{u2, succ u4} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) ι (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) K) -> (forall (f : forall (i : ι), AlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K i)) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5), (forall (i : ι) (j : ι) (h : LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (K i) (K j)), Eq.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K i)) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) (f i) (AlgHom.comp.{u1, u2, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K i)) (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K j)) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K j)) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K j)) _inst_5 (f j) (Subalgebra.inclusion.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i) (K j) h))) -> (forall (T : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), (Eq.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) T (iSup.{u2, succ u4} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))) ι K)) -> (AlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) _inst_5)))
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {ι : Type.{u4}} [_inst_6 : Nonempty.{succ u4} ι] (K : ι -> (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)), (Directed.{u2, succ u4} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) ι (fun (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13136 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13138 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13136 x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13138) K) -> (forall (f : forall (i : ι), AlgHom.{u1, u2, u3} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5), (forall (i : ι) (j : ι) (h : LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (K i) (K j)), Eq.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) (f i) (AlgHom.comp.{u1, u2, u2, u3} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x (K j))) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K j)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K j)) _inst_5 (f j) (Subalgebra.inclusion.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i) (K j) h))) -> (forall (T : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), (Eq.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) T (supᵢ.{u2, succ u4} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))) ι K)) -> (AlgHom.{u1, u2, u3} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T)) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) _inst_5)))
-Case conversion may be inaccurate. Consider using '#align subalgebra.supr_lift Subalgebra.supᵢLiftₓ'. -/
+  forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {ι : Type.{u4}} [_inst_6 : Nonempty.{succ u4} ι] (K : ι -> (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)), (Directed.{u2, succ u4} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) ι (fun (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13136 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13138 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13136 x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13138) K) -> (forall (f : forall (i : ι), AlgHom.{u1, u2, u3} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5), (forall (i : ι) (j : ι) (h : LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A 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+Case conversion may be inaccurate. Consider using '#align subalgebra.supr_lift Subalgebra.iSupLiftₓ'. -/
 /-- Define an algebra homomorphism on a directed supremum of subalgebras by defining
 it on each subalgebra, and proving that it agrees on the intersection of subalgebras. -/
-noncomputable def supᵢLift [Nonempty ι] (K : ι → Subalgebra R A) (dir : Directed (· ≤ ·) K)
+noncomputable def iSupLift [Nonempty ι] (K : ι → Subalgebra R A) (dir : Directed (· ≤ ·) K)
     (f : ∀ i, K i →ₐ[R] B) (hf : ∀ (i j : ι) (h : K i ≤ K j), f i = (f j).comp (inclusion h))
-    (T : Subalgebra R A) (hT : T = supᵢ K) : ↥T →ₐ[R] B := by
+    (T : Subalgebra R A) (hT : T = iSup K) : ↥T →ₐ[R] B := by
   subst hT <;>
     exact
       { toFun :=
-          Set.unionᵢLift (fun i => ↑(K i)) (fun i x => f i x)
+          Set.iUnionLift (fun i => ↑(K i)) (fun i x => f i x)
             (fun i j x hxi hxj => by
               let ⟨k, hik, hjk⟩ := dir i j
               rw [hf i k hik, hf j k hjk]
               rfl)
-            (↑(supᵢ K)) (by rw [coe_supr_of_directed dir] <;> rfl)
-        map_one' := Set.unionᵢLift_const _ (fun _ => 1) (fun _ => rfl) _ (by simp)
-        map_zero' := Set.unionᵢLift_const _ (fun _ => 0) (fun _ => rfl) _ (by simp)
+            (↑(iSup K)) (by rw [coe_supr_of_directed dir] <;> rfl)
+        map_one' := Set.iUnionLift_const _ (fun _ => 1) (fun _ => rfl) _ (by simp)
+        map_zero' := Set.iUnionLift_const _ (fun _ => 0) (fun _ => rfl) _ (by simp)
         map_mul' :=
-          Set.unionᵢLift_binary (coe_supr_of_directed dir) dir _ (fun _ => (· * ·))
+          Set.iUnionLift_binary (coe_supr_of_directed dir) dir _ (fun _ => (· * ·))
             (fun _ _ _ => rfl) _ (by simp)
         map_add' :=
-          Set.unionᵢLift_binary (coe_supr_of_directed dir) dir _ (fun _ => (· + ·))
+          Set.iUnionLift_binary (coe_supr_of_directed dir) dir _ (fun _ => (· + ·))
             (fun _ _ _ => rfl) _ (by simp)
         commutes' := fun r =>
-          Set.unionᵢLift_const _ (fun _ => algebraMap _ _ r) (fun _ => rfl) _ fun i => by
+          Set.iUnionLift_const _ (fun _ => algebraMap _ _ r) (fun _ => rfl) _ fun i => by
             erw [AlgHom.commutes (f i)] }
-#align subalgebra.supr_lift Subalgebra.supᵢLift
+#align subalgebra.supr_lift Subalgebra.iSupLift
 
 variable [Nonempty ι] {K : ι → Subalgebra R A} {dir : Directed (· ≤ ·) K} {f : ∀ i, K i →ₐ[R] B}
   {hf : ∀ (i j : ι) (h : K i ≤ K j), f i = (f j).comp (inclusion h)} {T : Subalgebra R A}
-  {hT : T = supᵢ K}
+  {hT : T = iSup K}
 
-/- warning: subalgebra.supr_lift_inclusion -> Subalgebra.supᵢLift_inclusion is a dubious translation:
+/- warning: subalgebra.supr_lift_inclusion -> Subalgebra.iSupLift_inclusion is a dubious translation:
 lean 3 declaration is
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 but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align subalgebra.supr_lift_inclusion Subalgebra.supᵢLift_inclusionₓ'. -/
+  forall {R : Type.{u2}} {A : Type.{u3}} {B : Type.{u4}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u3} A] [_inst_3 : Algebra.{u2, u3} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u4} B] [_inst_5 : Algebra.{u2, u4} R B _inst_1 _inst_4] {ι : Type.{u1}} [_inst_6 : Nonempty.{succ u1} ι] {K : ι -> (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)} {dir : Directed.{u3, succ u1} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) ι (fun (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13724 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13726 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) => LE.le.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) 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+Case conversion may be inaccurate. Consider using '#align subalgebra.supr_lift_inclusion Subalgebra.iSupLift_inclusionₓ'. -/
 @[simp]
-theorem supᵢLift_inclusion {i : ι} (x : K i) (h : K i ≤ T) :
-    supᵢLift K dir f hf T hT (inclusion h x) = f i x := by
-  subst T <;> exact Set.unionᵢLift_inclusion _ _
-#align subalgebra.supr_lift_inclusion Subalgebra.supᵢLift_inclusion
+theorem iSupLift_inclusion {i : ι} (x : K i) (h : K i ≤ T) :
+    iSupLift K dir f hf T hT (inclusion h x) = f i x := by
+  subst T <;> exact Set.iUnionLift_inclusion _ _
+#align subalgebra.supr_lift_inclusion Subalgebra.iSupLift_inclusion
 
-/- warning: subalgebra.supr_lift_comp_inclusion -> Subalgebra.supᵢLift_comp_inclusion is a dubious translation:
+/- warning: subalgebra.supr_lift_comp_inclusion -> Subalgebra.iSupLift_comp_inclusion is a dubious translation:
 lean 3 declaration is
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+  forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {ι : Type.{u4}} [_inst_6 : Nonempty.{succ u4} ι] {K : ι -> (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {dir : Directed.{u2, succ u4} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) ι (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) K} {f : forall (i : ι), AlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} 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(Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (K i) T), Eq.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K i)) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) (AlgHom.comp.{u1, u2, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K i)) (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) _inst_5 (Subalgebra.iSupLift.{u1, u2, u3, u4} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 ι _inst_6 K dir f hf T hT) (Subalgebra.inclusion.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i) T h)) (f i)
 but is expected to have type
-  forall {R : Type.{u2}} {A : Type.{u3}} {B : Type.{u4}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u3} A] [_inst_3 : Algebra.{u2, u3} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u4} B] [_inst_5 : Algebra.{u2, u4} R B _inst_1 _inst_4] {ι : Type.{u1}} [_inst_6 : Nonempty.{succ u1} ι] {K : ι -> (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)} {dir : Directed.{u3, succ u1} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) ι (fun (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13879 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13881 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) => LE.le.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3))))) x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13879 x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13881) K} {f : forall (i : ι), AlgHom.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5} {hf : forall (i : ι) (j : ι) (h : LE.le.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 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(Subalgebra.inclusion.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i) (K j) h))} {T : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3} {hT : Eq.{succ u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) T (supᵢ.{u3, succ u1} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3))) ι K)} {i : ι} (h : LE.le.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3))))) (K i) T), Eq.{max (succ u3) (succ u4)} (AlgHom.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) (AlgHom.comp.{u2, u3, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subtype.{succ u3} A (fun (x : A) => 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-Case conversion may be inaccurate. Consider using '#align subalgebra.supr_lift_comp_inclusion Subalgebra.supᵢLift_comp_inclusionₓ'. -/
+  forall {R : Type.{u2}} {A : Type.{u3}} {B : Type.{u4}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u3} A] [_inst_3 : Algebra.{u2, u3} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u4} B] [_inst_5 : Algebra.{u2, u4} R B _inst_1 _inst_4] {ι : Type.{u1}} [_inst_6 : Nonempty.{succ u1} ι] {K : ι -> (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)} {dir : Directed.{u3, succ u1} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) ι (fun (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13879 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13881 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) => LE.le.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) 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+Case conversion may be inaccurate. Consider using '#align subalgebra.supr_lift_comp_inclusion Subalgebra.iSupLift_comp_inclusionₓ'. -/
 @[simp]
-theorem supᵢLift_comp_inclusion {i : ι} (h : K i ≤ T) :
-    (supᵢLift K dir f hf T hT).comp (inclusion h) = f i := by ext <;> simp
-#align subalgebra.supr_lift_comp_inclusion Subalgebra.supᵢLift_comp_inclusion
+theorem iSupLift_comp_inclusion {i : ι} (h : K i ≤ T) :
+    (iSupLift K dir f hf T hT).comp (inclusion h) = f i := by ext <;> simp
+#align subalgebra.supr_lift_comp_inclusion Subalgebra.iSupLift_comp_inclusion
 
-/- warning: subalgebra.supr_lift_mk -> Subalgebra.supᵢLift_mk is a dubious translation:
+/- warning: subalgebra.supr_lift_mk -> Subalgebra.iSupLift_mk is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align subalgebra.supr_lift_mk Subalgebra.supᵢLift_mkₓ'. -/
+  forall {R : Type.{u2}} {A : Type.{u3}} {B : Type.{u4}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u3} A] [_inst_3 : Algebra.{u2, u3} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u4} B] [_inst_5 : Algebra.{u2, u4} R B _inst_1 _inst_4] {ι : Type.{u1}} [_inst_6 : Nonempty.{succ u1} ι] {K : ι -> (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)} {dir : Directed.{u3, succ u1} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) ι (fun (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.14006 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.14008 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) => LE.le.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) 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+Case conversion may be inaccurate. Consider using '#align subalgebra.supr_lift_mk Subalgebra.iSupLift_mkₓ'. -/
 @[simp]
-theorem supᵢLift_mk {i : ι} (x : K i) (hx : (x : A) ∈ T) :
-    supᵢLift K dir f hf T hT ⟨x, hx⟩ = f i x := by subst hT <;> exact Set.unionᵢLift_mk x hx
-#align subalgebra.supr_lift_mk Subalgebra.supᵢLift_mk
+theorem iSupLift_mk {i : ι} (x : K i) (hx : (x : A) ∈ T) :
+    iSupLift K dir f hf T hT ⟨x, hx⟩ = f i x := by subst hT <;> exact Set.iUnionLift_mk x hx
+#align subalgebra.supr_lift_mk Subalgebra.iSupLift_mk
 
-/- warning: subalgebra.supr_lift_of_mem -> Subalgebra.supᵢLift_of_mem is a dubious translation:
+/- warning: subalgebra.supr_lift_of_mem -> Subalgebra.iSupLift_of_mem is a dubious translation:
 lean 3 declaration is
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A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i))))) (Algebra.toModule.{u2, u3} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, 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_inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i))))) (Algebra.toModule.{u2, u3} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A 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_inst_3 (K i)) _inst_5) (AlgHom.algHomClass.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5))))) (f i) (Subtype.mk.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i)) (Subtype.val.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Set.{u3} A) (Set.instMembershipSet.{u3} A) x (SetLike.coe.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) T)) x) hx))
-Case conversion may be inaccurate. Consider using '#align subalgebra.supr_lift_of_mem Subalgebra.supᵢLift_of_memₓ'. -/
-theorem supᵢLift_of_mem {i : ι} (x : T) (hx : (x : A) ∈ K i) :
-    supᵢLift K dir f hf T hT x = f i ⟨x, hx⟩ := by subst hT <;> exact Set.unionᵢLift_of_mem x hx
-#align subalgebra.supr_lift_of_mem Subalgebra.supᵢLift_of_mem
+  forall {R : Type.{u2}} {A : Type.{u3}} {B : Type.{u4}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u3} A] [_inst_3 : Algebra.{u2, u3} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u4} B] [_inst_5 : Algebra.{u2, u4} R B _inst_1 _inst_4] {ι : Type.{u1}} [_inst_6 : Nonempty.{succ u1} ι] {K : ι -> (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)} {dir : Directed.{u3, succ u1} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) ι (fun (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.14161 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.14163 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) => LE.le.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3))))) x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.14161 x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.14163) K} {f : forall (i : ι), AlgHom.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5} {hf : forall (i : ι) (j : ι) (h : LE.le.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3))))) (K i) (K j)), Eq.{max (succ u3) (succ u4)} (AlgHom.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) (f i) (AlgHom.comp.{u2, u3, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K j))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K j)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K j)) _inst_5 (f j) 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_inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i))))) (Algebra.toModule.{u2, u3} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i))))))) (SMulZeroClass.toSMul.{u2, u4} R B (AddMonoid.toZero.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))))) (DistribSMul.toSMulZeroClass.{u2, u4} R B (AddMonoid.toAddZeroClass.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))))) (DistribMulAction.toDistribSMul.{u2, u4} R B (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))) (Module.toDistribMulAction.{u2, u4} R B (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u2, u4} R B _inst_1 _inst_4 _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u4, u2, u3, u4} (AlgHom.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) 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(SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)))))) (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))) (Module.toDistribMulAction.{u2, u3} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i))))) (Algebra.toModule.{u2, u3} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)))) (Module.toDistribMulAction.{u2, u4} R B (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u2, u4} R B _inst_1 _inst_4 _inst_5)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u3 u4, u2, u3, u4} (AlgHom.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)) (Module.toDistribMulAction.{u2, u3} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i))))) (Algebra.toModule.{u2, u3} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)))) (Module.toDistribMulAction.{u2, u4} R B (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u2, u4} R B _inst_1 _inst_4 _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u3, u4, max u3 u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5 (AlgHom.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) (AlgHom.algHomClass.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5))))) (f i) (Subtype.mk.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i)) (Subtype.val.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Set.{u3} A) (Set.instMembershipSet.{u3} A) x (SetLike.coe.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) T)) x) hx))
+Case conversion may be inaccurate. Consider using '#align subalgebra.supr_lift_of_mem Subalgebra.iSupLift_of_memₓ'. -/
+theorem iSupLift_of_mem {i : ι} (x : T) (hx : (x : A) ∈ K i) :
+    iSupLift K dir f hf T hT x = f i ⟨x, hx⟩ := by subst hT <;> exact Set.iUnionLift_of_mem x hx
+#align subalgebra.supr_lift_of_mem Subalgebra.iSupLift_of_mem
 
 end SuprLift

bump to nightly-2023-05-08-22

mathlib commit https://github.com/leanprover-community/mathlib/commit/08e1d8d4d989df3a6df86f385e9053ec8a372cc1

63e712c6

Diff

@@ -496,7 +496,7 @@ instance toRing {R A} [CommRing R] [Ring A] [Algebra R A] (S : Subalgebra R A) :
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_8 : CommRing.{u1} R] [_inst_9 : CommRing.{u2} A] [_inst_10 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_9))] (S : Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_9)) _inst_10), CommRing.{u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_9)) _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_9)) _inst_10) A (Subalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_9)) _inst_10)) S)
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_8 : CommRing.{u1} R] [_inst_9 : CommRing.{u2} A] [_inst_10 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_9))] (S : Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_9)) _inst_10), CommRing.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_9)) _inst_10) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_9)) _inst_10) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_9)) _inst_10)) x S))
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_8 : CommRing.{u1} R] [_inst_9 : CommRing.{u2} A] [_inst_10 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_9))] (S : Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_9)) _inst_10), CommRing.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_9)) _inst_10) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_9)) _inst_10) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_9)) _inst_10)) x S))
 Case conversion may be inaccurate. Consider using '#align subalgebra.to_comm_ring Subalgebra.toCommRingₓ'. -/
 instance toCommRing {R A} [CommRing R] [CommRing A] [Algebra R A] (S : Subalgebra R A) :
     CommRing S :=
@@ -878,7 +878,7 @@ theorem toSubsemiring_subtype : S.toSubsemiring.Subtype = (S.val : S →+* A) :=
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_8 : CommRing.{u1} R] [_inst_9 : Ring.{u2} A] [_inst_10 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9)] (S : Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10), Eq.{succ u2} (RingHom.{u2, u2} (coeSort.{succ u2, succ (succ u2)} (Subring.{u2} A _inst_9) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subring.{u2} A _inst_9) A (Subring.setLike.{u2} A _inst_9)) (Subalgebra.toSubring.{u1, u2} R A _inst_8 _inst_9 _inst_10 S)) A (NonAssocRing.toNonAssocSemiring.{u2} (coeSort.{succ u2, succ (succ u2)} (Subring.{u2} A _inst_9) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subring.{u2} A _inst_9) A (Subring.setLike.{u2} A _inst_9)) (Subalgebra.toSubring.{u1, u2} R A _inst_8 _inst_9 _inst_10 S)) (Ring.toNonAssocRing.{u2} (coeSort.{succ u2, succ (succ u2)} (Subring.{u2} A _inst_9) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subring.{u2} A _inst_9) A (Subring.setLike.{u2} A _inst_9)) (Subalgebra.toSubring.{u1, u2} R A _inst_8 _inst_9 _inst_10 S)) (Subring.toRing.{u2} A _inst_9 (Subalgebra.toSubring.{u1, u2} R A _inst_8 _inst_9 _inst_10 S)))) (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A _inst_9))) (Subring.subtype.{u2} A _inst_9 (Subalgebra.toSubring.{u1, u2} R A _inst_8 _inst_9 _inst_10 S)) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (AlgHom.{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) A (Subalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10)) S) A (CommRing.toCommSemiring.{u1} R _inst_8) (Subalgebra.toSemiring.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10 S) (Ring.toSemiring.{u2} A _inst_9) (Subalgebra.algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10 S) _inst_10) (RingHom.{u2, u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) A (Subalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10)) S) A (NonAssocRing.toNonAssocSemiring.{u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) A (Subalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10)) S) (Ring.toNonAssocRing.{u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) A (Subalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10)) S) (Subalgebra.toRing.{u1, u2} R A _inst_8 _inst_9 _inst_10 S))) (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A _inst_9))) (HasLiftT.mk.{succ u2, succ u2} (AlgHom.{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) A (Subalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10)) S) A (CommRing.toCommSemiring.{u1} R _inst_8) (Subalgebra.toSemiring.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10 S) (Ring.toSemiring.{u2} A _inst_9) (Subalgebra.algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10 S) _inst_10) (RingHom.{u2, u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) A (Subalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10)) S) A (NonAssocRing.toNonAssocSemiring.{u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) A (Subalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10)) S) (Ring.toNonAssocRing.{u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) A (Subalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10)) S) (Subalgebra.toRing.{u1, u2} R A _inst_8 _inst_9 _inst_10 S))) (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A _inst_9))) (CoeTCₓ.coe.{succ u2, succ u2} (AlgHom.{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) A (Subalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10)) S) A (CommRing.toCommSemiring.{u1} R _inst_8) (Subalgebra.toSemiring.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10 S) (Ring.toSemiring.{u2} A _inst_9) (Subalgebra.algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10 S) _inst_10) (RingHom.{u2, u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) A (Subalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10)) S) A (NonAssocRing.toNonAssocSemiring.{u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) A (Subalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10)) S) (Ring.toNonAssocRing.{u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) A (Subalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10)) S) (Subalgebra.toRing.{u1, u2} R A _inst_8 _inst_9 _inst_10 S))) (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A _inst_9))) (RingHom.hasCoeT.{u2, u2, u2} (AlgHom.{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) A (Subalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10)) S) A (CommRing.toCommSemiring.{u1} R _inst_8) (Subalgebra.toSemiring.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10 S) (Ring.toSemiring.{u2} A _inst_9) (Subalgebra.algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10 S) _inst_10) (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) A (Subalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10)) S) A (NonAssocRing.toNonAssocSemiring.{u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) A (Subalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10)) S) (Ring.toNonAssocRing.{u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) A (Subalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10)) S) (Subalgebra.toRing.{u1, u2} R A _inst_8 _inst_9 _inst_10 S))) (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A _inst_9)) (AlgHomClass.toRingHomClass.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) A (Subalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10)) S) A (CommRing.toCommSemiring.{u1} R _inst_8) (Subalgebra.toSemiring.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10 S) (Ring.toSemiring.{u2} A _inst_9) (Subalgebra.algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10 S) _inst_10) R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) A (Subalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10)) S) A (CommRing.toCommSemiring.{u1} R _inst_8) (Subalgebra.toSemiring.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10 S) (Ring.toSemiring.{u2} A _inst_9) (Subalgebra.algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10 S) _inst_10 (AlgHom.algHomClass.{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) A (Subalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10)) S) A (CommRing.toCommSemiring.{u1} R _inst_8) (Subalgebra.toSemiring.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10 S) (Ring.toSemiring.{u2} A _inst_9) (Subalgebra.algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10 S) _inst_10))))) (Subalgebra.val.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10 S))
 but is expected to have type
-  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_8 : CommRing.{u2} R] [_inst_9 : Ring.{u1} A] [_inst_10 : Algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9)] (S : Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10), Eq.{succ u1} (RingHom.{u1, u1} (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subring.{u1} A _inst_9) (SetLike.instMembership.{u1, u1} (Subring.{u1} A _inst_9) A (Subring.instSetLikeSubring.{u1} A _inst_9)) x (Subalgebra.toSubring.{u2, u1} R A _inst_8 _inst_9 _inst_10 S))) A (Subsemiring.toNonAssocSemiring.{u1} A (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A _inst_9)) (Subring.toSubsemiring.{u1} A _inst_9 (Subalgebra.toSubring.{u2, u1} R A _inst_8 _inst_9 _inst_10 S))) (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A _inst_9))) (Subring.subtype.{u1} A _inst_9 (Subalgebra.toSubring.{u2, u1} R A _inst_8 _inst_9 _inst_10 S)) (RingHomClass.toRingHom.{u1, u1, u1} (AlgHom.{u2, u1, u1} R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10)) x S)) A (CommRing.toCommSemiring.{u2} R _inst_8) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10 S) (Ring.toSemiring.{u1} A _inst_9) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10 S) _inst_10) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10)) x S)) A (Subsemiring.toNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_9)) (Subalgebra.toSubsemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10 S)) (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_9)) (AlgHomClass.toRingHomClass.{u1, u2, u1, u1} (AlgHom.{u2, u1, u1} R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10)) x S)) A (CommRing.toCommSemiring.{u2} R _inst_8) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10 S) (Ring.toSemiring.{u1} A _inst_9) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10 S) _inst_10) R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10)) x S)) A (CommRing.toCommSemiring.{u2} R _inst_8) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10 S) (Ring.toSemiring.{u1} A _inst_9) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10 S) _inst_10 (AlgHom.algHomClass.{u2, u1, u1} R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10)) x S)) A (CommRing.toCommSemiring.{u2} R _inst_8) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10 S) (Ring.toSemiring.{u1} A _inst_9) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10 S) _inst_10)) (Subalgebra.val.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10 S))
+  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_8 : CommRing.{u2} R] [_inst_9 : Ring.{u1} A] [_inst_10 : Algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9)] (S : Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10), Eq.{succ u1} (RingHom.{u1, u1} (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subring.{u1} A _inst_9) (SetLike.instMembership.{u1, u1} (Subring.{u1} A _inst_9) A (Subring.instSetLikeSubring.{u1} A _inst_9)) x (Subalgebra.toSubring.{u2, u1} R A _inst_8 _inst_9 _inst_10 S))) A (Subsemiring.toNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_9)) (Subring.toSubsemiring.{u1} A _inst_9 (Subalgebra.toSubring.{u2, u1} R A _inst_8 _inst_9 _inst_10 S))) (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_9))) (Subring.subtype.{u1} A _inst_9 (Subalgebra.toSubring.{u2, u1} R A _inst_8 _inst_9 _inst_10 S)) (RingHomClass.toRingHom.{u1, u1, u1} (AlgHom.{u2, u1, u1} R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10)) x S)) A (CommRing.toCommSemiring.{u2} R _inst_8) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10 S) (Ring.toSemiring.{u1} A _inst_9) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10 S) _inst_10) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10)) x S)) A (Subsemiring.toNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_9)) (Subalgebra.toSubsemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10 S)) (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_9)) (AlgHomClass.toRingHomClass.{u1, u2, u1, u1} (AlgHom.{u2, u1, u1} R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10)) x S)) A (CommRing.toCommSemiring.{u2} R _inst_8) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10 S) (Ring.toSemiring.{u1} A _inst_9) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10 S) _inst_10) R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10)) x S)) A (CommRing.toCommSemiring.{u2} R _inst_8) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10 S) (Ring.toSemiring.{u1} A _inst_9) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10 S) _inst_10 (AlgHom.algHomClass.{u2, u1, u1} R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10)) x S)) A (CommRing.toCommSemiring.{u2} R _inst_8) (Subalgebra.toSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10 S) (Ring.toSemiring.{u1} A _inst_9) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10 S) _inst_10)) (Subalgebra.val.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_10 S))
 Case conversion may be inaccurate. Consider using '#align subalgebra.to_subring_subtype Subalgebra.toSubring_subtypeₓ'. -/
 @[simp]
 theorem toSubring_subtype {R A : Type _} [CommRing R] [Ring A] [Algebra R A] (S : Subalgebra R A) :
@@ -2418,7 +2418,7 @@ theorem rangeS_algebraMap {R A : Type _} [CommSemiring R] [CommSemiring A] [Alge
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_6 : CommRing.{u1} R] [_inst_7 : CommRing.{u2} A] [_inst_8 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_6) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_7))] (S : Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_6) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_7)) _inst_8), Eq.{succ u2} (Subring.{u2} A (CommRing.toRing.{u2} A _inst_7)) (RingHom.range.{u2, u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_6) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_7)) _inst_8) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_6) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_7)) _inst_8) A (Subalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_6) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_7)) _inst_8)) S) A (Subalgebra.toRing.{u1, u2} R A _inst_6 (CommRing.toRing.{u2} A _inst_7) _inst_8 S) (CommRing.toRing.{u2} A _inst_7) (algebraMap.{u2, u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_6) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_7)) _inst_8) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_6) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_7)) _inst_8) A (Subalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_6) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_7)) _inst_8)) S) A (Subalgebra.toCommSemiring.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_6) (CommRing.toCommSemiring.{u2} A _inst_7) _inst_8 S) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_7)) (Subalgebra.toAlgebra.{u2, u1, u2} A R A (CommRing.toCommSemiring.{u1} R _inst_6) (CommRing.toCommSemiring.{u2} A _inst_7) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_7)) _inst_8 (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_7)) S))) (Subalgebra.toSubring.{u1, u2} R A _inst_6 (CommRing.toRing.{u2} A _inst_7) _inst_8 S)
 but is expected to have type
-  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_6 : CommRing.{u2} R] [_inst_7 : CommRing.{u1} A] [_inst_8 : Algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_6) (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_7))] (S : Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_6) (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_7)) _inst_8), Eq.{succ u1} (Subring.{u1} A (CommRing.toRing.{u1} A _inst_7)) (RingHom.range.{u1, u1} (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_6) (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_7)) _inst_8) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_6) (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_7)) _inst_8) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_6) (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_7)) _inst_8)) x S)) A (Subalgebra.toRing.{u2, u1} R A _inst_6 (CommRing.toRing.{u1} A _inst_7) _inst_8 S) (CommRing.toRing.{u1} A _inst_7) (algebraMap.{u1, u1} (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_6) (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_7)) _inst_8) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_6) (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_7)) _inst_8) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_6) (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_7)) _inst_8)) x S)) A (Subalgebra.toCommSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_6) (CommRing.toCommSemiring.{u1} A _inst_7) _inst_8 S) (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_7)) (Subalgebra.toAlgebra.{u1, u2, u1} A R A (CommRing.toCommSemiring.{u2} R _inst_6) (CommRing.toCommSemiring.{u1} A _inst_7) (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_7)) _inst_8 (Algebra.id.{u1} A (CommRing.toCommSemiring.{u1} A _inst_7)) S))) (Subalgebra.toSubring.{u2, u1} R A _inst_6 (CommRing.toRing.{u1} A _inst_7) _inst_8 S)
+  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_6 : CommRing.{u2} R] [_inst_7 : CommRing.{u1} A] [_inst_8 : Algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_6) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_7))] (S : Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_6) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_7)) _inst_8), Eq.{succ u1} (Subring.{u1} A (CommRing.toRing.{u1} A _inst_7)) (RingHom.range.{u1, u1} (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_6) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_7)) _inst_8) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_6) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_7)) _inst_8) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_6) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_7)) _inst_8)) x S)) A (Subalgebra.toRing.{u2, u1} R A _inst_6 (CommRing.toRing.{u1} A _inst_7) _inst_8 S) (CommRing.toRing.{u1} A _inst_7) (algebraMap.{u1, u1} (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_6) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_7)) _inst_8) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_6) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_7)) _inst_8) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_6) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_7)) _inst_8)) x S)) A (Subalgebra.toCommSemiring.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_6) (CommRing.toCommSemiring.{u1} A _inst_7) _inst_8 S) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_7)) (Subalgebra.toAlgebra.{u1, u2, u1} A R A (CommRing.toCommSemiring.{u2} R _inst_6) (CommRing.toCommSemiring.{u1} A _inst_7) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_7)) _inst_8 (Algebra.id.{u1} A (CommRing.toCommSemiring.{u1} A _inst_7)) S))) (Subalgebra.toSubring.{u2, u1} R A _inst_6 (CommRing.toRing.{u1} A _inst_7) _inst_8 S)
 Case conversion may be inaccurate. Consider using '#align subalgebra.range_algebra_map Subalgebra.range_algebraMapₓ'. -/
 @[simp]
 theorem range_algebraMap {R A : Type _} [CommRing R] [CommRing A] [Algebra R A]
@@ -2589,7 +2589,7 @@ end Centralizer
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {S : Type.{u2}} [_inst_6 : CommRing.{u2} S] [_inst_7 : Algebra.{u1, u2} R S _inst_1 (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6))] (S' : Subalgebra.{u1, u2} R S _inst_1 (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_7) {ι : Type.{u3}} (ι' : Finset.{u3} ι) (s : ι -> S) (l : ι -> S), (Eq.{succ u2} S (Finset.sum.{u2, u3} S ι (AddCommGroup.toAddCommMonoid.{u2} S (NonUnitalNonAssocRing.toAddCommGroup.{u2} S (NonAssocRing.toNonUnitalNonAssocRing.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_6))))) ι' (fun (i : ι) => HMul.hMul.{u2, u2, u2} S S S (instHMul.{u2} S (Distrib.toHasMul.{u2} S (Ring.toDistrib.{u2} S (CommRing.toRing.{u2} S _inst_6)))) (l i) (s i))) (OfNat.ofNat.{u2} S 1 (OfNat.mk.{u2} S 1 (One.one.{u2} S (AddMonoidWithOne.toOne.{u2} S (AddGroupWithOne.toAddMonoidWithOne.{u2} S (AddCommGroupWithOne.toAddGroupWithOne.{u2} S (Ring.toAddCommGroupWithOne.{u2} S (CommRing.toRing.{u2} S _inst_6))))))))) -> (forall (i : ι), Membership.Mem.{u2, u2} S (Subalgebra.{u1, u2} R S _inst_1 (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_7) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R S _inst_1 (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_7) S (Subalgebra.setLike.{u1, u2} R S _inst_1 (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_7)) (s i) S') -> (forall (i : ι), Membership.Mem.{u2, u2} S (Subalgebra.{u1, u2} R S _inst_1 (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_7) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R S _inst_1 (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_7) S (Subalgebra.setLike.{u1, u2} R S _inst_1 (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_7)) (l i) S') -> (forall (x : S), (forall (i : ι), Exists.{1} Nat (fun (n : Nat) => Membership.Mem.{u2, u2} S (Subalgebra.{u1, u2} R S _inst_1 (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_7) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R S _inst_1 (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_7) S (Subalgebra.setLike.{u1, u2} R S _inst_1 (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_7)) (SMul.smul.{u2, u2} S S (Mul.toSMul.{u2} S (Distrib.toHasMul.{u2} S (Ring.toDistrib.{u2} S (CommRing.toRing.{u2} S _inst_6)))) (HPow.hPow.{u2, 0, u2} S Nat S (instHPow.{u2, 0} S Nat (Monoid.Pow.{u2} S (Ring.toMonoid.{u2} S (CommRing.toRing.{u2} S _inst_6)))) (s i) n) x) S')) -> (Membership.Mem.{u2, u2} S (Subalgebra.{u1, u2} R S _inst_1 (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_7) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R S _inst_1 (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_7) S (Subalgebra.setLike.{u1, u2} R S _inst_1 (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_7)) x S'))
 but is expected to have type
-  forall {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] {S : Type.{u2}} [_inst_6 : CommRing.{u2} S] [_inst_7 : Algebra.{u3, u2} R S _inst_1 (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6))] (S' : Subalgebra.{u3, u2} R S _inst_1 (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_7) {ι : Type.{u1}} (ι' : Finset.{u1} ι) (s : ι -> S) (l : ι -> S), (Eq.{succ u2} S (Finset.sum.{u2, u1} S ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} S (NonAssocRing.toNonUnitalNonAssocRing.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_6))))) ι' (fun (i : ι) => HMul.hMul.{u2, u2, u2} S S S (instHMul.{u2} S (NonUnitalNonAssocRing.toMul.{u2} S (NonAssocRing.toNonUnitalNonAssocRing.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_6))))) (l i) (s i))) (OfNat.ofNat.{u2} S 1 (One.toOfNat1.{u2} S (NonAssocRing.toOne.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_6)))))) -> (forall (i : ι), Membership.mem.{u2, u2} S (Subalgebra.{u3, u2} R S _inst_1 (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_7) (SetLike.instMembership.{u2, u2} (Subalgebra.{u3, u2} R S _inst_1 (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_7) S (Subalgebra.instSetLikeSubalgebra.{u3, u2} R S _inst_1 (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_7)) (s i) S') -> (forall (i : ι), Membership.mem.{u2, u2} S (Subalgebra.{u3, u2} R S _inst_1 (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_7) (SetLike.instMembership.{u2, u2} (Subalgebra.{u3, u2} R S _inst_1 (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_7) S (Subalgebra.instSetLikeSubalgebra.{u3, u2} R S _inst_1 (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_7)) (l i) S') -> (forall (x : S), (forall (i : ι), Exists.{1} Nat (fun (n : Nat) => Membership.mem.{u2, u2} S (Subalgebra.{u3, u2} R S _inst_1 (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_7) (SetLike.instMembership.{u2, u2} (Subalgebra.{u3, u2} R S _inst_1 (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_7) S (Subalgebra.instSetLikeSubalgebra.{u3, u2} R S _inst_1 (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_7)) (HSMul.hSMul.{u2, u2, u2} S S S (instHSMul.{u2, u2} S S (Algebra.toSMul.{u2, u2} S S (CommRing.toCommSemiring.{u2} S _inst_6) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) (Algebra.id.{u2} S (CommRing.toCommSemiring.{u2} S _inst_6)))) (HPow.hPow.{u2, 0, u2} S Nat S (instHPow.{u2, 0} S Nat (Monoid.Pow.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)))))) (s i) n) x) S')) -> (Membership.mem.{u2, u2} S (Subalgebra.{u3, u2} R S _inst_1 (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_7) (SetLike.instMembership.{u2, u2} (Subalgebra.{u3, u2} R S _inst_1 (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_7) S (Subalgebra.instSetLikeSubalgebra.{u3, u2} R S _inst_1 (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_7)) x S'))
+  forall {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] {S : Type.{u2}} [_inst_6 : CommRing.{u2} S] [_inst_7 : Algebra.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_6))] (S' : Subalgebra.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_6)) _inst_7) {ι : Type.{u1}} (ι' : Finset.{u1} ι) (s : ι -> S) (l : ι -> S), (Eq.{succ u2} S (Finset.sum.{u2, u1} S ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} S (NonAssocRing.toNonUnitalNonAssocRing.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_6))))) ι' (fun (i : ι) => HMul.hMul.{u2, u2, u2} S S S (instHMul.{u2} S (NonUnitalNonAssocRing.toMul.{u2} S (NonAssocRing.toNonUnitalNonAssocRing.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_6))))) (l i) (s i))) (OfNat.ofNat.{u2} S 1 (One.toOfNat1.{u2} S (Semiring.toOne.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_6)))))) -> (forall (i : ι), Membership.mem.{u2, u2} S (Subalgebra.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_6)) _inst_7) (SetLike.instMembership.{u2, u2} (Subalgebra.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_6)) _inst_7) S (Subalgebra.instSetLikeSubalgebra.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_6)) _inst_7)) (s i) S') -> (forall (i : ι), Membership.mem.{u2, u2} S (Subalgebra.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_6)) _inst_7) (SetLike.instMembership.{u2, u2} (Subalgebra.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_6)) _inst_7) S (Subalgebra.instSetLikeSubalgebra.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_6)) _inst_7)) (l i) S') -> (forall (x : S), (forall (i : ι), Exists.{1} Nat (fun (n : Nat) => Membership.mem.{u2, u2} S (Subalgebra.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_6)) _inst_7) (SetLike.instMembership.{u2, u2} (Subalgebra.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_6)) _inst_7) S (Subalgebra.instSetLikeSubalgebra.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_6)) _inst_7)) (HSMul.hSMul.{u2, u2, u2} S S S (instHSMul.{u2, u2} S S (Algebra.toSMul.{u2, u2} S S (CommRing.toCommSemiring.{u2} S _inst_6) (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_6)) (Algebra.id.{u2} S (CommRing.toCommSemiring.{u2} S _inst_6)))) (HPow.hPow.{u2, 0, u2} S Nat S (instHPow.{u2, 0} S Nat (Monoid.Pow.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_6)))))) (s i) n) x) S')) -> (Membership.mem.{u2, u2} S (Subalgebra.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_6)) _inst_7) (SetLike.instMembership.{u2, u2} (Subalgebra.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_6)) _inst_7) S (Subalgebra.instSetLikeSubalgebra.{u3, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_6)) _inst_7)) x S'))
 Case conversion may be inaccurate. Consider using '#align subalgebra.mem_of_finset_sum_eq_one_of_pow_smul_mem Subalgebra.mem_of_finset_sum_eq_one_of_pow_smul_memₓ'. -/
 /-- Suppose we are given `∑ i, lᵢ * sᵢ = 1` in `S`, and `S'` a subalgebra of `S` that contains
 `lᵢ` and `sᵢ`. To check that an `x : S` falls in `S'`, we only need to show that
@@ -2630,7 +2630,7 @@ theorem mem_of_finset_sum_eq_one_of_pow_smul_mem {S : Type _} [CommRing S] [Alge
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {S : Type.{u2}} [_inst_6 : CommRing.{u2} S] [_inst_7 : Algebra.{u1, u2} R S _inst_1 (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6))] (S' : Subalgebra.{u1, u2} R S _inst_1 (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_7) (s : Set.{u2} S) (l : Finsupp.{u2, u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} S) Type.{u2} (Set.hasCoeToSort.{u2} S) s) S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} S (NonAssocRing.toNonUnitalNonAssocRing.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_6))))))), (Eq.{succ u2} S (coeFn.{succ u2, succ u2} (LinearMap.{u2, u2, u2, u2} S S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)))) (Finsupp.{u2, u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} S) Type.{u2} (Set.hasCoeToSort.{u2} S) s) S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6))))))) S (Finsupp.addCommMonoid.{u2, u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} S) Type.{u2} (Set.hasCoeToSort.{u2} S) s) S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)))))) (AddCommGroup.toAddCommMonoid.{u2} S (NonUnitalNonAssocRing.toAddCommGroup.{u2} S (NonAssocRing.toNonUnitalNonAssocRing.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_6))))) (Finsupp.module.{u2, u2, u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} S) Type.{u2} (Set.hasCoeToSort.{u2} S) s) S S (Ring.toSemiring.{u2} S 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 but is expected to have type
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(Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)))) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)))) (Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6))))) (fun (_x : Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6))))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6))))) => S) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} S S (Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6))))) S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) (Finsupp.addCommMonoid.{u1, u1} (Set.Elem.{u1} S s) S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_6))))) (Finsupp.module.{u1, u1, u1} (Set.Elem.{u1} S s) S S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6))))) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)))) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6))) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6))))) (Finsupp.total.{u1, u1, u1} (Set.Elem.{u1} S s) S S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_6))))) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6))) (Subtype.val.{succ u1} S (fun (x : S) => Membership.mem.{u1, u1} S (Set.{u1} S) (Set.instMembershipSet.{u1} S) x s))) l) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6))))) => S) l) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6))))) => S) l) (NonAssocRing.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6))))) => S) l) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6))))) => S) l) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6))))) => S) l) _inst_6)))))) -> (HasSubset.Subset.{u1} (Set.{u1} S) (Set.instHasSubsetSet.{u1} S) s (SetLike.coe.{u1, u1} (Subalgebra.{u2, u1} R S _inst_1 (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) _inst_7) S (Subalgebra.instSetLikeSubalgebra.{u2, u1} R S _inst_1 (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) _inst_7) S')) -> (forall (i : Set.Elem.{u1} S s), Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : Set.Elem.{u1} S s) => S) i) (Subalgebra.{u2, u1} R S _inst_1 (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) _inst_7) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R S _inst_1 (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) _inst_7) S (Subalgebra.instSetLikeSubalgebra.{u2, u1} R S _inst_1 (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) _inst_7)) (FunLike.coe.{succ u1, succ u1, succ u1} (Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (CommMonoidWithZero.toZero.{u1} S (CommSemiring.toCommMonoidWithZero.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)))) (Set.Elem.{u1} S s) (fun (_x : Set.Elem.{u1} S s) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : Set.Elem.{u1} S s) => S) _x) (Finsupp.funLike.{u1, u1} (Set.Elem.{u1} S s) S (CommMonoidWithZero.toZero.{u1} S (CommSemiring.toCommMonoidWithZero.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)))) l i) S') -> (forall (x : S), (forall (r : Set.Elem.{u1} S s), Exists.{1} Nat (fun (n : Nat) => Membership.mem.{u1, u1} S (Subalgebra.{u2, u1} R S _inst_1 (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) _inst_7) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R S _inst_1 (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) _inst_7) S (Subalgebra.instSetLikeSubalgebra.{u2, u1} R S _inst_1 (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) _inst_7)) (HSMul.hSMul.{u1, u1, u1} S S S (instHSMul.{u1, u1} S S (Algebra.toSMul.{u1, u1} S S (CommRing.toCommSemiring.{u1} S _inst_6) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) (Algebra.id.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)))) (HPow.hPow.{u1, 0, u1} S Nat S (instHPow.{u1, 0} S Nat (Monoid.Pow.{u1} S (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)))))) (Subtype.val.{succ u1} S (fun (x : S) => Membership.mem.{u1, u1} S (Set.{u1} S) (Set.instMembershipSet.{u1} S) x s) r) n) x) S')) -> (Membership.mem.{u1, u1} S (Subalgebra.{u2, u1} R S _inst_1 (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) _inst_7) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R S _inst_1 (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) _inst_7) S (Subalgebra.instSetLikeSubalgebra.{u2, u1} R S _inst_1 (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) _inst_7)) x S'))
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {S : Type.{u1}} [_inst_6 : CommRing.{u1} S] [_inst_7 : Algebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6))] (S' : Subalgebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)) _inst_7) (s : Set.{u1} S) (l : Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (CommMonoidWithZero.toZero.{u1} S (CommSemiring.toCommMonoidWithZero.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)))), (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6))))) => S) l) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} S S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)))) (Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6))))) S (Finsupp.addCommMonoid.{u1, u1} (Set.Elem.{u1} S s) S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_6))))) (Finsupp.module.{u1, u1, u1} (Set.Elem.{u1} S s) S S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6))))) (Semiring.toModule.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)))) (Semiring.toModule.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)))) (Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6))))) (fun (_x : Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6))))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6))))) => S) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} S S (Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6))))) S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)) (Finsupp.addCommMonoid.{u1, u1} (Set.Elem.{u1} S s) S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_6))))) (Finsupp.module.{u1, u1, u1} (Set.Elem.{u1} S s) S S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6))))) (Semiring.toModule.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)))) (Semiring.toModule.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6))) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6))))) (Finsupp.total.{u1, u1, u1} (Set.Elem.{u1} S s) S S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_6))))) (Semiring.toModule.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6))) (Subtype.val.{succ u1} S (fun (x : S) => Membership.mem.{u1, u1} S (Set.{u1} S) (Set.instMembershipSet.{u1} S) x s))) l) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6))))) => S) l) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6))))) => S) l) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6))))) => S) l) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6))))) => S) l) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6))))) => S) l) _inst_6)))))) -> (HasSubset.Subset.{u1} (Set.{u1} S) (Set.instHasSubsetSet.{u1} S) s (SetLike.coe.{u1, u1} (Subalgebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)) _inst_7) S (Subalgebra.instSetLikeSubalgebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)) _inst_7) S')) -> (forall (i : Set.Elem.{u1} S s), Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : Set.Elem.{u1} S s) => S) i) (Subalgebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)) _inst_7) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)) _inst_7) S (Subalgebra.instSetLikeSubalgebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)) _inst_7)) (FunLike.coe.{succ u1, succ u1, succ u1} (Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (CommMonoidWithZero.toZero.{u1} S (CommSemiring.toCommMonoidWithZero.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)))) (Set.Elem.{u1} S s) (fun (_x : Set.Elem.{u1} S s) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : Set.Elem.{u1} S s) => S) _x) (Finsupp.funLike.{u1, u1} (Set.Elem.{u1} S s) S (CommMonoidWithZero.toZero.{u1} S (CommSemiring.toCommMonoidWithZero.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)))) l i) S') -> (forall (x : S), (forall (r : Set.Elem.{u1} S s), Exists.{1} Nat (fun (n : Nat) => Membership.mem.{u1, u1} S (Subalgebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)) _inst_7) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)) _inst_7) S (Subalgebra.instSetLikeSubalgebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)) _inst_7)) (HSMul.hSMul.{u1, u1, u1} S S S (instHSMul.{u1, u1} S S (Algebra.toSMul.{u1, u1} S S (CommRing.toCommSemiring.{u1} S _inst_6) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)) (Algebra.id.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)))) (HPow.hPow.{u1, 0, u1} S Nat S (instHPow.{u1, 0} S Nat (Monoid.Pow.{u1} S (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)))))) (Subtype.val.{succ u1} S (fun (x : S) => Membership.mem.{u1, u1} S (Set.{u1} S) (Set.instMembershipSet.{u1} S) x s) r) n) x) S')) -> (Membership.mem.{u1, u1} S (Subalgebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)) _inst_7) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)) _inst_7) S (Subalgebra.instSetLikeSubalgebra.{u2, u1} R S _inst_1 (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)) _inst_7)) x S'))
 Case conversion may be inaccurate. Consider using '#align subalgebra.mem_of_span_eq_top_of_smul_pow_mem Subalgebra.mem_of_span_eq_top_of_smul_pow_memₓ'. -/
 theorem mem_of_span_eq_top_of_smul_pow_mem {S : Type _} [CommRing S] [Algebra R S]
     (S' : Subalgebra R S) (s : Set S) (l : s →₀ S) (hs : Finsupp.total s S S coe l = 1)

bump to nightly-2023-05-07-10

mathlib commit https://github.com/leanprover-community/mathlib/commit/4c8f86bdbe06f92960d0eb314da8ca64a9d33bca

11ec3a10

Diff

@@ -1101,7 +1101,7 @@ theorem coe_toSubalgebra (p : Submodule R A) (h_one h_mul) :
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (s : Set.{u2} A) (h0 : Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) (OfNat.ofNat.{u2} A 0 (OfNat.mk.{u2} A 0 (Zero.zero.{u2} A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))))))) s) (hadd : forall {a : A} {b : A}, (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) a s) -> (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) b s) -> (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (AddZeroClass.toHasAdd.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))))) a b) s)) (hsmul : forall (c : R) {x : A}, (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) x s) -> (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) (SMul.smul.{u1, u2} R A (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) c x) s)) (h1 : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (OfNat.ofNat.{u2} A 1 (OfNat.mk.{u2} A 1 (One.one.{u2} A (AddMonoidWithOne.toOne.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))))) (Submodule.mk.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) s hadd h0 hsmul)) (hmul : forall (x : A) (y : A), (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (Submodule.mk.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) s hadd h0 hsmul)) -> (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) y (Submodule.mk.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) s hadd h0 hsmul)) -> (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y) (Submodule.mk.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) s hadd h0 hsmul))), Eq.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (Submodule.mk.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) s hadd h0 hsmul) h1 hmul) (Subalgebra.mk.{u1, u2} R A _inst_1 _inst_2 _inst_3 s hmul h1 hadd h0 (fun (r : R) => Eq.mpr.{0} (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) s) (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) (SMul.smul.{u1, u2} R A (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) r (OfNat.ofNat.{u2} A 1 (OfNat.mk.{u2} A 1 (One.one.{u2} A (AddMonoidWithOne.toOne.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))))) s) (id_tag Tactic.IdTag.rw (Eq.{1} Prop (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) s) (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) (SMul.smul.{u1, u2} R A (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) r (OfNat.ofNat.{u2} A 1 (OfNat.mk.{u2} A 1 (One.one.{u2} A (AddMonoidWithOne.toOne.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))))) s)) (Eq.ndrec.{0, succ u2} A (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) (fun (_a : A) => Eq.{1} Prop (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) s) (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) _a s)) (rfl.{1} Prop (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) s)) (SMul.smul.{u1, u2} R A (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) r (OfNat.ofNat.{u2} A 1 (OfNat.mk.{u2} A 1 (One.one.{u2} A (AddMonoidWithOne.toOne.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))))) (Algebra.algebraMap_eq_smul_one.{u1, u2} R A _inst_1 _inst_2 _inst_3 r))) (hsmul r (OfNat.ofNat.{u2} A 1 (OfNat.mk.{u2} A 1 (One.one.{u2} A (AddMonoidWithOne.toOne.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))))) h1)))
 but is expected to have type
-  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u1} A] [_inst_3 : Algebra.{u2, u1} R A _inst_1 _inst_2] (s : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (h0 : Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) (OfNat.ofNat.{u1} A 1 (One.toOfNat1.{u1} A (Semiring.toOne.{u1} A _inst_2))) s) (hadd : forall (a : A) (b : A), (Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) a s) -> (Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) b s) -> (Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u1, u1, u1} A A A (instHMul.{u1} A (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) a b) s)), Eq.{succ u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 s h0 hadd) (Subalgebra.mk.{u2, u1} R A _inst_1 _inst_2 _inst_3 (Subsemiring.mk.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Submonoid.mk.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemigroup.mk.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) s) hadd) h0) (fun {a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6428 : A} {b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6429 : A} => Submodule.add_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6428 b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6429) (Submodule.zero_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s)) (fun (r : R) => Eq.mpr.{0} (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) (Set.{u1} A) (Set.instMembershipSet.{u1} A) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2) (RingHom.instRingHomClassRingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2))))) (algebraMap.{u2, u1} R A _inst_1 _inst_2 _inst_3) r) (Subsemigroup.carrier.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (Submonoid.toSubsemigroup.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemiring.toSubmonoid.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Subsemiring.mk.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Submonoid.mk.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemigroup.mk.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) s) hadd) h0) (fun {a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6428 : A} {b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6429 : A} => Submodule.add_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6428 b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6429) (Submodule.zero_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s)))))) (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) (Set.{u1} A) (Set.instMembershipSet.{u1} A) (HSMul.hSMul.{u2, u1, u1} R A A (instHSMul.{u2, u1} R A (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_2 _inst_3)) r (OfNat.ofNat.{u1} A 1 (One.toOfNat1.{u1} A (Semiring.toOne.{u1} A _inst_2)))) (Subsemigroup.carrier.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (Submonoid.toSubsemigroup.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemiring.toSubmonoid.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Subsemiring.mk.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Submonoid.mk.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemigroup.mk.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) s) hadd) h0) (fun {a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6428 : A} {b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6429 : A} => Submodule.add_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6428 b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6429) (Submodule.zero_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6428 b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6429) (Submodule.zero_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s))))))) (Eq.refl.{1} Prop (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) (Set.{u1} A) (Set.instMembershipSet.{u1} A) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) 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u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2) (RingHom.instRingHomClassRingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2))))) (algebraMap.{u2, u1} R A _inst_1 _inst_2 _inst_3) r) (Subsemigroup.carrier.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (Submonoid.toSubsemigroup.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemiring.toSubmonoid.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Subsemiring.mk.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Submonoid.mk.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemigroup.mk.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) s) hadd) h0) (fun {a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6428 : A} {b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6429 : A} => Submodule.add_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6428 b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6429) (Submodule.zero_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s))))))) (HSMul.hSMul.{u2, u1, u1} R A A (instHSMul.{u2, u1} R A (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_2 _inst_3)) r (OfNat.ofNat.{u1} A 1 (One.toOfNat1.{u1} A (Semiring.toOne.{u1} A _inst_2)))) (Algebra.algebraMap_eq_smul_one.{u2, u1} R A _inst_1 _inst_2 _inst_3 r))) (Submodule.smul_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s (OfNat.ofNat.{u1} A 1 (One.toOfNat1.{u1} A (Semiring.toOne.{u1} A _inst_2))) r h0)))
+  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u1} A] [_inst_3 : Algebra.{u2, u1} R A _inst_1 _inst_2] (s : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (h0 : Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) (OfNat.ofNat.{u1} A 1 (One.toOfNat1.{u1} A (Semiring.toOne.{u1} A _inst_2))) s) (hadd : forall (a : A) (b : A), (Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) a s) -> (Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) b s) -> (Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u1, u1, u1} A A A (instHMul.{u1} A (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) a b) s)), Eq.{succ u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 s h0 hadd) (Subalgebra.mk.{u2, u1} R A _inst_1 _inst_2 _inst_3 (Subsemiring.mk.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Submonoid.mk.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemigroup.mk.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) s) hadd) h0) (fun {a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6483 : A} {b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6484 : A} => Submodule.add_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6483 b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6484) (Submodule.zero_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s)) (fun (r : R) => Eq.mpr.{0} (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) (Set.{u1} A) (Set.instMembershipSet.{u1} A) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2) (RingHom.instRingHomClassRingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2))))) (algebraMap.{u2, u1} R A _inst_1 _inst_2 _inst_3) r) (Subsemigroup.carrier.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (Submonoid.toSubsemigroup.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemiring.toSubmonoid.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Subsemiring.mk.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Submonoid.mk.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemigroup.mk.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) s) hadd) h0) (fun {a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6483 : A} {b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6484 : A} => Submodule.add_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6483 b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6484) (Submodule.zero_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s)))))) (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) (Set.{u1} A) (Set.instMembershipSet.{u1} A) (HSMul.hSMul.{u2, u1, u1} R A A (instHSMul.{u2, u1} R A (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_2 _inst_3)) r (OfNat.ofNat.{u1} A 1 (One.toOfNat1.{u1} A (Semiring.toOne.{u1} A _inst_2)))) (Subsemigroup.carrier.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (Submonoid.toSubsemigroup.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemiring.toSubmonoid.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Subsemiring.mk.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Submonoid.mk.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemigroup.mk.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) 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_inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) s) hadd) h0) (fun {a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6483 : A} {b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6484 : A} => Submodule.add_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6483 b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6484) (Submodule.zero_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s)))))) (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) (Set.{u1} A) (Set.instMembershipSet.{u1} A) _a (Subsemigroup.carrier.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (Submonoid.toSubsemigroup.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemiring.toSubmonoid.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Subsemiring.mk.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Submonoid.mk.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemigroup.mk.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) s) hadd) h0) (fun {a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6483 : A} {b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6484 : A} => Submodule.add_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6483 b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6484) (Submodule.zero_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s))))))) (Eq.refl.{1} Prop (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) (Set.{u1} A) (Set.instMembershipSet.{u1} A) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2) (RingHom.instRingHomClassRingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2))))) (algebraMap.{u2, u1} R A _inst_1 _inst_2 _inst_3) r) (Subsemigroup.carrier.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (Submonoid.toSubsemigroup.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemiring.toSubmonoid.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Subsemiring.mk.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Submonoid.mk.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemigroup.mk.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) s) hadd) h0) (fun {a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6483 : A} {b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6484 : A} => Submodule.add_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6483 b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6484) (Submodule.zero_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s))))))) (HSMul.hSMul.{u2, u1, u1} R A A (instHSMul.{u2, u1} R A (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_2 _inst_3)) r (OfNat.ofNat.{u1} A 1 (One.toOfNat1.{u1} A (Semiring.toOne.{u1} A _inst_2)))) (Algebra.algebraMap_eq_smul_one.{u2, u1} R A _inst_1 _inst_2 _inst_3 r))) (Submodule.smul_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s (OfNat.ofNat.{u1} A 1 (One.toOfNat1.{u1} A (Semiring.toOne.{u1} A _inst_2))) r h0)))
 Case conversion may be inaccurate. Consider using '#align submodule.to_subalgebra_mk Submodule.toSubalgebra_mkₓ'. -/
 @[simp]
 theorem toSubalgebra_mk (s : Set A) (h0 hadd hsmul h1 hmul) :
@@ -2169,7 +2169,7 @@ variable {ι : Type _}
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {ι : Type.{u3}} [_inst_6 : Nonempty.{succ u3} ι] {S : ι -> (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)}, (Directed.{u2, succ u3} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) ι (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) S) -> (Eq.{succ u2} (Set.{u2} A) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (supᵢ.{u2, succ u3} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))) ι S)) (Set.unionᵢ.{u2, succ u3} A ι (fun (i : ι) => (fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (S i))))
 but is expected to have type
-  forall {R : Type.{u2}} {A : Type.{u3}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u3} A] [_inst_3 : Algebra.{u2, u3} R A _inst_1 _inst_2] {ι : Type.{u1}} [_inst_6 : Nonempty.{succ u1} ι] {S : ι -> (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)}, (Directed.{u3, succ u1} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) ι (fun (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.12698 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.12700 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) => LE.le.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3))))) x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.12698 x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.12700) S) -> (Eq.{succ u3} (Set.{u3} A) (SetLike.coe.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (supᵢ.{u3, succ u1} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3))) ι S)) (Set.unionᵢ.{u3, succ u1} A ι (fun (i : ι) => SetLike.coe.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (S i))))
+  forall {R : Type.{u2}} {A : Type.{u3}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u3} A] [_inst_3 : Algebra.{u2, u3} R A _inst_1 _inst_2] {ι : Type.{u1}} [_inst_6 : Nonempty.{succ u1} ι] {S : ι -> (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)}, (Directed.{u3, succ u1} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) ι (fun (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.12753 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.12755 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) => LE.le.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3))))) x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.12753 x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.12755) S) -> (Eq.{succ u3} (Set.{u3} A) (SetLike.coe.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (supᵢ.{u3, succ u1} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3))) ι S)) (Set.unionᵢ.{u3, succ u1} A ι (fun (i : ι) => SetLike.coe.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (S i))))
 Case conversion may be inaccurate. Consider using '#align subalgebra.coe_supr_of_directed Subalgebra.coe_supᵢ_of_directedₓ'. -/
 theorem coe_supᵢ_of_directed [Nonempty ι] {S : ι → Subalgebra R A} (dir : Directed (· ≤ ·) S) :
     ↑(supᵢ S) = ⋃ i, (S i : Set A) :=
@@ -2198,7 +2198,7 @@ theorem coe_supᵢ_of_directed [Nonempty ι] {S : ι → Subalgebra R A} (dir :
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {ι : Type.{u4}} [_inst_6 : Nonempty.{succ u4} ι] (K : ι -> (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)), (Directed.{u2, succ u4} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) ι (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) K) -> (forall (f : forall (i : ι), AlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K i)) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5), (forall (i : ι) (j : ι) (h : LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (K i) (K j)), Eq.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K i)) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) (f i) (AlgHom.comp.{u1, u2, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K i)) (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K j)) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K j)) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K j)) _inst_5 (f j) (Subalgebra.inclusion.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i) (K j) h))) -> (forall (T : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), (Eq.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) T (supᵢ.{u2, succ u4} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))) ι K)) -> (AlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) _inst_5)))
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {ι : Type.{u4}} [_inst_6 : Nonempty.{succ u4} ι] (K : ι -> (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)), (Directed.{u2, succ u4} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) ι (fun (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13081 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13083 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13081 x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13083) K) -> (forall (f : forall (i : ι), AlgHom.{u1, u2, u3} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5), (forall (i : ι) (j : ι) (h : LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (K i) (K j)), Eq.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) (f i) (AlgHom.comp.{u1, u2, u2, u3} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x (K j))) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K j)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K j)) _inst_5 (f j) (Subalgebra.inclusion.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i) (K j) h))) -> (forall (T : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), (Eq.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) T (supᵢ.{u2, succ u4} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))) ι K)) -> (AlgHom.{u1, u2, u3} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T)) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) _inst_5)))
+  forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {ι : Type.{u4}} [_inst_6 : Nonempty.{succ u4} ι] (K : ι -> (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)), (Directed.{u2, succ u4} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) ι (fun (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13136 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13138 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13136 x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13138) K) -> (forall (f : forall (i : ι), AlgHom.{u1, u2, u3} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5), (forall (i : ι) (j : ι) (h : LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (K i) (K j)), Eq.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) (f i) (AlgHom.comp.{u1, u2, u2, u3} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x (K j))) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K j)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K j)) _inst_5 (f j) (Subalgebra.inclusion.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i) (K j) h))) -> (forall (T : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), (Eq.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) T (supᵢ.{u2, succ u4} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))) ι K)) -> (AlgHom.{u1, u2, u3} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T)) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) _inst_5)))
 Case conversion may be inaccurate. Consider using '#align subalgebra.supr_lift Subalgebra.supᵢLiftₓ'. -/
 /-- Define an algebra homomorphism on a directed supremum of subalgebras by defining
 it on each subalgebra, and proving that it agrees on the intersection of subalgebras. -/
@@ -2235,7 +2235,7 @@ variable [Nonempty ι] {K : ι → Subalgebra R A} {dir : Directed (· ≤ ·) K
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {ι : Type.{u4}} [_inst_6 : Nonempty.{succ u4} ι] {K : ι -> (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {dir : Directed.{u2, succ u4} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) ι (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) K} {f : forall (i : ι), AlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K i)) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5} {hf : forall (i : ι) (j : ι) (h : LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (K i) (K j)), Eq.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, 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 but is expected to have type
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+  forall {R : Type.{u2}} {A : Type.{u3}} {B : Type.{u4}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u3} A] [_inst_3 : Algebra.{u2, u3} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u4} B] [_inst_5 : Algebra.{u2, u4} R B _inst_1 _inst_4] {ι : Type.{u1}} [_inst_6 : Nonempty.{succ u1} ι] {K : ι -> (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)} {dir : Directed.{u3, succ u1} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) ι (fun (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13724 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13726 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) => LE.le.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) 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(Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)) (Module.toDistribMulAction.{u2, u3} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i))))) (Algebra.toModule.{u2, u3} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)))) (Module.toDistribMulAction.{u2, u4} R B (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u2, u4} R B _inst_1 _inst_4 _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u3, u4, max u3 u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5 (AlgHom.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) (AlgHom.algHomClass.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5))))) (f i) x)
 Case conversion may be inaccurate. Consider using '#align subalgebra.supr_lift_inclusion Subalgebra.supᵢLift_inclusionₓ'. -/
 @[simp]
 theorem supᵢLift_inclusion {i : ι} (x : K i) (h : K i ≤ T) :
@@ -2247,7 +2247,7 @@ theorem supᵢLift_inclusion {i : ι} (x : K i) (h : K i ≤ T) :
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {ι : Type.{u4}} [_inst_6 : Nonempty.{succ u4} ι] {K : ι -> (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {dir : Directed.{u2, succ u4} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) ι (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) K} {f : forall (i : ι), AlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K i)) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5} {hf : forall (i : ι) (j : ι) (h : LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (K i) (K j)), Eq.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K i)) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) (f i) (AlgHom.comp.{u1, u2, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K i)) (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K j)) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K j)) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K j)) _inst_5 (f j) (Subalgebra.inclusion.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i) (K j) h))} {T : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3} {hT : Eq.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) T (supᵢ.{u2, succ u4} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))) ι K)} {i : ι} (h : LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (K i) T), Eq.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K i)) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) (AlgHom.comp.{u1, u2, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K i)) (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) _inst_5 (Subalgebra.supᵢLift.{u1, u2, u3, u4} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 ι _inst_6 K dir f hf T hT) (Subalgebra.inclusion.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i) T h)) (f i)
 but is expected to have type
-  forall {R : Type.{u2}} {A : Type.{u3}} {B : Type.{u4}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u3} A] [_inst_3 : Algebra.{u2, u3} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u4} B] [_inst_5 : Algebra.{u2, u4} R B _inst_1 _inst_4] {ι : Type.{u1}} [_inst_6 : Nonempty.{succ u1} ι] {K : ι -> (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)} {dir : Directed.{u3, succ u1} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) ι (fun (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13824 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13826 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) => LE.le.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3))))) x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13824 x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13826) K} {f : forall (i : ι), AlgHom.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5} {hf : forall (i : ι) (j : ι) (h : LE.le.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3))))) (K i) (K j)), Eq.{max (succ u3) (succ u4)} (AlgHom.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) (f i) (AlgHom.comp.{u2, u3, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K j))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K j)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K j)) _inst_5 (f j) (Subalgebra.inclusion.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i) (K j) h))} {T : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3} {hT : Eq.{succ u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) T (supᵢ.{u3, succ u1} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3))) ι K)} {i : ι} (h : LE.le.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3))))) (K i) T), Eq.{max (succ u3) (succ u4)} (AlgHom.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) (AlgHom.comp.{u2, u3, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x T)) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 T) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 T) _inst_5 (Subalgebra.supᵢLift.{u2, u3, u4, u1} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 ι _inst_6 K dir f hf T hT) (Subalgebra.inclusion.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i) T h)) (f i)
+  forall {R : Type.{u2}} {A : Type.{u3}} {B : Type.{u4}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u3} A] [_inst_3 : Algebra.{u2, u3} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u4} B] [_inst_5 : Algebra.{u2, u4} R B _inst_1 _inst_4] {ι : Type.{u1}} [_inst_6 : Nonempty.{succ u1} ι] {K : ι -> (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)} {dir : Directed.{u3, succ u1} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) ι (fun (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13879 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13881 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) => LE.le.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3))))) x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13879 x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13881) K} {f : forall (i : ι), AlgHom.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5} {hf : forall (i : ι) (j : ι) (h : LE.le.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3))))) (K i) (K j)), Eq.{max (succ u3) (succ u4)} (AlgHom.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) (f i) (AlgHom.comp.{u2, u3, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K j))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K j)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K j)) _inst_5 (f j) (Subalgebra.inclusion.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i) (K j) h))} {T : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3} {hT : Eq.{succ u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) T (supᵢ.{u3, succ u1} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3))) ι K)} {i : ι} (h : LE.le.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3))))) (K i) T), Eq.{max (succ u3) (succ u4)} (AlgHom.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) (AlgHom.comp.{u2, u3, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x T)) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 T) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 T) _inst_5 (Subalgebra.supᵢLift.{u2, u3, u4, u1} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 ι _inst_6 K dir f hf T hT) (Subalgebra.inclusion.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i) T h)) (f i)
 Case conversion may be inaccurate. Consider using '#align subalgebra.supr_lift_comp_inclusion Subalgebra.supᵢLift_comp_inclusionₓ'. -/
 @[simp]
 theorem supᵢLift_comp_inclusion {i : ι} (h : K i ≤ T) :
@@ -2258,7 +2258,7 @@ theorem supᵢLift_comp_inclusion {i : ι} (h : K i ≤ T) :
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {ι : Type.{u4}} [_inst_6 : Nonempty.{succ u4} ι] {K : ι -> (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {dir : Directed.{u2, succ u4} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) ι (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) K} {f : forall (i : ι), AlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K i)) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5} {hf : forall (i : ι) (j : ι) (h : LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (K i) (K j)), Eq.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K i)) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) (f i) (AlgHom.comp.{u1, u2, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K i)) (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K j)) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 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_inst_4))))) (DistribSMul.toSMulZeroClass.{u2, u4} R B (AddMonoid.toAddZeroClass.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))))) (DistribMulAction.toDistribSMul.{u2, u4} R B (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))) (Module.toDistribMulAction.{u2, u4} R B (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u2, u4} R B _inst_1 _inst_4 _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u4, u2, u3, u4} (AlgHom.{u2, u3, u4} R 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(Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)))))) (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))) (Module.toDistribMulAction.{u2, u3} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i))))) (Algebra.toModule.{u2, u3} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) 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u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)) (Module.toDistribMulAction.{u2, u3} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i))))) (Algebra.toModule.{u2, u3} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)))) (Module.toDistribMulAction.{u2, u4} R B (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u2, u4} R B _inst_1 _inst_4 _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u3, u4, max u3 u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5 (AlgHom.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) (AlgHom.algHomClass.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5))))) (f i) x)
+  forall {R : Type.{u2}} {A : Type.{u3}} {B : Type.{u4}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u3} A] [_inst_3 : Algebra.{u2, u3} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u4} B] [_inst_5 : Algebra.{u2, u4} R B _inst_1 _inst_4] {ι : Type.{u1}} [_inst_6 : Nonempty.{succ u1} ι] {K : ι -> (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)} {dir : Directed.{u3, succ u1} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) ι (fun (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.14006 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.14008 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) => LE.le.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3))))) x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.14006 x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.14008) K} {f : forall (i : ι), AlgHom.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5} {hf : forall (i : ι) (j : ι) (h : LE.le.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 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A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5 (AlgHom.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) (AlgHom.algHomClass.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5))))) (f i) x)
 Case conversion may be inaccurate. Consider using '#align subalgebra.supr_lift_mk Subalgebra.supᵢLift_mkₓ'. -/
 @[simp]
 theorem supᵢLift_mk {i : ι} (x : K i) (hx : (x : A) ∈ T) :
@@ -2269,7 +2269,7 @@ theorem supᵢLift_mk {i : ι} (x : K i) (hx : (x : A) ∈ T) :
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {ι : Type.{u4}} [_inst_6 : Nonempty.{succ u4} ι] {K : ι -> (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {dir : Directed.{u2, succ u4} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) ι (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) K} {f : forall (i : ι), AlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K i)) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5} {hf : forall (i : ι) (j : ι) (h : LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (K i) (K j)), Eq.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, 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_inst_2 _inst_3 (K j)) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K j)) _inst_5 (f j) (Subalgebra.inclusion.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i) (K j) h))} {T : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3} {hT : Eq.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) T (supᵢ.{u2, succ u4} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))) ι K)} {i : ι} (x : coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T) (hx : Membership.Mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T) A (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T) A (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T) A (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T) A (coeSubtype.{succ u2} A (fun (x : A) => Membership.Mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T))))) x) (K i)), Eq.{succ u3} B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) _inst_5) (fun (_x : AlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) _inst_5) => (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T) -> B) ([anonymous].{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) _inst_5) (Subalgebra.supᵢLift.{u1, u2, u3, u4} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 ι _inst_6 K dir f hf T hT) x) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K i)) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) (fun (_x : AlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K i)) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) => (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K i)) -> B) ([anonymous].{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K i)) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) (f i) (Subtype.mk.{succ u2} A (fun (x : A) => Membership.Mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x (K i)) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T) A (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T) A (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T) A (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T) A (coeSubtype.{succ u2} A (fun (x : A) => Membership.Mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T))))) x) hx))
 but is expected to have type
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A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i))))) (Algebra.toModule.{u2, u3} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, 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_inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)) (Module.toDistribMulAction.{u2, u3} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i))))) (Algebra.toModule.{u2, u3} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A 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_inst_3 (K i)) _inst_5) (AlgHom.algHomClass.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5))))) (f i) (Subtype.mk.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i)) (Subtype.val.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Set.{u3} A) (Set.instMembershipSet.{u3} A) x (SetLike.coe.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) T)) x) hx))
 Case conversion may be inaccurate. Consider using '#align subalgebra.supr_lift_of_mem Subalgebra.supᵢLift_of_memₓ'. -/
 theorem supᵢLift_of_mem {i : ι} (x : T) (hx : (x : A) ∈ K i) :
     supᵢLift K dir f hf T hT x = f i ⟨x, hx⟩ := by subst hT <;> exact Set.unionᵢLift_of_mem x hx

bump to nightly-2023-05-02-02

mathlib commit https://github.com/leanprover-community/mathlib/commit/39478763114722f0ec7613cb2f3f7701f9b86c8d

e5023853

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau, Yury Kudryashov
 
 ! This file was ported from Lean 3 source module algebra.algebra.subalgebra.basic
-! leanprover-community/mathlib commit 69c6a5a12d8a2b159f20933e60115a4f2de62b58
+! leanprover-community/mathlib commit 8130e5155d637db35907c272de9aec9dc851c03a
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -209,6 +209,8 @@ theorem smul_mem {x : A} (hx : x ∈ S) (r : R) : r • x ∈ S :=
   (Algebra.smul_def r x).symm ▸ mul_mem (S.algebraMap_mem r) hx
 #align subalgebra.smul_mem Subalgebra.smul_mem
 
+instance : SMulMemClass (Subalgebra R A) R A where smul_mem S r x hx := smul_mem S hx r
+
 /- warning: subalgebra.one_mem -> Subalgebra.one_mem is a dubious translation:
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), Membership.Mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OfNat.ofNat.{u2} A 1 (OfNat.mk.{u2} A 1 (One.one.{u2} A (AddMonoidWithOne.toOne.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))))) S
@@ -706,7 +708,7 @@ end
 
 /- warning: subalgebra.no_zero_smul_divisors_bot -> Subalgebra.noZeroSMulDivisors_bot is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) [_inst_8 : NoZeroSMulDivisors.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u2} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A 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(AddSubmonoidClass.to_zeroMemClass.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SubsemiringClass.to_addSubmonoidClass.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Semiring.toNonAssocSemiring.{u2} A _inst_2) (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Subalgebra.subsemiringClass.{u1, u2} R A _inst_1 _inst_2 _inst_3))) S) (SMulZeroClass.toHasSmul.{u1, u2} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) (AddZeroClass.toHasZero.{u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, 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_inst_2 _inst_3)) S) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) (Semiring.toNonAssocSemiring.{u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) (AddMonoid.toAddZeroClass.{u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) (AddCommMonoid.toAddMonoid.{u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) (Semiring.toNonAssocSemiring.{u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) (AddMonoid.toAddZeroClass.{u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) (AddCommMonoid.toAddMonoid.{u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) (Semiring.toNonAssocSemiring.{u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S))))))) (Module.toMulActionWithZero.{u1, u2} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) (Semiring.toNonAssocSemiring.{u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S)))) (Subalgebra.module.{u1, u2} R A _inst_1 _inst_2 _inst_3 S)))))
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) [_inst_8 : NoZeroSMulDivisors.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u2} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))], NoZeroSMulDivisors.{u1, u2} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (ZeroMemClass.zero.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (AddSubmonoidClass.to_zeroMemClass.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SubsemiringClass.to_addSubmonoidClass.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Semiring.toNonAssocSemiring.{u2} A _inst_2) (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Subalgebra.subsemiringClass.{u1, u2} R A _inst_1 _inst_2 _inst_3))) S) (SetLike.smul.{u1, u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) R A (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Subalgebra.smulMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3) S)
 but is expected to have type
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) [_inst_8 : NoZeroSMulDivisors.{u1, u2} R A (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3)], NoZeroSMulDivisors.{u1, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (ZeroMemClass.zero.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (AddSubmonoidClass.toZeroMemClass.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SubsemiringClass.toAddSubmonoidClass.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Semiring.toNonAssocSemiring.{u2} A _inst_2) (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Subalgebra.SubsemiringClass.{u1, u2} R A _inst_1 _inst_2 _inst_3))) S) (Algebra.toSMul.{u1, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S))
 Case conversion may be inaccurate. Consider using '#align subalgebra.no_zero_smul_divisors_bot Subalgebra.noZeroSMulDivisors_botₓ'. -/
@@ -2336,7 +2338,7 @@ instance isScalarTower_left [SMul α β] [SMul A α] [SMul A β] [IsScalarTower
 
 /- warning: subalgebra.is_scalar_tower_mid -> Subalgebra.isScalarTower_mid is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {S : Type.{u2}} {T : Type.{u3}} [_inst_6 : CommSemiring.{u1} R] [_inst_7 : Semiring.{u2} S] [_inst_8 : AddCommMonoid.{u3} T] [_inst_9 : Algebra.{u1, u2} R S _inst_6 _inst_7] [_inst_10 : Module.{u1, u3} R T (CommSemiring.toSemiring.{u1} R _inst_6) _inst_8] [_inst_11 : Module.{u2, u3} S T _inst_7 _inst_8] [_inst_12 : IsScalarTower.{u1, u2, u3} R S T (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_7)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_6))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_7)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_6)) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_7)))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_7))) (Algebra.toModule.{u1, u2} R S _inst_6 _inst_7 _inst_9))))) (SMulZeroClass.toHasSmul.{u2, u3} S T (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8))) (SMulWithZero.toSmulZeroClass.{u2, u3} S T (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_7)))) (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8))) (MulActionWithZero.toSMulWithZero.{u2, u3} S T (Semiring.toMonoidWithZero.{u2} S _inst_7) (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8))) (Module.toMulActionWithZero.{u2, u3} S T _inst_7 _inst_8 _inst_11)))) (SMulZeroClass.toHasSmul.{u1, u3} R T (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8))) (SMulWithZero.toSmulZeroClass.{u1, u3} R T (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_6))))) (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8))) (MulActionWithZero.toSMulWithZero.{u1, u3} R T (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_6)) (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8))) (Module.toMulActionWithZero.{u1, u3} R T (CommSemiring.toSemiring.{u1} R _inst_6) _inst_8 _inst_10))))] (S' : Subalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9), IsScalarTower.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9) S (Subalgebra.setLike.{u1, u2} R S _inst_6 _inst_7 _inst_9)) S') T (SMulZeroClass.toHasSmul.{u1, u2} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9) S (Subalgebra.setLike.{u1, u2} R S _inst_6 _inst_7 _inst_9)) S') (AddZeroClass.toHasZero.{u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9) S (Subalgebra.setLike.{u1, u2} R S _inst_6 _inst_7 _inst_9)) S') (AddMonoid.toAddZeroClass.{u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9) S (Subalgebra.setLike.{u1, u2} R S _inst_6 _inst_7 _inst_9)) S') (AddCommMonoid.toAddMonoid.{u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9) S (Subalgebra.setLike.{u1, u2} R S _inst_6 _inst_7 _inst_9)) S') (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9) S (Subalgebra.setLike.{u1, u2} R S _inst_6 _inst_7 _inst_9)) S') (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9) S (Subalgebra.setLike.{u1, u2} R S _inst_6 _inst_7 _inst_9)) S') (Semiring.toNonAssocSemiring.{u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9) S (Subalgebra.setLike.{u1, u2} R S _inst_6 _inst_7 _inst_9)) S') (Subalgebra.toSemiring.{u1, u2} R S _inst_6 _inst_7 _inst_9 S'))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9) S (Subalgebra.setLike.{u1, u2} R S _inst_6 _inst_7 _inst_9)) S') (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_6))))) (AddZeroClass.toHasZero.{u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9) S (Subalgebra.setLike.{u1, u2} R S _inst_6 _inst_7 _inst_9)) S') (AddMonoid.toAddZeroClass.{u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9) S (Subalgebra.setLike.{u1, u2} R S _inst_6 _inst_7 _inst_9)) S') (AddCommMonoid.toAddMonoid.{u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9) S (Subalgebra.setLike.{u1, u2} R S _inst_6 _inst_7 _inst_9)) S') (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9) S (Subalgebra.setLike.{u1, u2} R S _inst_6 _inst_7 _inst_9)) S') (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9) S (Subalgebra.setLike.{u1, u2} R S _inst_6 _inst_7 _inst_9)) S') (Semiring.toNonAssocSemiring.{u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9) S (Subalgebra.setLike.{u1, u2} R S _inst_6 _inst_7 _inst_9)) S') (Subalgebra.toSemiring.{u1, u2} R S _inst_6 _inst_7 _inst_9 S'))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9) S (Subalgebra.setLike.{u1, u2} R S _inst_6 _inst_7 _inst_9)) S') (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_6)) (AddZeroClass.toHasZero.{u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9) S (Subalgebra.setLike.{u1, u2} R S _inst_6 _inst_7 _inst_9)) S') (AddMonoid.toAddZeroClass.{u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9) S (Subalgebra.setLike.{u1, u2} R S _inst_6 _inst_7 _inst_9)) S') (AddCommMonoid.toAddMonoid.{u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9) S (Subalgebra.setLike.{u1, u2} R S _inst_6 _inst_7 _inst_9)) S') (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9) S (Subalgebra.setLike.{u1, u2} R S _inst_6 _inst_7 _inst_9)) S') (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9) S (Subalgebra.setLike.{u1, u2} R S _inst_6 _inst_7 _inst_9)) S') (Semiring.toNonAssocSemiring.{u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9) S (Subalgebra.setLike.{u1, u2} R S _inst_6 _inst_7 _inst_9)) S') (Subalgebra.toSemiring.{u1, u2} R S _inst_6 _inst_7 _inst_9 S'))))))) (Module.toMulActionWithZero.{u1, u2} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9) S (Subalgebra.setLike.{u1, u2} R S _inst_6 _inst_7 _inst_9)) S') (CommSemiring.toSemiring.{u1} R _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9) S (Subalgebra.setLike.{u1, u2} R S _inst_6 _inst_7 _inst_9)) S') (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9) S (Subalgebra.setLike.{u1, u2} R S _inst_6 _inst_7 _inst_9)) S') (Semiring.toNonAssocSemiring.{u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9) S (Subalgebra.setLike.{u1, u2} R S _inst_6 _inst_7 _inst_9)) S') (Subalgebra.toSemiring.{u1, u2} R S _inst_6 _inst_7 _inst_9 S')))) (Subalgebra.module.{u1, u2} R S _inst_6 _inst_7 _inst_9 S'))))) (Subalgebra.hasSmul.{u1, u2, u3} R S _inst_6 _inst_7 _inst_9 T (SMulZeroClass.toHasSmul.{u2, u3} S T (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8))) (SMulWithZero.toSmulZeroClass.{u2, u3} S T (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_7)))) (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8))) (MulActionWithZero.toSMulWithZero.{u2, u3} S T (Semiring.toMonoidWithZero.{u2} S _inst_7) (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8))) (Module.toMulActionWithZero.{u2, u3} S T _inst_7 _inst_8 _inst_11)))) S') (SMulZeroClass.toHasSmul.{u1, u3} R T (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8))) (SMulWithZero.toSmulZeroClass.{u1, u3} R T (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_6))))) (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8))) (MulActionWithZero.toSMulWithZero.{u1, u3} R T (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_6)) (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8))) (Module.toMulActionWithZero.{u1, u3} R T (CommSemiring.toSemiring.{u1} R _inst_6) _inst_8 _inst_10))))
+  forall {R : Type.{u1}} {S : Type.{u2}} {T : Type.{u3}} [_inst_6 : CommSemiring.{u1} R] [_inst_7 : Semiring.{u2} S] [_inst_8 : AddCommMonoid.{u3} T] [_inst_9 : Algebra.{u1, u2} R S _inst_6 _inst_7] [_inst_10 : Module.{u1, u3} R T (CommSemiring.toSemiring.{u1} R _inst_6) _inst_8] [_inst_11 : Module.{u2, u3} S T _inst_7 _inst_8] [_inst_12 : IsScalarTower.{u1, u2, u3} R S T (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_7)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_6))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_7)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_6)) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_7)))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_7))) (Algebra.toModule.{u1, u2} R S _inst_6 _inst_7 _inst_9))))) (SMulZeroClass.toHasSmul.{u2, u3} S T (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8))) (SMulWithZero.toSmulZeroClass.{u2, u3} S T (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_7)))) (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8))) (MulActionWithZero.toSMulWithZero.{u2, u3} S T (Semiring.toMonoidWithZero.{u2} S _inst_7) (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8))) (Module.toMulActionWithZero.{u2, u3} S T _inst_7 _inst_8 _inst_11)))) (SMulZeroClass.toHasSmul.{u1, u3} R T (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8))) (SMulWithZero.toSmulZeroClass.{u1, u3} R T (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_6))))) (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8))) (MulActionWithZero.toSMulWithZero.{u1, u3} R T (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_6)) (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8))) (Module.toMulActionWithZero.{u1, u3} R T (CommSemiring.toSemiring.{u1} R _inst_6) _inst_8 _inst_10))))] (S' : Subalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9), IsScalarTower.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9) S (Subalgebra.setLike.{u1, u2} R S _inst_6 _inst_7 _inst_9)) S') T (SetLike.smul.{u1, u2, u2} (Subalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9) R S (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_7)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_6))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_7)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_6)) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_7)))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_6) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_7))) (Algebra.toModule.{u1, u2} R S _inst_6 _inst_7 _inst_9))))) (Subalgebra.setLike.{u1, u2} R S _inst_6 _inst_7 _inst_9) (Subalgebra.smulMemClass.{u1, u2} R S _inst_6 _inst_7 _inst_9) S') (Subalgebra.hasSmul.{u1, u2, u3} R S _inst_6 _inst_7 _inst_9 T (SMulZeroClass.toHasSmul.{u2, u3} S T (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8))) (SMulWithZero.toSmulZeroClass.{u2, u3} S T (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_7)))) (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8))) (MulActionWithZero.toSMulWithZero.{u2, u3} S T (Semiring.toMonoidWithZero.{u2} S _inst_7) (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8))) (Module.toMulActionWithZero.{u2, u3} S T _inst_7 _inst_8 _inst_11)))) S') (SMulZeroClass.toHasSmul.{u1, u3} R T (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8))) (SMulWithZero.toSmulZeroClass.{u1, u3} R T (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_6))))) (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8))) (MulActionWithZero.toSMulWithZero.{u1, u3} R T (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_6)) (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8))) (Module.toMulActionWithZero.{u1, u3} R T (CommSemiring.toSemiring.{u1} R _inst_6) _inst_8 _inst_10))))
 but is expected to have type
   forall {R : Type.{u1}} {S : Type.{u2}} {T : Type.{u3}} [_inst_6 : CommSemiring.{u1} R] [_inst_7 : Semiring.{u2} S] [_inst_8 : AddCommMonoid.{u3} T] [_inst_9 : Algebra.{u1, u2} R S _inst_6 _inst_7] [_inst_10 : Module.{u1, u3} R T (CommSemiring.toSemiring.{u1} R _inst_6) _inst_8] [_inst_11 : Module.{u2, u3} S T _inst_7 _inst_8] [_inst_12 : IsScalarTower.{u1, u2, u3} R S T (Algebra.toSMul.{u1, u2} R S _inst_6 _inst_7 _inst_9) (SMulZeroClass.toSMul.{u2, u3} S T (AddMonoid.toZero.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8)) (SMulWithZero.toSMulZeroClass.{u2, u3} S T (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_7)) (AddMonoid.toZero.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8)) (MulActionWithZero.toSMulWithZero.{u2, u3} S T (Semiring.toMonoidWithZero.{u2} S _inst_7) (AddMonoid.toZero.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8)) (Module.toMulActionWithZero.{u2, u3} S T _inst_7 _inst_8 _inst_11)))) (SMulZeroClass.toSMul.{u1, u3} R T (AddMonoid.toZero.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8)) (SMulWithZero.toSMulZeroClass.{u1, u3} R T (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_6)) (AddMonoid.toZero.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8)) (MulActionWithZero.toSMulWithZero.{u1, u3} R T (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_6)) (AddMonoid.toZero.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8)) (Module.toMulActionWithZero.{u1, u3} R T (CommSemiring.toSemiring.{u1} R _inst_6) _inst_8 _inst_10))))] (S' : Subalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9), IsScalarTower.{u1, u2, u3} R (Subtype.{succ u2} S (fun (x : S) => Membership.mem.{u2, u2} S (Subalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9) S (Subalgebra.instSetLikeSubalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9)) x S')) T (Algebra.toSMul.{u1, u2} R (Subtype.{succ u2} S (fun (x : S) => Membership.mem.{u2, u2} S (Subalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9) S (Subalgebra.instSetLikeSubalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9)) x S')) _inst_6 (Subalgebra.toSemiring.{u1, u2} R S _inst_6 _inst_7 _inst_9 S') (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R S _inst_6 _inst_7 _inst_9 S')) (Subalgebra.instSMulSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebra.{u1, u2, u3} R S _inst_6 _inst_7 _inst_9 T (SMulZeroClass.toSMul.{u2, u3} S T (AddMonoid.toZero.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8)) (SMulWithZero.toSMulZeroClass.{u2, u3} S T (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_7)) (AddMonoid.toZero.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8)) (MulActionWithZero.toSMulWithZero.{u2, u3} S T (Semiring.toMonoidWithZero.{u2} S _inst_7) (AddMonoid.toZero.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8)) (Module.toMulActionWithZero.{u2, u3} S T _inst_7 _inst_8 _inst_11)))) S') (SMulZeroClass.toSMul.{u1, u3} R T (AddMonoid.toZero.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8)) (SMulWithZero.toSMulZeroClass.{u1, u3} R T (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_6)) (AddMonoid.toZero.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8)) (MulActionWithZero.toSMulWithZero.{u1, u3} R T (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_6)) (AddMonoid.toZero.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8)) (Module.toMulActionWithZero.{u1, u3} R T (CommSemiring.toSemiring.{u1} R _inst_6) _inst_8 _inst_10))))
 Case conversion may be inaccurate. Consider using '#align subalgebra.is_scalar_tower_mid Subalgebra.isScalarTower_midₓ'. -/

bump to nightly-2023-04-27-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/9b2b58d6b14b895b2f375108e765cb47de71aebd

c8f7a684

Diff

@@ -2628,7 +2628,7 @@ theorem mem_of_finset_sum_eq_one_of_pow_smul_mem {S : Type _} [CommRing S] [Alge
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {S : Type.{u2}} [_inst_6 : CommRing.{u2} S] [_inst_7 : Algebra.{u1, u2} R S _inst_1 (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6))] (S' : Subalgebra.{u1, u2} R S _inst_1 (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_7) (s : Set.{u2} S) (l : Finsupp.{u2, u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} S) Type.{u2} (Set.hasCoeToSort.{u2} S) s) S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} S (NonAssocRing.toNonUnitalNonAssocRing.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_6))))))), (Eq.{succ u2} S (coeFn.{succ u2, succ u2} (LinearMap.{u2, u2, u2, u2} S S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)))) (Finsupp.{u2, u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} S) Type.{u2} (Set.hasCoeToSort.{u2} S) s) S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6))))))) S (Finsupp.addCommMonoid.{u2, u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} S) Type.{u2} (Set.hasCoeToSort.{u2} S) s) S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)))))) (AddCommGroup.toAddCommMonoid.{u2} S (NonUnitalNonAssocRing.toAddCommGroup.{u2} S (NonAssocRing.toNonUnitalNonAssocRing.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_6))))) (Finsupp.module.{u2, u2, u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} S) Type.{u2} (Set.hasCoeToSort.{u2} S) s) S S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6))))) (Semiring.toModule.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)))) (Semiring.toModule.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)))) (fun (_x : LinearMap.{u2, u2, u2, u2} S S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)))) (Finsupp.{u2, u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} S) Type.{u2} (Set.hasCoeToSort.{u2} S) s) S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6))))))) S (Finsupp.addCommMonoid.{u2, u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} S) Type.{u2} (Set.hasCoeToSort.{u2} S) s) S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)))))) (AddCommGroup.toAddCommMonoid.{u2} S (NonUnitalNonAssocRing.toAddCommGroup.{u2} S (NonAssocRing.toNonUnitalNonAssocRing.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_6))))) (Finsupp.module.{u2, u2, u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} S) Type.{u2} (Set.hasCoeToSort.{u2} S) s) S S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6))))) (Semiring.toModule.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)))) (Semiring.toModule.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)))) => (Finsupp.{u2, u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} S) Type.{u2} (Set.hasCoeToSort.{u2} S) s) S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6))))))) -> S) (LinearMap.hasCoeToFun.{u2, u2, u2, u2} S S (Finsupp.{u2, u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} S) Type.{u2} (Set.hasCoeToSort.{u2} S) s) S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6))))))) S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) (Finsupp.addCommMonoid.{u2, u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} S) Type.{u2} (Set.hasCoeToSort.{u2} S) s) S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)))))) (AddCommGroup.toAddCommMonoid.{u2} S (NonUnitalNonAssocRing.toAddCommGroup.{u2} S (NonAssocRing.toNonUnitalNonAssocRing.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_6))))) (Finsupp.module.{u2, u2, u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} S) Type.{u2} (Set.hasCoeToSort.{u2} S) s) S S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6))))) (Semiring.toModule.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)))) (Semiring.toModule.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6))) 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 but is expected to have type
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(Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6))))) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)))) (_private.Mathlib.RingTheory.Ideal.Operations.0.Ideal.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRing.{u1, u1} S S (CommRing.toCommSemiring.{u1} S _inst_6) _inst_6 (Algebra.id.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6))) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6))))) (Finsupp.total.{u1, u1, u1} (Set.Elem.{u1} S s) S S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_6))))) (_private.Mathlib.RingTheory.Ideal.Operations.0.Ideal.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRing.{u1, u1} S S (CommRing.toCommSemiring.{u1} S _inst_6) _inst_6 (Algebra.id.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6))) (Subtype.val.{succ u1} S (fun (x : S) => Membership.mem.{u1, u1} S (Set.{u1} S) (Set.instMembershipSet.{u1} S) x s))) l) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6))))) => S) l) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6))))) => S) l) (NonAssocRing.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6))))) => S) l) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6))))) => S) l) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6))))) => S) l) _inst_6)))))) -> (HasSubset.Subset.{u1} (Set.{u1} S) (Set.instHasSubsetSet.{u1} S) s (SetLike.coe.{u1, u1} (Subalgebra.{u2, u1} R S _inst_1 (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) _inst_7) S (Subalgebra.instSetLikeSubalgebra.{u2, u1} R S _inst_1 (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) _inst_7) S')) -> (forall (i : Set.Elem.{u1} S s), Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : Set.Elem.{u1} S s) => S) i) (Subalgebra.{u2, u1} R S _inst_1 (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) _inst_7) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R S _inst_1 (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) _inst_7) S (Subalgebra.instSetLikeSubalgebra.{u2, u1} R S _inst_1 (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) _inst_7)) (FunLike.coe.{succ u1, succ u1, succ u1} (Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (CommMonoidWithZero.toZero.{u1} S (CommSemiring.toCommMonoidWithZero.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)))) (Set.Elem.{u1} S s) (fun (_x : Set.Elem.{u1} S s) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : Set.Elem.{u1} S s) => S) _x) (Finsupp.funLike.{u1, u1} (Set.Elem.{u1} S s) S (CommMonoidWithZero.toZero.{u1} S (CommSemiring.toCommMonoidWithZero.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)))) l i) S') -> (forall (x : S), (forall (r : Set.Elem.{u1} S s), Exists.{1} Nat (fun (n : Nat) => Membership.mem.{u1, u1} S (Subalgebra.{u2, u1} R S _inst_1 (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) _inst_7) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R S _inst_1 (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) _inst_7) S (Subalgebra.instSetLikeSubalgebra.{u2, u1} R S _inst_1 (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) _inst_7)) (HSMul.hSMul.{u1, u1, u1} S S S (instHSMul.{u1, u1} S S (Algebra.toSMul.{u1, u1} S S (CommRing.toCommSemiring.{u1} S _inst_6) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) (Algebra.id.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)))) (HPow.hPow.{u1, 0, u1} S Nat S (instHPow.{u1, 0} S Nat (Monoid.Pow.{u1} S (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)))))) (Subtype.val.{succ u1} S (fun (x : S) => Membership.mem.{u1, u1} S (Set.{u1} S) (Set.instMembershipSet.{u1} S) x s) r) n) x) S')) -> (Membership.mem.{u1, u1} S (Subalgebra.{u2, u1} R S _inst_1 (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) _inst_7) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R S _inst_1 (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) _inst_7) S (Subalgebra.instSetLikeSubalgebra.{u2, u1} R S _inst_1 (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) _inst_7)) x S'))
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {S : Type.{u1}} [_inst_6 : CommRing.{u1} S] [_inst_7 : Algebra.{u2, u1} R S _inst_1 (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6))] (S' : Subalgebra.{u2, u1} R S _inst_1 (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) _inst_7) (s : Set.{u1} S) (l : Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (CommMonoidWithZero.toZero.{u1} S (CommSemiring.toCommMonoidWithZero.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)))), (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6))))) => S) l) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} S S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)))) (Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6))))) S (Finsupp.addCommMonoid.{u1, u1} (Set.Elem.{u1} S s) S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_6))))) (Finsupp.module.{u1, u1, u1} (Set.Elem.{u1} S s) S S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6))))) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)))) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)))) (Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6))))) (fun (_x : Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6))))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6))))) => S) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} S S (Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6))))) S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) (Finsupp.addCommMonoid.{u1, u1} (Set.Elem.{u1} S s) S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_6))))) (Finsupp.module.{u1, u1, u1} (Set.Elem.{u1} S s) S S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6))))) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)))) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6))) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6))))) (Finsupp.total.{u1, u1, u1} (Set.Elem.{u1} S s) S S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_6))))) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6))) (Subtype.val.{succ u1} S (fun (x : S) => Membership.mem.{u1, u1} S (Set.{u1} S) (Set.instMembershipSet.{u1} S) x s))) l) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6))))) => S) l) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6))))) => S) l) (NonAssocRing.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6))))) => S) l) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6))))) => S) l) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6))))) => S) l) _inst_6)))))) -> (HasSubset.Subset.{u1} (Set.{u1} S) (Set.instHasSubsetSet.{u1} S) s (SetLike.coe.{u1, u1} (Subalgebra.{u2, u1} R S _inst_1 (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) _inst_7) S (Subalgebra.instSetLikeSubalgebra.{u2, u1} R S _inst_1 (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) _inst_7) S')) -> (forall (i : Set.Elem.{u1} S s), Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : Set.Elem.{u1} S s) => S) i) (Subalgebra.{u2, u1} R S _inst_1 (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) _inst_7) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R S _inst_1 (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) _inst_7) S (Subalgebra.instSetLikeSubalgebra.{u2, u1} R S _inst_1 (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) _inst_7)) (FunLike.coe.{succ u1, succ u1, succ u1} (Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (CommMonoidWithZero.toZero.{u1} S (CommSemiring.toCommMonoidWithZero.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)))) (Set.Elem.{u1} S s) (fun (_x : Set.Elem.{u1} S s) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : Set.Elem.{u1} S s) => S) _x) (Finsupp.funLike.{u1, u1} (Set.Elem.{u1} S s) S (CommMonoidWithZero.toZero.{u1} S (CommSemiring.toCommMonoidWithZero.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)))) l i) S') -> (forall (x : S), (forall (r : Set.Elem.{u1} S s), Exists.{1} Nat (fun (n : Nat) => Membership.mem.{u1, u1} S (Subalgebra.{u2, u1} R S _inst_1 (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) _inst_7) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R S _inst_1 (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) _inst_7) S (Subalgebra.instSetLikeSubalgebra.{u2, u1} R S _inst_1 (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) _inst_7)) (HSMul.hSMul.{u1, u1, u1} S S S (instHSMul.{u1, u1} S S (Algebra.toSMul.{u1, u1} S S (CommRing.toCommSemiring.{u1} S _inst_6) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) (Algebra.id.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)))) (HPow.hPow.{u1, 0, u1} S Nat S (instHPow.{u1, 0} S Nat (Monoid.Pow.{u1} S (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)))))) (Subtype.val.{succ u1} S (fun (x : S) => Membership.mem.{u1, u1} S (Set.{u1} S) (Set.instMembershipSet.{u1} S) x s) r) n) x) S')) -> (Membership.mem.{u1, u1} S (Subalgebra.{u2, u1} R S _inst_1 (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) _inst_7) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R S _inst_1 (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) _inst_7) S (Subalgebra.instSetLikeSubalgebra.{u2, u1} R S _inst_1 (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) _inst_7)) x S'))
 Case conversion may be inaccurate. Consider using '#align subalgebra.mem_of_span_eq_top_of_smul_pow_mem Subalgebra.mem_of_span_eq_top_of_smul_pow_memₓ'. -/
 theorem mem_of_span_eq_top_of_smul_pow_mem {S : Type _} [CommRing S] [Algebra R S]
     (S' : Subalgebra R S) (s : Set S) (l : s →₀ S) (hs : Finsupp.total s S S coe l = 1)

bump to nightly-2023-04-20-10

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

fbfe5c3e

Diff

@@ -638,7 +638,7 @@ def toSubmodule : Subalgebra R A ↪o Submodule R A
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) {x : A}, Iff (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (coeFn.{succ u2, succ u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (fun (_x : RelEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) => (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) -> (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (RelEmbedding.hasCoeToFun.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) S)) (Membership.Mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) {x : A}, Iff (Membership.mem.{u2, u2} A ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) (SetLike.instMembership.{u2, u2} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (FunLike.coe.{succ u2, succ u2, succ u2} (Function.Embedding.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (fun (_x : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) _x) (EmbeddingLike.toFunLike.{succ u2, succ u2, succ u2} (Function.Embedding.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Function.instEmbeddingLikeEmbedding.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (RelEmbedding.toEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S)) (Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) {x : A}, Iff (Membership.mem.{u2, u2} A ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) (SetLike.instMembership.{u2, u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (FunLike.coe.{succ u2, succ u2, succ u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (fun (_x : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) _x) (RelHomClass.toFunLike.{u2, u2, u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) S)) (Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)
 Case conversion may be inaccurate. Consider using '#align subalgebra.mem_to_submodule Subalgebra.mem_toSubmoduleₓ'. -/
 /- TODO: bundle other forgetful maps between algebraic substructures, e.g.
   `to_subsemiring` and `to_subring` in this file. -/
@@ -651,7 +651,7 @@ theorem mem_toSubmodule {x} : x ∈ S.toSubmodule ↔ x ∈ S :=
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), Eq.{succ u2} (Set.{u2} A) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (coeFn.{succ u2, succ u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A 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(Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (fun (_x : RelEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) => (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) -> (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (RelEmbedding.hasCoeToFun.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) S)) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) S)
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), Eq.{succ u2} (Set.{u2} A) (SetLike.coe.{u2, u2} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (FunLike.coe.{succ u2, succ u2, succ u2} (Function.Embedding.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (fun (_x : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) _x) (EmbeddingLike.toFunLike.{succ u2, succ u2, succ u2} (Function.Embedding.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Function.instEmbeddingLikeEmbedding.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (RelEmbedding.toEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S)) (SetLike.coe.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) S)
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), Eq.{succ u2} (Set.{u2} A) (SetLike.coe.{u2, u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (FunLike.coe.{succ u2, succ u2, succ u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (fun (_x : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) _x) (RelHomClass.toFunLike.{u2, u2, u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A 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(Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) S)) (SetLike.coe.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) S)
 Case conversion may be inaccurate. Consider using '#align subalgebra.coe_to_submodule Subalgebra.coe_toSubmoduleₓ'. -/
 @[simp]
 theorem coe_toSubmodule (S : Subalgebra R A) : (↑S.toSubmodule : Set A) = S :=
@@ -888,7 +888,7 @@ theorem toSubring_subtype {R A : Type _} [CommRing R] [Ring A] [Algebra R A] (S
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Subalgebra.toSubmoduleEquiv._proof_1.{u1} R _inst_1) (Subalgebra.toSubmoduleEquiv._proof_2.{u1} R _inst_1) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R A 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A 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(Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) S)) (Subalgebra.module.{u1, u2} R A _inst_1 _inst_2 _inst_3 S)
 but is expected to have type
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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A 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x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Subsemiring.toNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2) (Subalgebra.toSubsemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S)))) (Submodule.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (FunLike.coe.{succ u2, succ u2, succ u2} (Function.Embedding.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (fun (_x : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) _x) (EmbeddingLike.toFunLike.{succ u2, succ u2, succ u2} (Function.Embedding.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Function.instEmbeddingLikeEmbedding.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (RelEmbedding.toEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S)) (Subalgebra.instModuleSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToNonAssocSemiringToSubsemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S)
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) (SetLike.instMembership.{u2, u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (FunLike.coe.{succ u2, succ u2, succ u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A 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_inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) S)) (Subalgebra.instModuleSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToNonAssocSemiringToSubsemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S)
 Case conversion may be inaccurate. Consider using '#align subalgebra.to_submodule_equiv Subalgebra.toSubmoduleEquivₓ'. -/
 /-- Linear equivalence between `S : submodule R A` and `S`. Though these types are equal,
 we define it as a `linear_equiv` to avoid type equalities. -/
@@ -949,7 +949,7 @@ theorem mem_map {S : Subalgebra R A} {f : A →ₐ[R] B} {y : B} : y ∈ map f S
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3} {f : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5}, Eq.{succ u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (coeFn.{succ u3, succ u3} (OrderEmbedding.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R 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(Submodule.completeLattice.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)))))))) (Subalgebra.toSubmodule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Subalgebra.map.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 f S)) (Submodule.map.{u1, u1, u2, u3, max u2 u3} R R A B (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (RingHom.id.{u1} R 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(Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) => (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) -> (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (RelEmbedding.hasCoeToFun.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) S))
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3} {f : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5}, Eq.{succ u3} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) => Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Subalgebra.map.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 f S)) (FunLike.coe.{succ u3, succ u3, succ u3} (Function.Embedding.{succ u3, succ u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Submodule.{u1, u3} R B 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_inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) => LE.le.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Preorder.toLE.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (PartialOrder.toPreorder.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instPartialOrder.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) => LE.le.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Preorder.toLE.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (PartialOrder.toPreorder.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Submodule.completeLattice.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Subalgebra.toSubmodule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Subalgebra.map.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 f S)) (Submodule.map.{u1, u1, u2, u3, max u2 u3} R R A B (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u3} R R A B (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AlgHom.toLinearMap.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 f) (FunLike.coe.{succ u2, succ u2, succ u2} (Function.Embedding.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (fun (_x : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) _x) (EmbeddingLike.toFunLike.{succ u2, succ u2, succ u2} (Function.Embedding.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Function.instEmbeddingLikeEmbedding.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (RelEmbedding.toEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S))
+  forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3} {f : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5}, Eq.{succ u3} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) => Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Subalgebra.map.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 f S)) (FunLike.coe.{succ u3, succ u3, succ u3} (OrderEmbedding.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Preorder.toLE.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (PartialOrder.toPreorder.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instPartialOrder.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)))) (Preorder.toLE.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (PartialOrder.toPreorder.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Submodule.completeLattice.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5))))))) (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (fun (_x : Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) => Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) _x) (RelHomClass.toFunLike.{u3, u3, u3} (OrderEmbedding.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Preorder.toLE.{u3} 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Submodule.completeLattice.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5))))))) (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) => LE.le.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Preorder.toLE.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (PartialOrder.toPreorder.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instPartialOrder.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) => LE.le.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Preorder.toLE.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) 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_inst_5)) (Submodule.completeLattice.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) => LE.le.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) 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(CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) S))
 Case conversion may be inaccurate. Consider using '#align subalgebra.map_to_submodule Subalgebra.map_toSubmoduleₓ'. -/
 theorem map_toSubmodule {S : Subalgebra R A} {f : A →ₐ[R] B} :
     (S.map f).toSubmodule = S.toSubmodule.map f.toLinearMap :=
@@ -1115,7 +1115,7 @@ theorem toSubalgebra_mk (s : Set A) (h0 hadd hsmul h1 hmul) :
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (p : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (h_one : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (OfNat.ofNat.{u2} A 1 (OfNat.mk.{u2} A 1 (One.one.{u2} A (AddMonoidWithOne.toOne.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))))) p) (h_mul : forall (x : A) (y : A), (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x p) -> (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) y p) -> (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y) p)), Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (coeFn.{succ u2, succ u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (fun (_x : RelEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) => (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) -> (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (RelEmbedding.hasCoeToFun.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 p h_one h_mul)) p
 but is expected to have type
-  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u1} A] [_inst_3 : Algebra.{u2, u1} R A _inst_1 _inst_2] (p : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (h_one : Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) (OfNat.ofNat.{u1} A 1 (One.toOfNat1.{u1} A (Semiring.toOne.{u1} A _inst_2))) p) (h_mul : forall (x : A) (y : A), (Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) x p) -> (Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) y p) -> (Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u1, u1, u1} A A A (instHMul.{u1} A (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) x y) p)), Eq.{succ u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Submodule.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 p h_one h_mul)) (FunLike.coe.{succ u1, succ u1, succ u1} (Function.Embedding.{succ u1, succ u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (fun (_x : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) _x) (EmbeddingLike.toFunLike.{succ u1, succ u1, succ u1} (Function.Embedding.{succ u1, succ u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Function.instEmbeddingLikeEmbedding.{succ u1, succ u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)))) (RelEmbedding.toEmbedding.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => LE.le.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Subalgebra.toSubmodule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Submodule.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 p h_one h_mul)) p
+  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u1} A] [_inst_3 : Algebra.{u2, u1} R A _inst_1 _inst_2] (p : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (h_one : Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) (OfNat.ofNat.{u1} A 1 (One.toOfNat1.{u1} A (Semiring.toOne.{u1} A _inst_2))) p) (h_mul : forall (x : A) (y : A), (Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) x p) -> (Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) y p) -> (Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u1, u1, u1} A A A (instHMul.{u1} A (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) x y) p)), Eq.{succ u1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Submodule.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 p h_one h_mul)) (FunLike.coe.{succ u1, succ u1, succ u1} (OrderEmbedding.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (fun (_x : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) _x) (RelHomClass.toFunLike.{u1, u1, u1} (OrderEmbedding.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => LE.le.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => LE.le.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Subalgebra.toSubmodule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 p h_one h_mul)) p
 Case conversion may be inaccurate. Consider using '#align submodule.to_subalgebra_to_submodule Submodule.toSubalgebra_toSubmoduleₓ'. -/
 @[simp]
 theorem toSubalgebra_toSubmodule (p : Submodule R A) (h_one h_mul) :
@@ -1127,7 +1127,7 @@ theorem toSubalgebra_toSubmodule (p : Submodule R A) (h_one h_mul) :
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), Eq.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (coeFn.{succ u2, succ u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (fun (_x : RelEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) => (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) -> (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (RelEmbedding.hasCoeToFun.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) S) (Subalgebra.one_mem.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (fun (_x : A) (_x_1 : A) => Subalgebra.mul_mem.{u1, u2} R A _inst_1 _inst_2 _inst_3 S _x _x_1)) S
 but is expected to have type
-  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u1} A] [_inst_3 : Algebra.{u2, u1} R A _inst_1 _inst_2] (S : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3), Eq.{succ u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 (FunLike.coe.{succ u1, succ u1, succ u1} (Function.Embedding.{succ u1, succ u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (fun (_x : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) _x) (EmbeddingLike.toFunLike.{succ u1, succ u1, succ u1} (Function.Embedding.{succ u1, succ u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Function.instEmbeddingLikeEmbedding.{succ u1, succ u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)))) (RelEmbedding.toEmbedding.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => LE.le.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Subalgebra.toSubmodule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) S) (Subalgebra.one_mem.{u2, u1} R A _inst_1 _inst_2 _inst_3 S) (fun (_x : A) (_x_1 : A) => Subalgebra.mul_mem.{u2, u1} R A _inst_1 _inst_2 _inst_3 S _x _x_1)) S
+  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u1} A] [_inst_3 : Algebra.{u2, u1} R A _inst_1 _inst_2] (S : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3), Eq.{succ u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 (FunLike.coe.{succ u1, succ u1, succ u1} (OrderEmbedding.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (fun (_x : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) _x) (RelHomClass.toFunLike.{u1, u1, u1} (OrderEmbedding.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => LE.le.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => LE.le.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Subalgebra.toSubmodule.{u2, u1} R A _inst_1 _inst_2 _inst_3) S) (Subalgebra.one_mem.{u2, u1} R A _inst_1 _inst_2 _inst_3 S) (fun (_x : A) (_x_1 : A) => Subalgebra.mul_mem.{u2, u1} R A _inst_1 _inst_2 _inst_3 S _x _x_1)) S
 Case conversion may be inaccurate. Consider using '#align subalgebra.to_submodule_to_subalgebra Subalgebra.toSubmodule_toSubalgebraₓ'. -/
 @[simp]
 theorem Subalgebra.toSubmodule_toSubalgebra (S : Subalgebra R A) :
@@ -1459,7 +1459,7 @@ theorem mem_top {x : A} : x ∈ (⊤ : Subalgebra R A) :=
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (coeFn.{succ u2, succ u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A 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(LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) => (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) -> (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (RelEmbedding.hasCoeToFun.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Top.top.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toHasTop.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Top.top.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.hasTop.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], Eq.{succ u2} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Top.top.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toTop.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (FunLike.coe.{succ u2, succ u2, succ u2} (Function.Embedding.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (fun (_x : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) _x) (EmbeddingLike.toFunLike.{succ u2, succ u2, succ u2} (Function.Embedding.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Function.instEmbeddingLikeEmbedding.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (RelEmbedding.toEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Top.top.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toTop.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Top.top.{u2} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Top.top.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toTop.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Submodule.instTopSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], Eq.{succ u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Top.top.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toTop.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (FunLike.coe.{succ u2, succ u2, succ u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (fun (_x : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) _x) (RelHomClass.toFunLike.{u2, u2, u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Top.top.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toTop.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Top.top.{u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Top.top.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toTop.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Submodule.instTopSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))
 Case conversion may be inaccurate. Consider using '#align algebra.top_to_submodule Algebra.top_toSubmoduleₓ'. -/
 @[simp]
 theorem top_toSubmodule : (⊤ : Subalgebra R A).toSubmodule = ⊤ :=
@@ -1493,7 +1493,7 @@ theorem top_toSubring {R A : Type _} [CommRing R] [Ring A] [Algebra R A] :
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3}, Iff (Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (coeFn.{succ u2, succ u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (fun (_x : RelEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) => (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) -> (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (RelEmbedding.hasCoeToFun.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) S) (Top.top.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.hasTop.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Eq.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) S (Top.top.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toHasTop.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))))
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3}, Iff (Eq.{succ u2} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) (FunLike.coe.{succ u2, succ u2, succ u2} (Function.Embedding.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (fun (_x : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) _x) (EmbeddingLike.toFunLike.{succ u2, succ u2, succ u2} (Function.Embedding.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Function.instEmbeddingLikeEmbedding.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (RelEmbedding.toEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) (Top.top.{u2} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) (Submodule.instTopSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Eq.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) S (Top.top.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toTop.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))))
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3}, Iff (Eq.{succ u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) (FunLike.coe.{succ u2, succ u2, succ u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (fun (_x : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) _x) (RelHomClass.toFunLike.{u2, u2, u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) S) (Top.top.{u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) (Submodule.instTopSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Eq.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) S (Top.top.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toTop.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))))
 Case conversion may be inaccurate. Consider using '#align algebra.to_submodule_eq_top Algebra.toSubmodule_eq_topₓ'. -/
 @[simp]
 theorem toSubmodule_eq_top {S : Subalgebra R A} : S.toSubmodule = ⊤ ↔ S = ⊤ :=
@@ -1589,7 +1589,7 @@ theorem mem_inf {S T : Subalgebra R A} {x : A} : x ∈ S ⊓ T ↔ x ∈ S ∧ x
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (T : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (coeFn.{succ u2, succ u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) => (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) -> (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (RelEmbedding.hasCoeToFun.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) 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u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) T))
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (T : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), Eq.{succ u2} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Inf.inf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Lattice.toInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) S T)) (FunLike.coe.{succ u2, succ u2, succ u2} (Function.Embedding.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (fun (_x : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) _x) (EmbeddingLike.toFunLike.{succ u2, succ u2, succ u2} (Function.Embedding.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Function.instEmbeddingLikeEmbedding.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (RelEmbedding.toEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Inf.inf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Lattice.toInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) S T)) (Inf.inf.{u2} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) (Submodule.instInfSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (FunLike.coe.{succ u2, succ u2, succ u2} (Function.Embedding.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (fun (_x : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) _x) (EmbeddingLike.toFunLike.{succ u2, succ u2, succ u2} (Function.Embedding.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Function.instEmbeddingLikeEmbedding.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (RelEmbedding.toEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) (FunLike.coe.{succ u2, succ u2, succ u2} (Function.Embedding.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (fun (_x : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) _x) (EmbeddingLike.toFunLike.{succ u2, succ u2, succ u2} (Function.Embedding.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Function.instEmbeddingLikeEmbedding.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (RelEmbedding.toEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T))
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (T : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), Eq.{succ u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Inf.inf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Lattice.toInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) S T)) (FunLike.coe.{succ u2, succ u2, succ u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (fun (_x : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) _x) (RelHomClass.toFunLike.{u2, u2, u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A 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(Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 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(CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A 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(PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A 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Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) _x) (RelHomClass.toFunLike.{u2, u2, u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) T))
 Case conversion may be inaccurate. Consider using '#align algebra.inf_to_submodule Algebra.inf_toSubmoduleₓ'. -/
 @[simp]
 theorem inf_toSubmodule (S T : Subalgebra R A) :
@@ -1634,7 +1634,7 @@ theorem mem_infₛ {S : Set (Subalgebra R A)} {x : A} : x ∈ infₛ S ↔ ∀ p
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Set.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)), Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (coeFn.{succ u2, succ u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (fun (_x : RelEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} 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(CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) => (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) -> (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (RelEmbedding.hasCoeToFun.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (InfSet.infₛ.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))) S)) (InfSet.infₛ.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.hasInf.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A 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A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) => (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) -> (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (RelEmbedding.hasCoeToFun.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S))
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Set.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)), Eq.{succ u2} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (InfSet.infₛ.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toInfSet.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))) S)) (FunLike.coe.{succ u2, succ u2, succ u2} (Function.Embedding.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (fun (_x : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) _x) (EmbeddingLike.toFunLike.{succ u2, succ u2, succ u2} (Function.Embedding.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Function.instEmbeddingLikeEmbedding.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (RelEmbedding.toEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (InfSet.infₛ.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toInfSet.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))) S)) (InfSet.infₛ.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.instInfSetSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.image.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (FunLike.coe.{succ u2, succ u2, succ u2} (Function.Embedding.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (fun (_x : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) _x) (EmbeddingLike.toFunLike.{succ u2, succ u2, succ u2} (Function.Embedding.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Function.instEmbeddingLikeEmbedding.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (RelEmbedding.toEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) S))
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Set.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)), Eq.{succ u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (InfSet.infₛ.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toInfSet.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))) S)) (FunLike.coe.{succ u2, succ u2, succ u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S))
 Case conversion may be inaccurate. Consider using '#align algebra.Inf_to_submodule Algebra.infₛ_toSubmoduleₓ'. -/
 @[simp]
 theorem infₛ_toSubmodule (S : Set (Subalgebra R A)) :
@@ -1679,7 +1679,7 @@ theorem mem_infᵢ {ι : Sort _} {S : ι → Subalgebra R A} {x : A} : (x ∈ 
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {ι : Sort.{u3}} (S : ι -> (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)), Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (coeFn.{succ u2, succ u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (fun (_x : RelEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) => (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) -> (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (RelEmbedding.hasCoeToFun.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (infᵢ.{u2, u3} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => S i))) (infᵢ.{u2, u3} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.hasInf.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) ι (fun (i : ι) => coeFn.{succ u2, succ u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A 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(Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (fun (_x : RelEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) => (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) -> (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (RelEmbedding.hasCoeToFun.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (S i)))
 but is expected to have type
-  forall {R : Type.{u2}} {A : Type.{u3}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u3} A] [_inst_3 : Algebra.{u2, u3} R A _inst_1 _inst_2] {ι : Sort.{u1}} (S : ι -> (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)), Eq.{succ u3} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (infᵢ.{u3, u1} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toInfSet.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => S i))) (FunLike.coe.{succ u3, succ u3, succ u3} (Function.Embedding.{succ u3, succ u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3))) (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (fun (_x : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) _x) (EmbeddingLike.toFunLike.{succ u3, succ u3, succ u3} (Function.Embedding.{succ u3, succ u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3))) (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Function.instEmbeddingLikeEmbedding.{succ u3, succ u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)))) (RelEmbedding.toEmbedding.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) => LE.le.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Subalgebra.toSubmodule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (infᵢ.{u3, u1} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toInfSet.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => S i))) (infᵢ.{u3, u1} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.instInfSetSubmodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) ι (fun (i : ι) => FunLike.coe.{succ u3, succ u3, succ u3} (Function.Embedding.{succ u3, succ u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3))) (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (fun (_x : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) _x) (EmbeddingLike.toFunLike.{succ u3, succ u3, succ u3} (Function.Embedding.{succ u3, succ u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3))) (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Function.instEmbeddingLikeEmbedding.{succ u3, succ u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)))) (RelEmbedding.toEmbedding.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) => LE.le.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Subalgebra.toSubmodule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (S i)))
+  forall {R : Type.{u2}} {A : Type.{u3}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u3} A] [_inst_3 : Algebra.{u2, u3} R A _inst_1 _inst_2] {ι : Sort.{u1}} (S : ι -> (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)), Eq.{succ u3} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (infᵢ.{u3, u1} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toInfSet.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => S i))) (FunLike.coe.{succ u3, succ u3, succ u3} (OrderEmbedding.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (fun (_x : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) _x) (RelHomClass.toFunLike.{u3, u3, u3} (OrderEmbedding.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A 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_inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) => LE.le.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A 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(Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) => LE.le.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Subalgebra.toSubmodule.{u2, u3} R A _inst_1 _inst_2 _inst_3) (S i)))
 Case conversion may be inaccurate. Consider using '#align algebra.infi_to_submodule Algebra.infᵢ_toSubmoduleₓ'. -/
 @[simp]
 theorem infᵢ_toSubmodule {ι : Sort _} (S : ι → Subalgebra R A) :
@@ -1708,7 +1708,7 @@ theorem mem_bot {x : A} : x ∈ (⊥ : Subalgebra R A) ↔ x ∈ Set.range (alge
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (coeFn.{succ u2, succ u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (fun (_x : RelEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) => (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) -> (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (RelEmbedding.hasCoeToFun.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Bot.bot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toHasBot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Submodule.span.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.hasSingleton.{u2} A) (OfNat.ofNat.{u2} A 1 (OfNat.mk.{u2} A 1 (One.one.{u2} A (AddMonoidWithOne.toOne.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))))))
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], Eq.{succ u2} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Bot.bot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toBot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (FunLike.coe.{succ u2, succ u2, succ u2} (Function.Embedding.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (fun (_x : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) _x) (EmbeddingLike.toFunLike.{succ u2, succ u2, succ u2} (Function.Embedding.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Function.instEmbeddingLikeEmbedding.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (RelEmbedding.toEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Bot.bot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toBot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Submodule.span.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) (OfNat.ofNat.{u2} A 1 (One.toOfNat1.{u2} A (Semiring.toOne.{u2} A _inst_2)))))
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], Eq.{succ u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Bot.bot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toBot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (FunLike.coe.{succ u2, succ u2, succ u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (fun (_x : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) _x) (RelHomClass.toFunLike.{u2, u2, u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Bot.bot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toBot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Submodule.span.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) (OfNat.ofNat.{u2} A 1 (One.toOfNat1.{u2} A (Semiring.toOne.{u2} A _inst_2)))))
 Case conversion may be inaccurate. Consider using '#align algebra.to_submodule_bot Algebra.toSubmodule_botₓ'. -/
 theorem toSubmodule_bot : (⊥ : Subalgebra R A).toSubmodule = R ∙ 1 :=
   by
@@ -2106,7 +2106,7 @@ theorem coe_prod : (prod S S₁ : Set (A × B)) = S ×ˢ S₁ :=
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (S₁ : Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5), Eq.{succ (max u2 u3)} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.semiring.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (coeFn.{succ (max u2 u3), succ (max u2 u3)} (OrderEmbedding.{max u2 u3, max u2 u3} 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u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (SetLike.partialOrder.{max u2 u3, max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (Prod.{u2, u3} A B) (Subalgebra.setLike.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))))) (Preorder.toLE.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.semiring.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (PartialOrder.toPreorder.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.semiring.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (CompleteSemilatticeInf.toPartialOrder.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.semiring.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (CompleteLattice.toCompleteSemilatticeInf.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.semiring.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (Submodule.completeLattice.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.semiring.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)))))))) (fun (_x : RelEmbedding.{max u2 u3, max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.semiring.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (LE.le.{max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (Preorder.toLE.{max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (PartialOrder.toPreorder.{max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (SetLike.partialOrder.{max u2 u3, max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (Prod.{u2, u3} A B) (Subalgebra.setLike.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)))))) (LE.le.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.semiring.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (Preorder.toLE.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.semiring.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (PartialOrder.toPreorder.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.semiring.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (CompleteSemilatticeInf.toPartialOrder.{max 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A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (Submodule.completeLattice.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.semiring.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))))))))) => (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) -> (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) 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u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (LE.le.{max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (Preorder.toLE.{max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (PartialOrder.toPreorder.{max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (SetLike.partialOrder.{max u2 u3, max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Submodule.completeLattice.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)))))))) (Subalgebra.toSubmodule.{u1, u3} R B _inst_1 _inst_4 _inst_5) S₁))
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (S₁ : Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5), Eq.{max (succ u2) (succ u3)} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) => Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) 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max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (OmegaCompletePartialOrder.toPartialOrder.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (CompleteLattice.instOmegaCompletePartialOrder.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (Submodule.completeLattice.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Subalgebra.toSubmodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (Subalgebra.prod.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 S S₁)) (Submodule.prod.{u1, u2, u3} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (FunLike.coe.{succ u2, succ u2, succ u2} (Function.Embedding.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (fun (_x : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) _x) (EmbeddingLike.toFunLike.{succ u2, succ u2, succ u2} (Function.Embedding.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Function.instEmbeddingLikeEmbedding.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (RelEmbedding.toEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5) (FunLike.coe.{succ u3, succ u3, succ u3} (Function.Embedding.{succ u3, succ u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5))) (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (fun (_x : Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) => Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) _x) (EmbeddingLike.toFunLike.{succ u3, succ u3, succ u3} (Function.Embedding.{succ u3, succ u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5))) (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Function.instEmbeddingLikeEmbedding.{succ u3, succ u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)))) (RelEmbedding.toEmbedding.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) => LE.le.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Preorder.toLE.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (PartialOrder.toPreorder.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instPartialOrder.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) => LE.le.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Preorder.toLE.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (PartialOrder.toPreorder.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Submodule.completeLattice.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Subalgebra.toSubmodule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) S₁))
+  forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (S₁ : Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5), Eq.{max (succ u2) (succ u3)} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) => Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (Subalgebra.prod.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 S S₁)) (FunLike.coe.{succ (max u2 u3), succ (max u2 u3), succ (max u2 u3)} (OrderEmbedding.{max u2 u3, max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 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_inst_2 _inst_3 _inst_4 _inst_5))))) (Preorder.toLE.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (PartialOrder.toPreorder.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (OmegaCompletePartialOrder.toPartialOrder.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (CompleteLattice.instOmegaCompletePartialOrder.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) 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_inst_2 _inst_3 _inst_4 _inst_5)))))))) (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (fun (_x : Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) => Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) _x) (RelHomClass.toFunLike.{max u2 u3, max u2 u3, max u2 u3} (OrderEmbedding.{max u2 u3, max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (Preorder.toLE.{max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (PartialOrder.toPreorder.{max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (SetLike.instPartialOrder.{max u2 u3, max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (Prod.{u2, u3} A B) (Subalgebra.instSetLikeSubalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))))) (Preorder.toLE.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (PartialOrder.toPreorder.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (OmegaCompletePartialOrder.toPartialOrder.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (CompleteLattice.instOmegaCompletePartialOrder.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (Submodule.completeLattice.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)))))))) (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) => LE.le.{max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (Preorder.toLE.{max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (PartialOrder.toPreorder.{max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (SetLike.instPartialOrder.{max u2 u3, max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (Prod.{u2, u3} A B) (Subalgebra.instSetLikeSubalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) => LE.le.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (Preorder.toLE.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (PartialOrder.toPreorder.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (OmegaCompletePartialOrder.toPartialOrder.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (CompleteLattice.instOmegaCompletePartialOrder.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (Submodule.completeLattice.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{max u2 u3, max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) => LE.le.{max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (Preorder.toLE.{max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (PartialOrder.toPreorder.{max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (SetLike.instPartialOrder.{max u2 u3, max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (Prod.{u2, u3} A B) (Subalgebra.instSetLikeSubalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) => LE.le.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (Preorder.toLE.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (PartialOrder.toPreorder.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (OmegaCompletePartialOrder.toPartialOrder.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (CompleteLattice.instOmegaCompletePartialOrder.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (Submodule.completeLattice.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Subalgebra.toSubmodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.instSemiringProd.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (Subalgebra.prod.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 S S₁)) (Submodule.prod.{u1, u2, u3} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (PartialOrder.toPreorder.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Submodule.completeLattice.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5))))))) (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) => LE.le.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Preorder.toLE.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (PartialOrder.toPreorder.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instPartialOrder.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) => LE.le.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Preorder.toLE.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (PartialOrder.toPreorder.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Submodule.completeLattice.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) => LE.le.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Preorder.toLE.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (PartialOrder.toPreorder.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instPartialOrder.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) => LE.le.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Preorder.toLE.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (PartialOrder.toPreorder.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Submodule.completeLattice.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Subalgebra.toSubmodule.{u1, u3} R B _inst_1 _inst_4 _inst_5) S₁))
 Case conversion may be inaccurate. Consider using '#align subalgebra.prod_to_submodule Subalgebra.prod_toSubmoduleₓ'. -/
 theorem prod_toSubmodule : (S.Prod S₁).toSubmodule = S.toSubmodule.Prod S₁.toSubmodule :=
   rfl

bump to nightly-2023-03-27-02

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce86f4e05e9a9b8da5e316b22c76ce76440c56a1

0e4ebd8c

Diff

@@ -348,7 +348,7 @@ instance {R A : Type _} [CommRing R] [Ring A] [Algebra R A] : SubringClass (Suba
 
 /- warning: subalgebra.neg_mem -> Subalgebra.neg_mem is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_8 : CommRing.{u1} R] [_inst_9 : Ring.{u2} A] [_inst_10 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9)] (S : Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) {x : A}, (Membership.Mem.{u2, u2} A (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) A (Subalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10)) x S) -> (Membership.Mem.{u2, u2} A (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) A (Subalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10)) (Neg.neg.{u2} A (SubNegMonoid.toHasNeg.{u2} A (AddGroup.toSubNegMonoid.{u2} A (AddGroupWithOne.toAddGroup.{u2} A (NonAssocRing.toAddGroupWithOne.{u2} A (Ring.toNonAssocRing.{u2} A _inst_9))))) x) S)
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_8 : CommRing.{u1} R] [_inst_9 : Ring.{u2} A] [_inst_10 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9)] (S : Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) {x : A}, (Membership.Mem.{u2, u2} A (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) A (Subalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10)) x S) -> (Membership.Mem.{u2, u2} A (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) A (Subalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10)) (Neg.neg.{u2} A (SubNegMonoid.toHasNeg.{u2} A (AddGroup.toSubNegMonoid.{u2} A (AddGroupWithOne.toAddGroup.{u2} A (AddCommGroupWithOne.toAddGroupWithOne.{u2} A (Ring.toAddCommGroupWithOne.{u2} A _inst_9))))) x) S)
 but is expected to have type
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_8 : CommRing.{u1} R] [_inst_9 : Ring.{u2} A] [_inst_10 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9)] (S : Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) {x : A}, (Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10)) x S) -> (Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10)) (Neg.neg.{u2} A (Ring.toNeg.{u2} A _inst_9) x) S)
 Case conversion may be inaccurate. Consider using '#align subalgebra.neg_mem Subalgebra.neg_memₓ'. -/
@@ -359,7 +359,7 @@ protected theorem neg_mem {R : Type u} {A : Type v} [CommRing R] [Ring A] [Algeb
 
 /- warning: subalgebra.sub_mem -> Subalgebra.sub_mem is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_8 : CommRing.{u1} R] [_inst_9 : Ring.{u2} A] [_inst_10 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9)] (S : Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) {x : A} {y : A}, (Membership.Mem.{u2, u2} A (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) A (Subalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10)) x S) -> (Membership.Mem.{u2, u2} A (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) A (Subalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10)) y S) -> (Membership.Mem.{u2, u2} A (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) A (Subalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10)) (HSub.hSub.{u2, u2, u2} A A A (instHSub.{u2} A (SubNegMonoid.toHasSub.{u2} A (AddGroup.toSubNegMonoid.{u2} A (AddGroupWithOne.toAddGroup.{u2} A (NonAssocRing.toAddGroupWithOne.{u2} A (Ring.toNonAssocRing.{u2} A _inst_9)))))) x y) S)
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_8 : CommRing.{u1} R] [_inst_9 : Ring.{u2} A] [_inst_10 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9)] (S : Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) {x : A} {y : A}, (Membership.Mem.{u2, u2} A (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) A (Subalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10)) x S) -> (Membership.Mem.{u2, u2} A (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) A (Subalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10)) y S) -> (Membership.Mem.{u2, u2} A (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) A (Subalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10)) (HSub.hSub.{u2, u2, u2} A A A (instHSub.{u2} A (SubNegMonoid.toHasSub.{u2} A (AddGroup.toSubNegMonoid.{u2} A (AddGroupWithOne.toAddGroup.{u2} A (AddCommGroupWithOne.toAddGroupWithOne.{u2} A (Ring.toAddCommGroupWithOne.{u2} A _inst_9)))))) x y) S)
 but is expected to have type
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_8 : CommRing.{u1} R] [_inst_9 : Ring.{u2} A] [_inst_10 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9)] (S : Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) {x : A} {y : A}, (Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10)) x S) -> (Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10)) y S) -> (Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10)) (HSub.hSub.{u2, u2, u2} A A A (instHSub.{u2} A (Ring.toSub.{u2} A _inst_9)) x y) S)
 Case conversion may be inaccurate. Consider using '#align subalgebra.sub_mem Subalgebra.sub_memₓ'. -/
@@ -370,7 +370,7 @@ protected theorem sub_mem {R : Type u} {A : Type v} [CommRing R] [Ring A] [Algeb
 
 /- warning: subalgebra.zsmul_mem -> Subalgebra.zsmul_mem is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_8 : CommRing.{u1} R] [_inst_9 : Ring.{u2} A] [_inst_10 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9)] (S : Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) {x : A}, (Membership.Mem.{u2, u2} A (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) A (Subalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10)) x S) -> (forall (n : Int), Membership.Mem.{u2, u2} A (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) A (Subalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10)) (SMul.smul.{0, u2} Int A (SubNegMonoid.SMulInt.{u2} A (AddGroup.toSubNegMonoid.{u2} A (AddGroupWithOne.toAddGroup.{u2} A (NonAssocRing.toAddGroupWithOne.{u2} A (Ring.toNonAssocRing.{u2} A _inst_9))))) n x) S)
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_8 : CommRing.{u1} R] [_inst_9 : Ring.{u2} A] [_inst_10 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9)] (S : Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) {x : A}, (Membership.Mem.{u2, u2} A (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) A (Subalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10)) x S) -> (forall (n : Int), Membership.Mem.{u2, u2} A (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) A (Subalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10)) (SMul.smul.{0, u2} Int A (SubNegMonoid.SMulInt.{u2} A (AddGroup.toSubNegMonoid.{u2} A (AddGroupWithOne.toAddGroup.{u2} A (AddCommGroupWithOne.toAddGroupWithOne.{u2} A (Ring.toAddCommGroupWithOne.{u2} A _inst_9))))) n x) S)
 but is expected to have type
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_8 : CommRing.{u1} R] [_inst_9 : Ring.{u2} A] [_inst_10 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9)] (S : Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) {x : A}, (Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10)) x S) -> (forall (n : Int), Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10)) (HSMul.hSMul.{0, u2, u2} Int A A (instHSMul.{0, u2} Int A (SubNegMonoid.SMulInt.{u2} A (AddGroup.toSubNegMonoid.{u2} A (AddGroupWithOne.toAddGroup.{u2} A (Ring.toAddGroupWithOne.{u2} A _inst_9))))) n x) S)
 Case conversion may be inaccurate. Consider using '#align subalgebra.zsmul_mem Subalgebra.zsmul_memₓ'. -/
@@ -381,7 +381,7 @@ protected theorem zsmul_mem {R : Type u} {A : Type v} [CommRing R] [Ring A] [Alg
 
 /- warning: subalgebra.coe_int_mem -> Subalgebra.coe_int_mem is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_8 : CommRing.{u1} R] [_inst_9 : Ring.{u2} A] [_inst_10 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9)] (S : Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) (n : Int), Membership.Mem.{u2, u2} A (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) A (Subalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10)) ((fun (a : Type) (b : Type.{u2}) [self : HasLiftT.{1, succ u2} a b] => self.0) Int A (HasLiftT.mk.{1, succ u2} Int A (CoeTCₓ.coe.{1, succ u2} Int A (Int.castCoe.{u2} A (AddGroupWithOne.toHasIntCast.{u2} A (NonAssocRing.toAddGroupWithOne.{u2} A (Ring.toNonAssocRing.{u2} A _inst_9)))))) n) S
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_8 : CommRing.{u1} R] [_inst_9 : Ring.{u2} A] [_inst_10 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9)] (S : Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) (n : Int), Membership.Mem.{u2, u2} A (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) A (Subalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10)) ((fun (a : Type) (b : Type.{u2}) [self : HasLiftT.{1, succ u2} a b] => self.0) Int A (HasLiftT.mk.{1, succ u2} Int A (CoeTCₓ.coe.{1, succ u2} Int A (Int.castCoe.{u2} A (AddGroupWithOne.toHasIntCast.{u2} A (AddCommGroupWithOne.toAddGroupWithOne.{u2} A (Ring.toAddCommGroupWithOne.{u2} A _inst_9)))))) n) S
 but is expected to have type
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_8 : CommRing.{u1} R] [_inst_9 : Ring.{u2} A] [_inst_10 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9)] (S : Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) (n : Int), Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10)) (Int.cast.{u2} A (Ring.toIntCast.{u2} A _inst_9) n) S
 Case conversion may be inaccurate. Consider using '#align subalgebra.coe_int_mem Subalgebra.coe_int_memₓ'. -/
@@ -754,7 +754,7 @@ protected theorem coe_one : ((1 : S) : A) = 1 :=
 
 /- warning: subalgebra.coe_neg -> Subalgebra.coe_neg is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_8 : CommRing.{u1} R] [_inst_9 : Ring.{u2} A] [_inst_10 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9)] {S : Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10} (x : coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) A (Subalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10)) S), Eq.{succ u2} A ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) Type.{u2} 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+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_8 : CommRing.{u1} R] [_inst_9 : Ring.{u2} A] [_inst_10 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9)] {S : Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10} (x : coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) A (Subalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10)) S), Eq.{succ u2} A ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) Type.{u2} 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(Ring.toSemiring.{u2} A _inst_9) _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) A (Subalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10)) S) A (coeSubtype.{succ u2} A (fun (x : A) => Membership.Mem.{u2, u2} A (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) A (Subalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10)) x S))))) x))
 but is expected to have type
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_8 : CommRing.{u1} R] [_inst_9 : Ring.{u2} A] [_inst_10 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9)] {S : Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10} (x : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10)) x S)), Eq.{succ u2} A (Subtype.val.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) x (SetLike.coe.{u2, u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) S)) (Neg.neg.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10)) x S)) (AddSubgroupClass.neg.{u2, u2} A (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) (AddGroup.toSubNegMonoid.{u2} A (AddGroupWithOne.toAddGroup.{u2} A (Ring.toAddGroupWithOne.{u2} A _inst_9))) (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) (SubringClass.addSubgroupClass.{u2, u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) _inst_9 (Subalgebra.instSubringClassSubalgebraToCommSemiringToSemiringInstSetLikeSubalgebra.{u1, u2} R A _inst_8 _inst_9 _inst_10)) S) x)) (Neg.neg.{u2} A (Ring.toNeg.{u2} A _inst_9) (Subtype.val.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) x (SetLike.coe.{u2, u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) S)) x))
 Case conversion may be inaccurate. Consider using '#align subalgebra.coe_neg Subalgebra.coe_negₓ'. -/
@@ -765,7 +765,7 @@ protected theorem coe_neg {R : Type u} {A : Type v} [CommRing R] [Ring A] [Algeb
 
 /- warning: subalgebra.coe_sub -> Subalgebra.coe_sub is a dubious translation:
 lean 3 declaration is
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 but is expected to have type
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(Ring.toSemiring.{u2} A _inst_9) _inst_10) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) S)) y))
 Case conversion may be inaccurate. Consider using '#align subalgebra.coe_sub Subalgebra.coe_subₓ'. -/
@@ -2585,7 +2585,7 @@ end Centralizer
 
 /- warning: subalgebra.mem_of_finset_sum_eq_one_of_pow_smul_mem -> Subalgebra.mem_of_finset_sum_eq_one_of_pow_smul_mem is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {S : Type.{u2}} [_inst_6 : CommRing.{u2} S] [_inst_7 : Algebra.{u1, u2} R S _inst_1 (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6))] (S' : Subalgebra.{u1, u2} R S _inst_1 (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_7) {ι : Type.{u3}} (ι' : Finset.{u3} ι) (s : ι -> S) (l : ι -> S), (Eq.{succ u2} S (Finset.sum.{u2, u3} S ι (AddCommGroup.toAddCommMonoid.{u2} S (NonUnitalNonAssocRing.toAddCommGroup.{u2} S (NonAssocRing.toNonUnitalNonAssocRing.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_6))))) ι' (fun (i : ι) => HMul.hMul.{u2, u2, u2} S S S (instHMul.{u2} S (Distrib.toHasMul.{u2} S (Ring.toDistrib.{u2} S (CommRing.toRing.{u2} S _inst_6)))) (l i) (s i))) (OfNat.ofNat.{u2} S 1 (OfNat.mk.{u2} S 1 (One.one.{u2} S (AddMonoidWithOne.toOne.{u2} S (AddGroupWithOne.toAddMonoidWithOne.{u2} S (NonAssocRing.toAddGroupWithOne.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_6))))))))) -> (forall (i : ι), Membership.Mem.{u2, u2} S (Subalgebra.{u1, u2} R S _inst_1 (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_7) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R S _inst_1 (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_7) S (Subalgebra.setLike.{u1, u2} R S _inst_1 (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_7)) (s i) S') -> (forall (i : ι), Membership.Mem.{u2, u2} S (Subalgebra.{u1, u2} R S _inst_1 (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_7) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R S _inst_1 (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_7) S (Subalgebra.setLike.{u1, u2} R S _inst_1 (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_7)) (l i) S') -> (forall (x : S), (forall (i : ι), Exists.{1} Nat (fun (n : Nat) => Membership.Mem.{u2, u2} S (Subalgebra.{u1, u2} R S _inst_1 (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_7) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R S _inst_1 (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_7) S (Subalgebra.setLike.{u1, u2} R S _inst_1 (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_7)) (SMul.smul.{u2, u2} S S (Mul.toSMul.{u2} S (Distrib.toHasMul.{u2} S (Ring.toDistrib.{u2} S (CommRing.toRing.{u2} S _inst_6)))) (HPow.hPow.{u2, 0, u2} S Nat S (instHPow.{u2, 0} S Nat (Monoid.Pow.{u2} S (Ring.toMonoid.{u2} S (CommRing.toRing.{u2} S _inst_6)))) (s i) n) x) S')) -> (Membership.Mem.{u2, u2} S (Subalgebra.{u1, u2} R S _inst_1 (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_7) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R S _inst_1 (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_7) S (Subalgebra.setLike.{u1, u2} R S _inst_1 (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_7)) x S'))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {S : Type.{u2}} [_inst_6 : CommRing.{u2} S] [_inst_7 : Algebra.{u1, u2} R S _inst_1 (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6))] (S' : Subalgebra.{u1, u2} R S _inst_1 (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_7) {ι : Type.{u3}} (ι' : Finset.{u3} ι) (s : ι -> S) (l : ι -> S), (Eq.{succ u2} S (Finset.sum.{u2, u3} S ι (AddCommGroup.toAddCommMonoid.{u2} S (NonUnitalNonAssocRing.toAddCommGroup.{u2} S (NonAssocRing.toNonUnitalNonAssocRing.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_6))))) ι' (fun (i : ι) => HMul.hMul.{u2, u2, u2} S S S (instHMul.{u2} S (Distrib.toHasMul.{u2} S (Ring.toDistrib.{u2} S (CommRing.toRing.{u2} S _inst_6)))) (l i) (s i))) (OfNat.ofNat.{u2} S 1 (OfNat.mk.{u2} S 1 (One.one.{u2} S (AddMonoidWithOne.toOne.{u2} S (AddGroupWithOne.toAddMonoidWithOne.{u2} S (AddCommGroupWithOne.toAddGroupWithOne.{u2} S (Ring.toAddCommGroupWithOne.{u2} S (CommRing.toRing.{u2} S _inst_6))))))))) -> (forall (i : ι), Membership.Mem.{u2, u2} S (Subalgebra.{u1, u2} R S _inst_1 (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_7) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R S _inst_1 (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_7) S (Subalgebra.setLike.{u1, u2} R S _inst_1 (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_7)) (s i) S') -> (forall (i : ι), Membership.Mem.{u2, u2} S (Subalgebra.{u1, u2} R S _inst_1 (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_7) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R S _inst_1 (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_7) S (Subalgebra.setLike.{u1, u2} R S _inst_1 (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_7)) (l i) S') -> (forall (x : S), (forall (i : ι), Exists.{1} Nat (fun (n : Nat) => Membership.Mem.{u2, u2} S (Subalgebra.{u1, u2} R S _inst_1 (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_7) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R S _inst_1 (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_7) S (Subalgebra.setLike.{u1, u2} R S _inst_1 (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_7)) (SMul.smul.{u2, u2} S S (Mul.toSMul.{u2} S (Distrib.toHasMul.{u2} S (Ring.toDistrib.{u2} S (CommRing.toRing.{u2} S _inst_6)))) (HPow.hPow.{u2, 0, u2} S Nat S (instHPow.{u2, 0} S Nat (Monoid.Pow.{u2} S (Ring.toMonoid.{u2} S (CommRing.toRing.{u2} S _inst_6)))) (s i) n) x) S')) -> (Membership.Mem.{u2, u2} S (Subalgebra.{u1, u2} R S _inst_1 (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_7) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R S _inst_1 (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_7) S (Subalgebra.setLike.{u1, u2} R S _inst_1 (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_7)) x S'))
 but is expected to have type
   forall {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] {S : Type.{u2}} [_inst_6 : CommRing.{u2} S] [_inst_7 : Algebra.{u3, u2} R S _inst_1 (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6))] (S' : Subalgebra.{u3, u2} R S _inst_1 (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_7) {ι : Type.{u1}} (ι' : Finset.{u1} ι) (s : ι -> S) (l : ι -> S), (Eq.{succ u2} S (Finset.sum.{u2, u1} S ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} S (NonAssocRing.toNonUnitalNonAssocRing.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_6))))) ι' (fun (i : ι) => HMul.hMul.{u2, u2, u2} S S S (instHMul.{u2} S (NonUnitalNonAssocRing.toMul.{u2} S (NonAssocRing.toNonUnitalNonAssocRing.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_6))))) (l i) (s i))) (OfNat.ofNat.{u2} S 1 (One.toOfNat1.{u2} S (NonAssocRing.toOne.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_6)))))) -> (forall (i : ι), Membership.mem.{u2, u2} S (Subalgebra.{u3, u2} R S _inst_1 (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_7) (SetLike.instMembership.{u2, u2} (Subalgebra.{u3, u2} R S _inst_1 (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_7) S (Subalgebra.instSetLikeSubalgebra.{u3, u2} R S _inst_1 (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_7)) (s i) S') -> (forall (i : ι), Membership.mem.{u2, u2} S (Subalgebra.{u3, u2} R S _inst_1 (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_7) (SetLike.instMembership.{u2, u2} (Subalgebra.{u3, u2} R S _inst_1 (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_7) S (Subalgebra.instSetLikeSubalgebra.{u3, u2} R S _inst_1 (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_7)) (l i) S') -> (forall (x : S), (forall (i : ι), Exists.{1} Nat (fun (n : Nat) => Membership.mem.{u2, u2} S (Subalgebra.{u3, u2} R S _inst_1 (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_7) (SetLike.instMembership.{u2, u2} (Subalgebra.{u3, u2} R S _inst_1 (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_7) S (Subalgebra.instSetLikeSubalgebra.{u3, u2} R S _inst_1 (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_7)) (HSMul.hSMul.{u2, u2, u2} S S S (instHSMul.{u2, u2} S S (Algebra.toSMul.{u2, u2} S S (CommRing.toCommSemiring.{u2} S _inst_6) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) (Algebra.id.{u2} S (CommRing.toCommSemiring.{u2} S _inst_6)))) (HPow.hPow.{u2, 0, u2} S Nat S (instHPow.{u2, 0} S Nat (Monoid.Pow.{u2} S (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)))))) (s i) n) x) S')) -> (Membership.mem.{u2, u2} S (Subalgebra.{u3, u2} R S _inst_1 (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_7) (SetLike.instMembership.{u2, u2} (Subalgebra.{u3, u2} R S _inst_1 (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_7) S (Subalgebra.instSetLikeSubalgebra.{u3, u2} R S _inst_1 (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_7)) x S'))
 Case conversion may be inaccurate. Consider using '#align subalgebra.mem_of_finset_sum_eq_one_of_pow_smul_mem Subalgebra.mem_of_finset_sum_eq_one_of_pow_smul_memₓ'. -/
@@ -2626,7 +2626,7 @@ theorem mem_of_finset_sum_eq_one_of_pow_smul_mem {S : Type _} [CommRing S] [Alge
 
 /- warning: subalgebra.mem_of_span_eq_top_of_smul_pow_mem -> Subalgebra.mem_of_span_eq_top_of_smul_pow_mem is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {S : Type.{u2}} [_inst_6 : CommRing.{u2} S] [_inst_7 : Algebra.{u1, u2} R S _inst_1 (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6))] (S' : Subalgebra.{u1, u2} R S _inst_1 (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_7) (s : Set.{u2} S) (l : Finsupp.{u2, u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} S) Type.{u2} (Set.hasCoeToSort.{u2} S) s) S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} S (NonAssocRing.toNonUnitalNonAssocRing.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_6))))))), (Eq.{succ u2} S (coeFn.{succ u2, succ u2} (LinearMap.{u2, u2, u2, u2} S S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)))) 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S _inst_6))))))) S (Finsupp.addCommMonoid.{u2, u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} S) Type.{u2} (Set.hasCoeToSort.{u2} S) s) S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)))))) (AddCommGroup.toAddCommMonoid.{u2} S (NonUnitalNonAssocRing.toAddCommGroup.{u2} S (NonAssocRing.toNonUnitalNonAssocRing.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_6))))) (Finsupp.module.{u2, u2, u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} S) Type.{u2} (Set.hasCoeToSort.{u2} S) s) S S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6))))) (Semiring.toModule.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)))) (Semiring.toModule.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)))) => (Finsupp.{u2, u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} S) Type.{u2} (Set.hasCoeToSort.{u2} S) s) S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6))))))) -> S) (LinearMap.hasCoeToFun.{u2, u2, u2, u2} S S (Finsupp.{u2, u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} S) Type.{u2} (Set.hasCoeToSort.{u2} S) s) S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6))))))) S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) (Finsupp.addCommMonoid.{u2, u2} (coeSort.{succ u2, succ (succ 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i) S') -> (forall (x : S), (forall (r : coeSort.{succ u2, succ (succ u2)} (Set.{u2} S) Type.{u2} (Set.hasCoeToSort.{u2} S) s), Exists.{1} Nat (fun (n : Nat) => Membership.Mem.{u2, u2} S (Subalgebra.{u1, u2} R S _inst_1 (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_7) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R S _inst_1 (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_7) S (Subalgebra.setLike.{u1, u2} R S _inst_1 (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_7)) (SMul.smul.{u2, u2} S S (Mul.toSMul.{u2} S (Distrib.toHasMul.{u2} S (Ring.toDistrib.{u2} S (CommRing.toRing.{u2} S _inst_6)))) (HPow.hPow.{u2, 0, u2} S Nat S (instHPow.{u2, 0} S Nat (Monoid.Pow.{u2} S (Ring.toMonoid.{u2} S (CommRing.toRing.{u2} S _inst_6)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} S) Type.{u2} (Set.hasCoeToSort.{u2} S) s) S (HasLiftT.mk.{succ u2, succ u2} 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 but is expected to have type
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(CommRing.toRing.{u1} S _inst_6)))) (Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6))))) S (Finsupp.addCommMonoid.{u1, u1} (Set.Elem.{u1} S s) S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_6))))) (Finsupp.module.{u1, u1, u1} (Set.Elem.{u1} S s) S S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6))))) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)))) (_private.Mathlib.RingTheory.Ideal.Operations.0.Ideal.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRing.{u1, u1} S S (CommRing.toCommSemiring.{u1} S _inst_6) _inst_6 (Algebra.id.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)))) (Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6))))) (fun (_x : Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6))))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6))))) => S) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} S S (Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6))))) S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) (Finsupp.addCommMonoid.{u1, u1} (Set.Elem.{u1} S s) S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_6))))) (Finsupp.module.{u1, u1, u1} (Set.Elem.{u1} S s) S S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6))))) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)))) (_private.Mathlib.RingTheory.Ideal.Operations.0.Ideal.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRing.{u1, u1} S S (CommRing.toCommSemiring.{u1} S _inst_6) _inst_6 (Algebra.id.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6))) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6))))) (Finsupp.total.{u1, u1, u1} (Set.Elem.{u1} S s) S S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_6))))) (_private.Mathlib.RingTheory.Ideal.Operations.0.Ideal.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRing.{u1, u1} S S (CommRing.toCommSemiring.{u1} S _inst_6) _inst_6 (Algebra.id.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6))) (Subtype.val.{succ u1} S (fun (x : S) => Membership.mem.{u1, u1} S (Set.{u1} S) (Set.instMembershipSet.{u1} S) x s))) l) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6))))) => S) l) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6))))) => S) l) (NonAssocRing.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6))))) => S) l) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6))))) => S) l) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6))))) => S) l) _inst_6)))))) -> (HasSubset.Subset.{u1} (Set.{u1} S) (Set.instHasSubsetSet.{u1} S) s (SetLike.coe.{u1, u1} (Subalgebra.{u2, u1} R S _inst_1 (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) _inst_7) S (Subalgebra.instSetLikeSubalgebra.{u2, u1} R S _inst_1 (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) _inst_7) S')) -> (forall (i : Set.Elem.{u1} S s), Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : Set.Elem.{u1} S s) => S) i) (Subalgebra.{u2, u1} R S _inst_1 (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) _inst_7) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R S _inst_1 (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) _inst_7) S (Subalgebra.instSetLikeSubalgebra.{u2, u1} R S _inst_1 (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) _inst_7)) (FunLike.coe.{succ u1, succ u1, succ u1} (Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (CommMonoidWithZero.toZero.{u1} S (CommSemiring.toCommMonoidWithZero.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)))) (Set.Elem.{u1} S s) (fun (_x : Set.Elem.{u1} S s) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : Set.Elem.{u1} S s) => S) _x) (Finsupp.funLike.{u1, u1} (Set.Elem.{u1} S s) S (CommMonoidWithZero.toZero.{u1} S (CommSemiring.toCommMonoidWithZero.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)))) l i) S') -> (forall (x : S), (forall (r : Set.Elem.{u1} S s), Exists.{1} Nat (fun (n : Nat) => Membership.mem.{u1, u1} S (Subalgebra.{u2, u1} R S _inst_1 (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) _inst_7) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R S _inst_1 (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) _inst_7) S (Subalgebra.instSetLikeSubalgebra.{u2, u1} R S _inst_1 (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) _inst_7)) (HSMul.hSMul.{u1, u1, u1} S S S (instHSMul.{u1, u1} S S (Algebra.toSMul.{u1, u1} S S (CommRing.toCommSemiring.{u1} S _inst_6) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) (Algebra.id.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)))) (HPow.hPow.{u1, 0, u1} S Nat S (instHPow.{u1, 0} S Nat (Monoid.Pow.{u1} S (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)))))) (Subtype.val.{succ u1} S (fun (x : S) => Membership.mem.{u1, u1} S (Set.{u1} S) (Set.instMembershipSet.{u1} S) x s) r) n) x) S')) -> (Membership.mem.{u1, u1} S (Subalgebra.{u2, u1} R S _inst_1 (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) _inst_7) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R S _inst_1 (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) _inst_7) S (Subalgebra.instSetLikeSubalgebra.{u2, u1} R S _inst_1 (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) _inst_7)) x S'))
 Case conversion may be inaccurate. Consider using '#align subalgebra.mem_of_span_eq_top_of_smul_pow_mem Subalgebra.mem_of_span_eq_top_of_smul_pow_memₓ'. -/

bump to nightly-2023-03-21-20

mathlib commit https://github.com/leanprover-community/mathlib/commit/290a7ba01fbcab1b64757bdaa270d28f4dcede35

563f4a0b

Diff

@@ -2300,27 +2300,27 @@ theorem smul_def [SMul A α] {S : Subalgebra R A} (g : S) (m : α) : g • m = (
   rfl
 #align subalgebra.smul_def Subalgebra.smul_def
 
-/- warning: subalgebra.smul_comm_class_left -> Subalgebra.sMulCommClass_left is a dubious translation:
+/- warning: subalgebra.smul_comm_class_left -> Subalgebra.smulCommClass_left is a dubious translation:
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {α : Type.{u3}} {β : Type.{u4}} [_inst_6 : SMul.{u2, u4} A β] [_inst_7 : SMul.{u3, u4} α β] [_inst_8 : SMulCommClass.{u2, u3, u4} A α β _inst_6 _inst_7] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), SMulCommClass.{u2, u3, u4} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) α β (Subalgebra.hasSmul.{u1, u2, u4} R A _inst_1 _inst_2 _inst_3 β _inst_6 S) _inst_7
 but is expected to have type
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {α : Type.{u3}} {β : Type.{u4}} [_inst_6 : SMul.{u2, u4} A β] [_inst_7 : SMul.{u3, u4} α β] [_inst_8 : SMulCommClass.{u2, u3, u4} A α β _inst_6 _inst_7] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), SMulCommClass.{u2, u3, u4} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) α β (Subalgebra.instSMulSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebra.{u1, u2, u4} R A _inst_1 _inst_2 _inst_3 β _inst_6 S) _inst_7
-Case conversion may be inaccurate. Consider using '#align subalgebra.smul_comm_class_left Subalgebra.sMulCommClass_leftₓ'. -/
-instance sMulCommClass_left [SMul A β] [SMul α β] [SMulCommClass A α β] (S : Subalgebra R A) :
+Case conversion may be inaccurate. Consider using '#align subalgebra.smul_comm_class_left Subalgebra.smulCommClass_leftₓ'. -/
+instance smulCommClass_left [SMul A β] [SMul α β] [SMulCommClass A α β] (S : Subalgebra R A) :
     SMulCommClass S α β :=
   S.toSubsemiring.smulCommClass_left
-#align subalgebra.smul_comm_class_left Subalgebra.sMulCommClass_left
+#align subalgebra.smul_comm_class_left Subalgebra.smulCommClass_left
 
-/- warning: subalgebra.smul_comm_class_right -> Subalgebra.sMulCommClass_right is a dubious translation:
+/- warning: subalgebra.smul_comm_class_right -> Subalgebra.smulCommClass_right is a dubious translation:
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {α : Type.{u3}} {β : Type.{u4}} [_inst_6 : SMul.{u3, u4} α β] [_inst_7 : SMul.{u2, u4} A β] [_inst_8 : SMulCommClass.{u3, u2, u4} α A β _inst_6 _inst_7] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), SMulCommClass.{u3, u2, u4} α (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) β _inst_6 (Subalgebra.hasSmul.{u1, u2, u4} R A _inst_1 _inst_2 _inst_3 β _inst_7 S)
 but is expected to have type
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {α : Type.{u3}} {β : Type.{u4}} [_inst_6 : SMul.{u3, u4} α β] [_inst_7 : SMul.{u2, u4} A β] [_inst_8 : SMulCommClass.{u3, u2, u4} α A β _inst_6 _inst_7] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), SMulCommClass.{u3, u2, u4} α (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) β _inst_6 (Subalgebra.instSMulSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebra.{u1, u2, u4} R A _inst_1 _inst_2 _inst_3 β _inst_7 S)
-Case conversion may be inaccurate. Consider using '#align subalgebra.smul_comm_class_right Subalgebra.sMulCommClass_rightₓ'. -/
-instance sMulCommClass_right [SMul α β] [SMul A β] [SMulCommClass α A β] (S : Subalgebra R A) :
+Case conversion may be inaccurate. Consider using '#align subalgebra.smul_comm_class_right Subalgebra.smulCommClass_rightₓ'. -/
+instance smulCommClass_right [SMul α β] [SMul A β] [SMulCommClass α A β] (S : Subalgebra R A) :
     SMulCommClass α S β :=
   S.toSubsemiring.smulCommClass_right
-#align subalgebra.smul_comm_class_right Subalgebra.sMulCommClass_right
+#align subalgebra.smul_comm_class_right Subalgebra.smulCommClass_right
 
 /- warning: subalgebra.is_scalar_tower_left -> Subalgebra.isScalarTower_left is a dubious translation:
 lean 3 declaration is

bump to nightly-2023-03-18-14

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

73d15350

Diff

@@ -638,7 +638,7 @@ def toSubmodule : Subalgebra R A ↪o Submodule R A
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) {x : A}, Iff (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A 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 but is expected to have type
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(Function.instEmbeddingLikeEmbedding.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (RelEmbedding.toEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S)) (Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) {x : A}, Iff (Membership.mem.{u2, u2} A ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) (SetLike.instMembership.{u2, u2} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (FunLike.coe.{succ u2, succ u2, succ u2} (Function.Embedding.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (fun (_x : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) _x) (EmbeddingLike.toFunLike.{succ u2, succ u2, succ u2} (Function.Embedding.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Function.instEmbeddingLikeEmbedding.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (RelEmbedding.toEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S)) (Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)
 Case conversion may be inaccurate. Consider using '#align subalgebra.mem_to_submodule Subalgebra.mem_toSubmoduleₓ'. -/
 /- TODO: bundle other forgetful maps between algebraic substructures, e.g.
   `to_subsemiring` and `to_subring` in this file. -/
@@ -651,7 +651,7 @@ theorem mem_toSubmodule {x} : x ∈ S.toSubmodule ↔ x ∈ S :=
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), Eq.{succ u2} (Set.{u2} A) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (coeFn.{succ u2, succ u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (fun (_x : RelEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) => (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) -> (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (RelEmbedding.hasCoeToFun.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) S)) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) S)
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), Eq.{succ u2} (Set.{u2} A) (SetLike.coe.{u2, u2} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (FunLike.coe.{succ u2, succ u2, succ u2} (Function.Embedding.{succ u2, 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(CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Function.instEmbeddingLikeEmbedding.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (RelEmbedding.toEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S)) (SetLike.coe.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) S)
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), Eq.{succ u2} (Set.{u2} A) (SetLike.coe.{u2, u2} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (FunLike.coe.{succ u2, succ u2, succ u2} (Function.Embedding.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (fun (_x : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) _x) (EmbeddingLike.toFunLike.{succ u2, succ u2, succ u2} (Function.Embedding.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Function.instEmbeddingLikeEmbedding.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (RelEmbedding.toEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S)) (SetLike.coe.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) S)
 Case conversion may be inaccurate. Consider using '#align subalgebra.coe_to_submodule Subalgebra.coe_toSubmoduleₓ'. -/
 @[simp]
 theorem coe_toSubmodule (S : Subalgebra R A) : (↑S.toSubmodule : Set A) = S :=
@@ -888,7 +888,7 @@ theorem toSubring_subtype {R A : Type _} [CommRing R] [Ring A] [Algebra R A] (S
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Subalgebra.toSubmoduleEquiv._proof_1.{u1} R _inst_1) (Subalgebra.toSubmoduleEquiv._proof_2.{u1} R _inst_1) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R A 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 but is expected to have type
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x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S)) (Subalgebra.instModuleSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToNonAssocSemiringToSubsemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S)
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (fun (a : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) a) (EmbeddingLike.toFunLike.{succ u2, succ u2, succ u2} (Function.Embedding.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A 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(Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S))) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Submodule.addCommMonoid.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) 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x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Subsemiring.toNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2) (Subalgebra.toSubsemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S)))) (Submodule.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (FunLike.coe.{succ u2, succ u2, succ u2} (Function.Embedding.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (fun (_x : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) _x) (EmbeddingLike.toFunLike.{succ u2, succ u2, succ u2} (Function.Embedding.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Function.instEmbeddingLikeEmbedding.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (RelEmbedding.toEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S)) (Subalgebra.instModuleSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToNonAssocSemiringToSubsemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S)
 Case conversion may be inaccurate. Consider using '#align subalgebra.to_submodule_equiv Subalgebra.toSubmoduleEquivₓ'. -/
 /-- Linear equivalence between `S : submodule R A` and `S`. Though these types are equal,
 we define it as a `linear_equiv` to avoid type equalities. -/
@@ -1059,7 +1059,7 @@ variable (p : Submodule R A)
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (p : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)), (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (OfNat.ofNat.{u2} A 1 (OfNat.mk.{u2} A 1 (One.one.{u2} A (AddMonoidWithOne.toOne.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))))) p) -> (forall (x : A) (y : A), (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x p) -> (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) y p) -> (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y) p)) -> (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (p : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)), (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (OfNat.ofNat.{u2} A 1 (One.toOfNat1.{u2} A (Semiring.toOne.{u2} A _inst_2))) p) -> (forall (x : A) (y : A), (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x p) -> (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) y p) -> (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) x y) p)) -> (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (p : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)), (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (OfNat.ofNat.{u2} A 1 (One.toOfNat1.{u2} A (Semiring.toOne.{u2} A _inst_2))) p) -> (forall (x : A) (y : A), (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x p) -> (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) y p) -> (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) x y) p)) -> (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)
 Case conversion may be inaccurate. Consider using '#align submodule.to_subalgebra Submodule.toSubalgebraₓ'. -/
 /-- A submodule containing `1` and closed under multiplication is a subalgebra. -/
 def toSubalgebra (p : Submodule R A) (h_one : (1 : A) ∈ p)
@@ -1075,7 +1075,7 @@ def toSubalgebra (p : Submodule R A) (h_one : (1 : A) ∈ p)
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {p : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {h_one : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (OfNat.ofNat.{u2} A 1 (OfNat.mk.{u2} A 1 (One.one.{u2} A (AddMonoidWithOne.toOne.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))))) p} {h_mul : forall (x : A) (y : A), (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x p) -> (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) y p) -> (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y) p)} {x : A}, Iff (Membership.Mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x (Submodule.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 p h_one h_mul)) (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x p)
 but is expected to have type
-  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u1} A] [_inst_3 : Algebra.{u2, u1} R A _inst_1 _inst_2] {p : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)} {h_one : Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) (OfNat.ofNat.{u1} A 1 (One.toOfNat1.{u1} A (Semiring.toOne.{u1} A _inst_2))) p} {h_mul : forall (x : A) (y : A), (Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) x p) -> (Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) y p) -> (Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u1, u1, u1} A A A (instHMul.{u1} A (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) x y) p)} {x : A}, Iff (Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3)) x (Submodule.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 p h_one h_mul)) (Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) x p)
+  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u1} A] [_inst_3 : Algebra.{u2, u1} R A _inst_1 _inst_2] {p : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)} {h_one : Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) (OfNat.ofNat.{u1} A 1 (One.toOfNat1.{u1} A (Semiring.toOne.{u1} A _inst_2))) p} {h_mul : forall (x : A) (y : A), (Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) x p) -> (Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) y p) -> (Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u1, u1, u1} A A A (instHMul.{u1} A (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) x y) p)} {x : A}, Iff (Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3)) x (Submodule.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 p h_one h_mul)) (Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) x p)
 Case conversion may be inaccurate. Consider using '#align submodule.mem_to_subalgebra Submodule.mem_toSubalgebraₓ'. -/
 @[simp]
 theorem mem_toSubalgebra {p : Submodule R A} {h_one h_mul} {x} :
@@ -1087,7 +1087,7 @@ theorem mem_toSubalgebra {p : Submodule R A} {h_one h_mul} {x} :
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (p : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (h_one : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (OfNat.ofNat.{u2} A 1 (OfNat.mk.{u2} A 1 (One.one.{u2} A (AddMonoidWithOne.toOne.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))))) p) (h_mul : forall (x : A) (y : A), (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x p) -> (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) y p) -> (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y) p)), Eq.{succ u2} (Set.{u2} A) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Submodule.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 p h_one h_mul)) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) p)
 but is expected to have type
-  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u1} A] [_inst_3 : Algebra.{u2, u1} R A _inst_1 _inst_2] (p : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (h_one : Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) (OfNat.ofNat.{u1} A 1 (One.toOfNat1.{u1} A (Semiring.toOne.{u1} A _inst_2))) p) (h_mul : forall (x : A) (y : A), (Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) x p) -> (Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) y p) -> (Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u1, u1, u1} A A A (instHMul.{u1} A (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) x y) p)), Eq.{succ u1} (Set.{u1} A) (SetLike.coe.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 p h_one h_mul)) (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) p)
+  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u1} A] [_inst_3 : Algebra.{u2, u1} R A _inst_1 _inst_2] (p : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (h_one : Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) (OfNat.ofNat.{u1} A 1 (One.toOfNat1.{u1} A (Semiring.toOne.{u1} A _inst_2))) p) (h_mul : forall (x : A) (y : A), (Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) x p) -> (Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) y p) -> (Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u1, u1, u1} A A A (instHMul.{u1} A (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) x y) p)), Eq.{succ u1} (Set.{u1} A) (SetLike.coe.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 p h_one h_mul)) (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) p)
 Case conversion may be inaccurate. Consider using '#align submodule.coe_to_subalgebra Submodule.coe_toSubalgebraₓ'. -/
 @[simp]
 theorem coe_toSubalgebra (p : Submodule R A) (h_one h_mul) :
@@ -1099,7 +1099,7 @@ theorem coe_toSubalgebra (p : Submodule R A) (h_one h_mul) :
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (s : Set.{u2} A) (h0 : Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) (OfNat.ofNat.{u2} A 0 (OfNat.mk.{u2} A 0 (Zero.zero.{u2} A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))))))) s) (hadd : forall {a : A} {b : A}, (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) a s) -> (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) b s) -> (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (AddZeroClass.toHasAdd.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))))) a b) s)) (hsmul : forall (c : R) {x : A}, (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) x s) -> (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) (SMul.smul.{u1, u2} R A (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) c x) s)) (h1 : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (OfNat.ofNat.{u2} A 1 (OfNat.mk.{u2} A 1 (One.one.{u2} A (AddMonoidWithOne.toOne.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))))) (Submodule.mk.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) s hadd h0 hsmul)) (hmul : forall (x : A) (y : A), (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (Submodule.mk.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) s hadd h0 hsmul)) -> (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) y (Submodule.mk.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) s hadd h0 hsmul)) -> (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y) (Submodule.mk.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) s hadd h0 hsmul))), Eq.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (Submodule.mk.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) s hadd h0 hsmul) h1 hmul) (Subalgebra.mk.{u1, u2} R A _inst_1 _inst_2 _inst_3 s hmul h1 hadd h0 (fun (r : R) => Eq.mpr.{0} (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) s) (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) (SMul.smul.{u1, u2} R A (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) r (OfNat.ofNat.{u2} A 1 (OfNat.mk.{u2} A 1 (One.one.{u2} A (AddMonoidWithOne.toOne.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))))) s) (id_tag Tactic.IdTag.rw (Eq.{1} Prop (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) s) (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) (SMul.smul.{u1, u2} R A (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) r (OfNat.ofNat.{u2} A 1 (OfNat.mk.{u2} A 1 (One.one.{u2} A (AddMonoidWithOne.toOne.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))))) s)) (Eq.ndrec.{0, succ u2} A (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) (fun (_a : A) => Eq.{1} Prop (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) s) (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) _a s)) (rfl.{1} Prop (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) s)) (SMul.smul.{u1, u2} R A (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) r (OfNat.ofNat.{u2} A 1 (OfNat.mk.{u2} A 1 (One.one.{u2} A (AddMonoidWithOne.toOne.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))))) (Algebra.algebraMap_eq_smul_one.{u1, u2} R A _inst_1 _inst_2 _inst_3 r))) (hsmul r (OfNat.ofNat.{u2} A 1 (OfNat.mk.{u2} A 1 (One.one.{u2} A (AddMonoidWithOne.toOne.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))))) h1)))
 but is expected to have type
-  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u1} A] [_inst_3 : Algebra.{u2, u1} R A _inst_1 _inst_2] (s : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (h0 : Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) (OfNat.ofNat.{u1} A 1 (One.toOfNat1.{u1} A (Semiring.toOne.{u1} A _inst_2))) s) (hadd : forall (a : A) (b : A), (Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) a s) -> (Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) b s) -> (Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u1, u1, u1} A A A (instHMul.{u1} A (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) a b) s)), Eq.{succ u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 s h0 hadd) (Subalgebra.mk.{u2, u1} R A _inst_1 _inst_2 _inst_3 (Subsemiring.mk.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Submonoid.mk.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemigroup.mk.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) s) hadd) h0) (fun {a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6428 : A} {b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6429 : A} => Submodule.add_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6428 b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6429) (Submodule.zero_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s)) (fun (r : R) => Eq.mpr.{0} (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) (Set.{u1} A) (Set.instMembershipSet.{u1} A) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2) (RingHom.instRingHomClassRingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2))))) (algebraMap.{u2, u1} R A _inst_1 _inst_2 _inst_3) r) (Subsemigroup.carrier.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (Submonoid.toSubsemigroup.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemiring.toSubmonoid.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Subsemiring.mk.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Submonoid.mk.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemigroup.mk.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) s) hadd) h0) (fun {a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6428 : A} {b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6429 : A} => Submodule.add_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6428 b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6429) (Submodule.zero_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s)))))) (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) (Set.{u1} A) (Set.instMembershipSet.{u1} A) (HSMul.hSMul.{u2, u1, u1} R A A (instHSMul.{u2, u1} R A (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_2 _inst_3)) r (OfNat.ofNat.{u1} A 1 (One.toOfNat1.{u1} A (Semiring.toOne.{u1} A _inst_2)))) (Subsemigroup.carrier.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (Submonoid.toSubsemigroup.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemiring.toSubmonoid.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Subsemiring.mk.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Submonoid.mk.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemigroup.mk.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) s) hadd) h0) (fun {a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6428 : A} {b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6429 : A} => Submodule.add_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6428 b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6429) (Submodule.zero_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6428 b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6429) (Submodule.zero_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s))))))) (Eq.refl.{1} Prop (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) (Set.{u1} A) (Set.instMembershipSet.{u1} A) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) 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u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2) (RingHom.instRingHomClassRingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2))))) (algebraMap.{u2, u1} R A _inst_1 _inst_2 _inst_3) r) (Subsemigroup.carrier.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (Submonoid.toSubsemigroup.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemiring.toSubmonoid.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Subsemiring.mk.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Submonoid.mk.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemigroup.mk.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) s) hadd) h0) (fun {a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6428 : A} {b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6429 : A} => Submodule.add_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6428 b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6429) (Submodule.zero_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s))))))) (HSMul.hSMul.{u2, u1, u1} R A A (instHSMul.{u2, u1} R A (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_2 _inst_3)) r (OfNat.ofNat.{u1} A 1 (One.toOfNat1.{u1} A (Semiring.toOne.{u1} A _inst_2)))) (Algebra.algebraMap_eq_smul_one.{u2, u1} R A _inst_1 _inst_2 _inst_3 r))) (Submodule.smul_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s (OfNat.ofNat.{u1} A 1 (One.toOfNat1.{u1} A (Semiring.toOne.{u1} A _inst_2))) r h0)))
+  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u1} A] [_inst_3 : Algebra.{u2, u1} R A _inst_1 _inst_2] (s : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (h0 : Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) (OfNat.ofNat.{u1} A 1 (One.toOfNat1.{u1} A (Semiring.toOne.{u1} A _inst_2))) s) (hadd : forall (a : A) (b : A), (Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) a s) -> (Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) b s) -> (Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u1, u1, u1} A A A (instHMul.{u1} A (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) a b) s)), Eq.{succ u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 s h0 hadd) (Subalgebra.mk.{u2, u1} R A _inst_1 _inst_2 _inst_3 (Subsemiring.mk.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Submonoid.mk.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemigroup.mk.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) s) hadd) h0) (fun {a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6428 : A} {b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6429 : A} => Submodule.add_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6428 b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6429) (Submodule.zero_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s)) (fun (r : R) => Eq.mpr.{0} (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) (Set.{u1} A) (Set.instMembershipSet.{u1} A) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2) (RingHom.instRingHomClassRingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2))))) (algebraMap.{u2, u1} R A _inst_1 _inst_2 _inst_3) r) (Subsemigroup.carrier.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (Submonoid.toSubsemigroup.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemiring.toSubmonoid.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Subsemiring.mk.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Submonoid.mk.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemigroup.mk.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) s) hadd) h0) (fun {a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6428 : A} {b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6429 : A} => Submodule.add_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6428 b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6429) (Submodule.zero_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s)))))) (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) (Set.{u1} A) (Set.instMembershipSet.{u1} A) (HSMul.hSMul.{u2, u1, u1} R A A (instHSMul.{u2, u1} R A (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_2 _inst_3)) r (OfNat.ofNat.{u1} A 1 (One.toOfNat1.{u1} A (Semiring.toOne.{u1} A _inst_2)))) (Subsemigroup.carrier.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (Submonoid.toSubsemigroup.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemiring.toSubmonoid.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Subsemiring.mk.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Submonoid.mk.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemigroup.mk.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) 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_inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) s) hadd) h0) (fun {a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6428 : A} {b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6429 : A} => Submodule.add_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6428 b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6429) (Submodule.zero_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s)))))) (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) (Set.{u1} A) (Set.instMembershipSet.{u1} A) _a (Subsemigroup.carrier.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (Submonoid.toSubsemigroup.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemiring.toSubmonoid.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Subsemiring.mk.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Submonoid.mk.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemigroup.mk.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) s) hadd) h0) (fun {a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6428 : A} {b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6429 : A} => Submodule.add_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6428 b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6429) (Submodule.zero_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s))))))) (Eq.refl.{1} Prop (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) (Set.{u1} A) (Set.instMembershipSet.{u1} A) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2) (RingHom.instRingHomClassRingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2))))) (algebraMap.{u2, u1} R A _inst_1 _inst_2 _inst_3) r) (Subsemigroup.carrier.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (Submonoid.toSubsemigroup.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemiring.toSubmonoid.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Subsemiring.mk.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Submonoid.mk.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemigroup.mk.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) s) hadd) h0) (fun {a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6428 : A} {b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6429 : A} => Submodule.add_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6428 b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6429) (Submodule.zero_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s))))))) (HSMul.hSMul.{u2, u1, u1} R A A (instHSMul.{u2, u1} R A (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_2 _inst_3)) r (OfNat.ofNat.{u1} A 1 (One.toOfNat1.{u1} A (Semiring.toOne.{u1} A _inst_2)))) (Algebra.algebraMap_eq_smul_one.{u2, u1} R A _inst_1 _inst_2 _inst_3 r))) (Submodule.smul_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s (OfNat.ofNat.{u1} A 1 (One.toOfNat1.{u1} A (Semiring.toOne.{u1} A _inst_2))) r h0)))
 Case conversion may be inaccurate. Consider using '#align submodule.to_subalgebra_mk Submodule.toSubalgebra_mkₓ'. -/
 @[simp]
 theorem toSubalgebra_mk (s : Set A) (h0 hadd hsmul h1 hmul) :
@@ -1115,7 +1115,7 @@ theorem toSubalgebra_mk (s : Set A) (h0 hadd hsmul h1 hmul) :
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (p : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (h_one : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (OfNat.ofNat.{u2} A 1 (OfNat.mk.{u2} A 1 (One.one.{u2} A (AddMonoidWithOne.toOne.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))))) p) (h_mul : forall (x : A) (y : A), (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x p) -> (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) y p) -> (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y) p)), Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (coeFn.{succ u2, succ u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (fun (_x : RelEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) => (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) -> (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (RelEmbedding.hasCoeToFun.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 p h_one h_mul)) p
 but is expected to have type
-  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u1} A] [_inst_3 : Algebra.{u2, u1} R A _inst_1 _inst_2] (p : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (h_one : Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) (OfNat.ofNat.{u1} A 1 (One.toOfNat1.{u1} A (Semiring.toOne.{u1} A _inst_2))) p) (h_mul : forall (x : A) (y : A), (Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) x p) -> (Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) y p) -> (Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u1, u1, u1} A A A (instHMul.{u1} A (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) x y) p)), Eq.{succ u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Submodule.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 p h_one h_mul)) (FunLike.coe.{succ u1, succ u1, succ u1} (Function.Embedding.{succ u1, succ u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (fun (_x : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) _x) (EmbeddingLike.toFunLike.{succ u1, succ u1, succ u1} (Function.Embedding.{succ u1, succ u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Function.instEmbeddingLikeEmbedding.{succ u1, succ u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)))) (RelEmbedding.toEmbedding.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => LE.le.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Subalgebra.toSubmodule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Submodule.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 p h_one h_mul)) p
+  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u1} A] [_inst_3 : Algebra.{u2, u1} R A _inst_1 _inst_2] (p : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (h_one : Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) (OfNat.ofNat.{u1} A 1 (One.toOfNat1.{u1} A (Semiring.toOne.{u1} A _inst_2))) p) (h_mul : forall (x : A) (y : A), (Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) x p) -> (Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) y p) -> (Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u1, u1, u1} A A A (instHMul.{u1} A (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) x y) p)), Eq.{succ u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Submodule.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 p h_one h_mul)) (FunLike.coe.{succ u1, succ u1, succ u1} (Function.Embedding.{succ u1, succ u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (fun (_x : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) _x) (EmbeddingLike.toFunLike.{succ u1, succ u1, succ u1} (Function.Embedding.{succ u1, succ u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Function.instEmbeddingLikeEmbedding.{succ u1, succ u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)))) (RelEmbedding.toEmbedding.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => LE.le.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Subalgebra.toSubmodule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Submodule.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 p h_one h_mul)) p
 Case conversion may be inaccurate. Consider using '#align submodule.to_subalgebra_to_submodule Submodule.toSubalgebra_toSubmoduleₓ'. -/
 @[simp]
 theorem toSubalgebra_toSubmodule (p : Submodule R A) (h_one h_mul) :

bump to nightly-2023-03-14-02

mathlib commit https://github.com/leanprover-community/mathlib/commit/2196ab363eb097c008d4497125e0dde23fb36db2

d4b38a42

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau, Yury Kudryashov
 
 ! This file was ported from Lean 3 source module algebra.algebra.subalgebra.basic
-! leanprover-community/mathlib commit c4658a649d216f57e99621708b09dcb3dcccbd23
+! leanprover-community/mathlib commit 69c6a5a12d8a2b159f20933e60115a4f2de62b58
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -16,6 +16,9 @@ import Mathbin.RingTheory.Ideal.Operations
 /-!
 # Subalgebras over Commutative Semiring
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 In this file we define `subalgebra`s and the usual operations on them (`map`, `comap`).
 
 More lemmas about `adjoin` can be found in `ring_theory.adjoin`.

bump to nightly-2023-03-11-22

mathlib commit https://github.com/leanprover-community/mathlib/commit/3180fab693e2cee3bff62675571264cb8778b212

a8ee822f

Diff

@@ -161,7 +161,7 @@ variable (S : Subalgebra R A)
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (r : R), Membership.Mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) S
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (r : R), Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => A) r) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) S
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (r : R), Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) S
 Case conversion may be inaccurate. Consider using '#align subalgebra.algebra_map_mem Subalgebra.algebraMap_memₓ'. -/
 theorem algebraMap_mem (r : R) : algebraMap R A r ∈ S :=
   S.algebraMap_mem' r
@@ -181,7 +181,7 @@ theorem rangeS_le : (algebraMap R A).srange ≤ S.toSubsemiring := fun x ⟨r, h
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), HasSubset.Subset.{u2} (Set.{u2} A) (Set.hasSubset.{u2} A) (Set.range.{u2, succ u1} A R (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) S)
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), HasSubset.Subset.{u2} (Set.{u2} A) (Set.instHasSubsetSet.{u2} A) (Set.range.{u2, succ u1} A R (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (SetLike.coe.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) S)
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), HasSubset.Subset.{u2} (Set.{u2} A) (Set.instHasSubsetSet.{u2} A) (Set.range.{u2, succ u1} A R (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (SetLike.coe.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) S)
 Case conversion may be inaccurate. Consider using '#align subalgebra.range_subset Subalgebra.range_subsetₓ'. -/
 theorem range_subset : Set.range (algebraMap R A) ⊆ S := fun x ⟨r, hr⟩ => hr ▸ S.algebraMap_mem r
 #align subalgebra.range_subset Subalgebra.range_subset
@@ -190,7 +190,7 @@ theorem range_subset : Set.range (algebraMap R A) ⊆ S := fun x ⟨r, hr⟩ =>
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), LE.le.{u2} (Set.{u2} A) (Set.hasLe.{u2} A) (Set.range.{u2, succ u1} A R (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) S)
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), LE.le.{u2} (Set.{u2} A) (Set.instLESet.{u2} A) (Set.range.{u2, succ u1} A R (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (SetLike.coe.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) S)
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), LE.le.{u2} (Set.{u2} A) (Set.instLESet.{u2} A) (Set.range.{u2, succ u1} A R (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (SetLike.coe.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) S)
 Case conversion may be inaccurate. Consider using '#align subalgebra.range_le Subalgebra.range_leₓ'. -/
 theorem range_le : Set.range (algebraMap R A) ≤ S :=
   S.range_subset
@@ -787,7 +787,7 @@ theorem coe_smul [Semiring R'] [SMul R' R] [Module R' A] [IsScalarTower R' R A]
 lean 3 declaration is
   forall {R' : Type.{u2}} {R : Type.{u1}} {A : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u3} A] [_inst_3 : Algebra.{u1, u3} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) [_inst_8 : CommSemiring.{u2} R'] [_inst_9 : SMul.{u2, u1} R' R] [_inst_10 : Algebra.{u2, u3} R' A _inst_8 _inst_2] [_inst_11 : IsScalarTower.{u2, u1, u3} R' R A _inst_9 (SMulZeroClass.toHasSmul.{u1, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u1, u3} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toHasSmul.{u2, u3} R' A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} R' A (MulZeroClass.toHasZero.{u2} R' (MulZeroOneClass.toMulZeroClass.{u2} R' (MonoidWithZero.toMulZeroOneClass.{u2} R' (Semiring.toMonoidWithZero.{u2} R' (CommSemiring.toSemiring.{u2} R' _inst_8))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} R' A (Semiring.toMonoidWithZero.{u2} R' (CommSemiring.toSemiring.{u2} R' _inst_8)) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2)))))) (Module.toMulActionWithZero.{u2, u3} R' A (CommSemiring.toSemiring.{u2} R' _inst_8) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R' A _inst_8 _inst_2 _inst_10)))))] (r : R'), Eq.{succ u3} A ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u3} R A _inst_1 _inst_2 _inst_3)) S) A (HasLiftT.mk.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u3} R A _inst_1 _inst_2 _inst_3)) S) A (CoeTCₓ.coe.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u3} R A _inst_1 _inst_2 _inst_3)) S) A (coeBase.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u3} R A _inst_1 _inst_2 _inst_3)) S) A (coeSubtype.{succ u3} A (fun (x : A) => Membership.Mem.{u3, u3} A (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u3, u3} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u3} R A _inst_1 _inst_2 _inst_3)) x S))))) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (RingHom.{u2, u3} R' (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u3} R A _inst_1 _inst_2 _inst_3)) S) (Semiring.toNonAssocSemiring.{u2} R' (CommSemiring.toSemiring.{u2} R' _inst_8)) (Semiring.toNonAssocSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u3} R A _inst_1 _inst_2 _inst_3)) S) (Subalgebra.toSemiring.{u1, u3} R A _inst_1 _inst_2 _inst_3 S))) (fun (_x : RingHom.{u2, u3} R' (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u3} R A _inst_1 _inst_2 _inst_3)) S) (Semiring.toNonAssocSemiring.{u2} R' (CommSemiring.toSemiring.{u2} R' _inst_8)) (Semiring.toNonAssocSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u3} R A _inst_1 _inst_2 _inst_3)) S) (Subalgebra.toSemiring.{u1, u3} R A _inst_1 _inst_2 _inst_3 S))) => R' -> (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u3} R A _inst_1 _inst_2 _inst_3)) S)) (RingHom.hasCoeToFun.{u2, u3} R' (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u3} R A _inst_1 _inst_2 _inst_3)) S) (Semiring.toNonAssocSemiring.{u2} R' (CommSemiring.toSemiring.{u2} R' _inst_8)) (Semiring.toNonAssocSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u3} R A _inst_1 _inst_2 _inst_3)) S) (Subalgebra.toSemiring.{u1, u3} R A _inst_1 _inst_2 _inst_3 S))) (algebraMap.{u2, u3} R' (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u3} R A _inst_1 _inst_2 _inst_3)) S) _inst_8 (Subalgebra.toSemiring.{u1, u3} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.algebra'.{u1, u2, u3} R' R A _inst_1 _inst_2 _inst_3 S _inst_8 _inst_9 _inst_10 _inst_11)) r)) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (RingHom.{u2, u3} R' A (Semiring.toNonAssocSemiring.{u2} R' (CommSemiring.toSemiring.{u2} R' _inst_8)) (Semiring.toNonAssocSemiring.{u3} A _inst_2)) (fun (_x : RingHom.{u2, u3} R' A (Semiring.toNonAssocSemiring.{u2} R' (CommSemiring.toSemiring.{u2} R' _inst_8)) (Semiring.toNonAssocSemiring.{u3} A _inst_2)) => R' -> A) (RingHom.hasCoeToFun.{u2, u3} R' A (Semiring.toNonAssocSemiring.{u2} R' (CommSemiring.toSemiring.{u2} R' _inst_8)) (Semiring.toNonAssocSemiring.{u3} A _inst_2)) (algebraMap.{u2, u3} R' A _inst_8 _inst_2 _inst_10) r)
 but is expected to have type
-  forall {R' : Type.{u2}} {R : Type.{u1}} {A : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u3} A] [_inst_3 : Algebra.{u1, u3} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) [_inst_8 : CommSemiring.{u2} R'] [_inst_9 : SMul.{u2, u1} R' R] [_inst_10 : Algebra.{u2, u3} R' A _inst_8 _inst_2] [_inst_11 : IsScalarTower.{u2, u1, u3} R' R A _inst_9 (Algebra.toSMul.{u1, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.toSMul.{u2, u3} R' A _inst_8 _inst_2 _inst_10)] (r : R'), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R') => A) r) (Subtype.val.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Set.{u3} A) (Set.instMembershipSet.{u3} A) x (SetLike.coe.{u3, u3} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) S)) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RingHom.{u2, u3} R' (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3)) x S)) (Semiring.toNonAssocSemiring.{u2} R' (CommSemiring.toSemiring.{u2} R' _inst_8)) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3)) x S)) (Subalgebra.toSemiring.{u1, u3} R A _inst_1 _inst_2 _inst_3 S))) R' (fun (_x : R') => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R') => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3)) x S)) _x) (MulHomClass.toFunLike.{max u2 u3, u2, u3} (RingHom.{u2, u3} R' (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3)) x S)) (Semiring.toNonAssocSemiring.{u2} R' (CommSemiring.toSemiring.{u2} R' _inst_8)) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3)) x S)) (Subalgebra.toSemiring.{u1, u3} R A _inst_1 _inst_2 _inst_3 S))) R' (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3)) x S)) (NonUnitalNonAssocSemiring.toMul.{u2} R' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R' (Semiring.toNonAssocSemiring.{u2} R' (CommSemiring.toSemiring.{u2} R' _inst_8)))) (NonUnitalNonAssocSemiring.toMul.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3)) x S)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3)) x S)) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3)) x S)) (Subalgebra.toSemiring.{u1, u3} R A _inst_1 _inst_2 _inst_3 S)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} R' (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3)) x S)) (Semiring.toNonAssocSemiring.{u2} R' (CommSemiring.toSemiring.{u2} R' _inst_8)) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3)) x S)) (Subalgebra.toSemiring.{u1, u3} R A _inst_1 _inst_2 _inst_3 S))) R' (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3)) x S)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R' (Semiring.toNonAssocSemiring.{u2} R' (CommSemiring.toSemiring.{u2} R' _inst_8))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3)) x S)) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3)) x S)) (Subalgebra.toSemiring.{u1, u3} R A _inst_1 _inst_2 _inst_3 S))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} R' (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3)) x S)) (Semiring.toNonAssocSemiring.{u2} R' (CommSemiring.toSemiring.{u2} R' _inst_8)) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3)) x S)) (Subalgebra.toSemiring.{u1, u3} R A _inst_1 _inst_2 _inst_3 S))) R' (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3)) x S)) (Semiring.toNonAssocSemiring.{u2} R' (CommSemiring.toSemiring.{u2} R' _inst_8)) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3)) x S)) (Subalgebra.toSemiring.{u1, u3} R A _inst_1 _inst_2 _inst_3 S)) (RingHom.instRingHomClassRingHom.{u2, u3} R' (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3)) x S)) (Semiring.toNonAssocSemiring.{u2} R' (CommSemiring.toSemiring.{u2} R' _inst_8)) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3)) x S)) (Subalgebra.toSemiring.{u1, u3} R A _inst_1 _inst_2 _inst_3 S)))))) (algebraMap.{u2, u3} R' (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3)) x S)) _inst_8 (Subalgebra.toSemiring.{u1, u3} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.algebra'.{u1, u2, u3} R' R A _inst_1 _inst_2 _inst_3 S _inst_8 _inst_9 _inst_10 _inst_11)) r)) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RingHom.{u2, u3} R' A (Semiring.toNonAssocSemiring.{u2} R' (CommSemiring.toSemiring.{u2} R' _inst_8)) (Semiring.toNonAssocSemiring.{u3} A _inst_2)) R' (fun (_x : R') => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R') => A) _x) (MulHomClass.toFunLike.{max u2 u3, u2, u3} (RingHom.{u2, u3} R' A (Semiring.toNonAssocSemiring.{u2} R' (CommSemiring.toSemiring.{u2} R' _inst_8)) (Semiring.toNonAssocSemiring.{u3} A _inst_2)) R' A (NonUnitalNonAssocSemiring.toMul.{u2} R' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R' (Semiring.toNonAssocSemiring.{u2} R' (CommSemiring.toSemiring.{u2} R' _inst_8)))) (NonUnitalNonAssocSemiring.toMul.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} R' A (Semiring.toNonAssocSemiring.{u2} R' (CommSemiring.toSemiring.{u2} R' _inst_8)) (Semiring.toNonAssocSemiring.{u3} A _inst_2)) R' A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R' (Semiring.toNonAssocSemiring.{u2} R' (CommSemiring.toSemiring.{u2} R' _inst_8))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} R' A (Semiring.toNonAssocSemiring.{u2} R' (CommSemiring.toSemiring.{u2} R' _inst_8)) (Semiring.toNonAssocSemiring.{u3} A _inst_2)) R' A (Semiring.toNonAssocSemiring.{u2} R' (CommSemiring.toSemiring.{u2} R' _inst_8)) (Semiring.toNonAssocSemiring.{u3} A _inst_2) (RingHom.instRingHomClassRingHom.{u2, u3} R' A (Semiring.toNonAssocSemiring.{u2} R' (CommSemiring.toSemiring.{u2} R' _inst_8)) (Semiring.toNonAssocSemiring.{u3} A _inst_2))))) (algebraMap.{u2, u3} R' A _inst_8 _inst_2 _inst_10) r)
+  forall {R' : Type.{u2}} {R : Type.{u1}} {A : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u3} A] [_inst_3 : Algebra.{u1, u3} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) [_inst_8 : CommSemiring.{u2} R'] [_inst_9 : SMul.{u2, u1} R' R] [_inst_10 : Algebra.{u2, u3} R' A _inst_8 _inst_2] [_inst_11 : IsScalarTower.{u2, u1, u3} R' R A _inst_9 (Algebra.toSMul.{u1, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.toSMul.{u2, u3} R' A _inst_8 _inst_2 _inst_10)] (r : R'), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R') => A) r) (Subtype.val.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Set.{u3} A) (Set.instMembershipSet.{u3} A) x (SetLike.coe.{u3, u3} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) S)) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RingHom.{u2, u3} R' (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3)) x S)) (Semiring.toNonAssocSemiring.{u2} R' (CommSemiring.toSemiring.{u2} R' _inst_8)) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3)) x S)) (Subalgebra.toSemiring.{u1, u3} R A _inst_1 _inst_2 _inst_3 S))) R' (fun (_x : R') => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R') => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3)) x S)) _x) (MulHomClass.toFunLike.{max u2 u3, u2, u3} (RingHom.{u2, u3} R' (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3)) x S)) (Semiring.toNonAssocSemiring.{u2} R' (CommSemiring.toSemiring.{u2} R' _inst_8)) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3)) x S)) (Subalgebra.toSemiring.{u1, u3} R A _inst_1 _inst_2 _inst_3 S))) R' (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3)) x S)) (NonUnitalNonAssocSemiring.toMul.{u2} R' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R' (Semiring.toNonAssocSemiring.{u2} R' (CommSemiring.toSemiring.{u2} R' _inst_8)))) (NonUnitalNonAssocSemiring.toMul.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3)) x S)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3)) x S)) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3)) x S)) (Subalgebra.toSemiring.{u1, u3} R A _inst_1 _inst_2 _inst_3 S)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} R' (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3)) x S)) (Semiring.toNonAssocSemiring.{u2} R' (CommSemiring.toSemiring.{u2} R' _inst_8)) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3)) x S)) (Subalgebra.toSemiring.{u1, u3} R A _inst_1 _inst_2 _inst_3 S))) R' (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3)) x S)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R' (Semiring.toNonAssocSemiring.{u2} R' (CommSemiring.toSemiring.{u2} R' _inst_8))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3)) x S)) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3)) x S)) (Subalgebra.toSemiring.{u1, u3} R A _inst_1 _inst_2 _inst_3 S))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} R' (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3)) x S)) (Semiring.toNonAssocSemiring.{u2} R' (CommSemiring.toSemiring.{u2} R' _inst_8)) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3)) x S)) (Subalgebra.toSemiring.{u1, u3} R A _inst_1 _inst_2 _inst_3 S))) R' (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3)) x S)) (Semiring.toNonAssocSemiring.{u2} R' (CommSemiring.toSemiring.{u2} R' _inst_8)) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3)) x S)) (Subalgebra.toSemiring.{u1, u3} R A _inst_1 _inst_2 _inst_3 S)) (RingHom.instRingHomClassRingHom.{u2, u3} R' (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3)) x S)) (Semiring.toNonAssocSemiring.{u2} R' (CommSemiring.toSemiring.{u2} R' _inst_8)) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3)) x S)) (Subalgebra.toSemiring.{u1, u3} R A _inst_1 _inst_2 _inst_3 S)))))) (algebraMap.{u2, u3} R' (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3)) x S)) _inst_8 (Subalgebra.toSemiring.{u1, u3} R A _inst_1 _inst_2 _inst_3 S) (Subalgebra.algebra'.{u1, u2, u3} R' R A _inst_1 _inst_2 _inst_3 S _inst_8 _inst_9 _inst_10 _inst_11)) r)) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RingHom.{u2, u3} R' A (Semiring.toNonAssocSemiring.{u2} R' (CommSemiring.toSemiring.{u2} R' _inst_8)) (Semiring.toNonAssocSemiring.{u3} A _inst_2)) R' (fun (_x : R') => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R') => A) _x) (MulHomClass.toFunLike.{max u2 u3, u2, u3} (RingHom.{u2, u3} R' A (Semiring.toNonAssocSemiring.{u2} R' (CommSemiring.toSemiring.{u2} R' _inst_8)) (Semiring.toNonAssocSemiring.{u3} A _inst_2)) R' A (NonUnitalNonAssocSemiring.toMul.{u2} R' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R' (Semiring.toNonAssocSemiring.{u2} R' (CommSemiring.toSemiring.{u2} R' _inst_8)))) (NonUnitalNonAssocSemiring.toMul.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} R' A (Semiring.toNonAssocSemiring.{u2} R' (CommSemiring.toSemiring.{u2} R' _inst_8)) (Semiring.toNonAssocSemiring.{u3} A _inst_2)) R' A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R' (Semiring.toNonAssocSemiring.{u2} R' (CommSemiring.toSemiring.{u2} R' _inst_8))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} R' A (Semiring.toNonAssocSemiring.{u2} R' (CommSemiring.toSemiring.{u2} R' _inst_8)) (Semiring.toNonAssocSemiring.{u3} A _inst_2)) R' A (Semiring.toNonAssocSemiring.{u2} R' (CommSemiring.toSemiring.{u2} R' _inst_8)) (Semiring.toNonAssocSemiring.{u3} A _inst_2) (RingHom.instRingHomClassRingHom.{u2, u3} R' A (Semiring.toNonAssocSemiring.{u2} R' (CommSemiring.toSemiring.{u2} R' _inst_8)) (Semiring.toNonAssocSemiring.{u3} A _inst_2))))) (algebraMap.{u2, u3} R' A _inst_8 _inst_2 _inst_10) r)
 Case conversion may be inaccurate. Consider using '#align subalgebra.coe_algebra_map Subalgebra.coe_algebraMapₓ'. -/
 @[simp, norm_cast]
 theorem coe_algebraMap [CommSemiring R'] [SMul R' R] [Algebra R' A] [IsScalarTower R' R A]
@@ -1096,7 +1096,7 @@ theorem coe_toSubalgebra (p : Submodule R A) (h_one h_mul) :
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (s : Set.{u2} A) (h0 : Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) (OfNat.ofNat.{u2} A 0 (OfNat.mk.{u2} A 0 (Zero.zero.{u2} A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))))))) s) (hadd : forall {a : A} {b : A}, (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) a s) -> (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) b s) -> (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (AddZeroClass.toHasAdd.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))))) a b) s)) (hsmul : forall (c : R) {x : A}, (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) x s) -> (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) (SMul.smul.{u1, u2} R A (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) c x) s)) (h1 : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (OfNat.ofNat.{u2} A 1 (OfNat.mk.{u2} A 1 (One.one.{u2} A (AddMonoidWithOne.toOne.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))))) (Submodule.mk.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) s hadd h0 hsmul)) (hmul : forall (x : A) (y : A), (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (Submodule.mk.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) s hadd h0 hsmul)) -> (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) y (Submodule.mk.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) s hadd h0 hsmul)) -> (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y) (Submodule.mk.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) s hadd h0 hsmul))), Eq.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (Submodule.mk.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) s hadd h0 hsmul) h1 hmul) (Subalgebra.mk.{u1, u2} R A _inst_1 _inst_2 _inst_3 s hmul h1 hadd h0 (fun (r : R) => Eq.mpr.{0} (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) s) (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) (SMul.smul.{u1, u2} R A (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A 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_inst_2)))))))) s) (id_tag Tactic.IdTag.rw (Eq.{1} Prop (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) s) (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) (SMul.smul.{u1, u2} R A (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A 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R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) s)) (SMul.smul.{u1, u2} R A (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) r (OfNat.ofNat.{u2} A 1 (OfNat.mk.{u2} A 1 (One.one.{u2} A (AddMonoidWithOne.toOne.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))))) (Algebra.algebraMap_eq_smul_one.{u1, u2} R A _inst_1 _inst_2 _inst_3 r))) (hsmul r (OfNat.ofNat.{u2} A 1 (OfNat.mk.{u2} A 1 (One.one.{u2} A (AddMonoidWithOne.toOne.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))))) h1)))
 but is expected to have type
-  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u1} A] [_inst_3 : Algebra.{u2, u1} R A _inst_1 _inst_2] (s : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (h0 : Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) (OfNat.ofNat.{u1} A 1 (One.toOfNat1.{u1} A (Semiring.toOne.{u1} A _inst_2))) s) (hadd : forall (a : A) (b : A), (Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) a s) -> (Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) b s) -> (Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u1, u1, u1} A A A (instHMul.{u1} A (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) a b) s)), Eq.{succ u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 s h0 hadd) (Subalgebra.mk.{u2, u1} R A _inst_1 _inst_2 _inst_3 (Subsemiring.mk.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Submonoid.mk.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemigroup.mk.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) s) hadd) h0) (fun {a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6404 : A} {b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6405 : A} => Submodule.add_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6404 b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6405) (Submodule.zero_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s)) (fun (r : R) => Eq.mpr.{0} (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => A) r) (Set.{u1} A) (Set.instMembershipSet.{u1} A) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => A) a) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2) (RingHom.instRingHomClassRingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2))))) (algebraMap.{u2, u1} R A _inst_1 _inst_2 _inst_3) r) (Subsemigroup.carrier.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (Submonoid.toSubsemigroup.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemiring.toSubmonoid.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Subsemiring.mk.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Submonoid.mk.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemigroup.mk.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) s) hadd) h0) (fun {a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6404 : A} {b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6405 : A} => Submodule.add_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6404 b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6405) (Submodule.zero_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s)))))) (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => A) r) (Set.{u1} A) (Set.instMembershipSet.{u1} A) (HSMul.hSMul.{u2, u1, u1} R A A (instHSMul.{u2, u1} R A (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_2 _inst_3)) r (OfNat.ofNat.{u1} A 1 (One.toOfNat1.{u1} A (Semiring.toOne.{u1} A _inst_2)))) (Subsemigroup.carrier.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (Submonoid.toSubsemigroup.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemiring.toSubmonoid.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Subsemiring.mk.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Submonoid.mk.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemigroup.mk.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) s) hadd) h0) (fun {a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6404 : A} {b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6405 : A} => Submodule.add_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6404 b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6405) (Submodule.zero_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) 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u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2) (RingHom.instRingHomClassRingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2))))) (algebraMap.{u2, u1} R A _inst_1 _inst_2 _inst_3) r) (Subsemigroup.carrier.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (Submonoid.toSubsemigroup.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemiring.toSubmonoid.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Subsemiring.mk.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Submonoid.mk.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemigroup.mk.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) s) hadd) h0) (fun {a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6404 : A} {b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6405 : A} => Submodule.add_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6404 b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6405) (Submodule.zero_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s))))))) (HSMul.hSMul.{u2, u1, u1} R A A (instHSMul.{u2, u1} R A (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_2 _inst_3)) r (OfNat.ofNat.{u1} A 1 (One.toOfNat1.{u1} A (Semiring.toOne.{u1} A _inst_2)))) (Algebra.algebraMap_eq_smul_one.{u2, u1} R A _inst_1 _inst_2 _inst_3 r))) (Submodule.smul_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s (OfNat.ofNat.{u1} A 1 (One.toOfNat1.{u1} A (Semiring.toOne.{u1} A _inst_2))) r h0)))
+  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u1} A] [_inst_3 : Algebra.{u2, u1} R A _inst_1 _inst_2] (s : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (h0 : Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) (OfNat.ofNat.{u1} A 1 (One.toOfNat1.{u1} A (Semiring.toOne.{u1} A _inst_2))) s) (hadd : forall (a : A) (b : A), (Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) a s) -> (Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) b s) -> (Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u1, u1, u1} A A A (instHMul.{u1} A (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) a b) s)), Eq.{succ u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 s h0 hadd) (Subalgebra.mk.{u2, u1} R A _inst_1 _inst_2 _inst_3 (Subsemiring.mk.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Submonoid.mk.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemigroup.mk.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) s) hadd) h0) (fun {a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6428 : A} {b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6429 : A} => Submodule.add_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6428 b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6429) (Submodule.zero_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s)) (fun (r : R) => Eq.mpr.{0} (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) (Set.{u1} A) (Set.instMembershipSet.{u1} A) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2) (RingHom.instRingHomClassRingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2))))) (algebraMap.{u2, u1} R A _inst_1 _inst_2 _inst_3) r) (Subsemigroup.carrier.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (Submonoid.toSubsemigroup.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemiring.toSubmonoid.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Subsemiring.mk.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Submonoid.mk.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemigroup.mk.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) s) hadd) h0) (fun {a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6428 : A} {b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6429 : A} => Submodule.add_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6428 b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6429) (Submodule.zero_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s)))))) (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) (Set.{u1} A) (Set.instMembershipSet.{u1} A) (HSMul.hSMul.{u2, u1, u1} R A A (instHSMul.{u2, u1} R A (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_2 _inst_3)) r (OfNat.ofNat.{u1} A 1 (One.toOfNat1.{u1} A (Semiring.toOne.{u1} A _inst_2)))) (Subsemigroup.carrier.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (Submonoid.toSubsemigroup.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemiring.toSubmonoid.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Subsemiring.mk.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Submonoid.mk.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemigroup.mk.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) 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_inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) s) hadd) h0) (fun {a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6428 : A} {b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6429 : A} => Submodule.add_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6428 b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6429) (Submodule.zero_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s)))))) (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) (Set.{u1} A) (Set.instMembershipSet.{u1} A) _a (Subsemigroup.carrier.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (Submonoid.toSubsemigroup.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemiring.toSubmonoid.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Subsemiring.mk.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Submonoid.mk.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemigroup.mk.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) s) hadd) h0) (fun {a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6428 : A} {b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6429 : A} => Submodule.add_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6428 b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6429) (Submodule.zero_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s))))))) (Eq.refl.{1} Prop (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) (Set.{u1} A) (Set.instMembershipSet.{u1} A) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) a) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2) (RingHom.instRingHomClassRingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2))))) (algebraMap.{u2, u1} R A _inst_1 _inst_2 _inst_3) r) (Subsemigroup.carrier.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (Submonoid.toSubsemigroup.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemiring.toSubmonoid.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Subsemiring.mk.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Submonoid.mk.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemigroup.mk.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) s) hadd) h0) (fun {a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6428 : A} {b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6429 : A} => Submodule.add_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6428 b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6429) (Submodule.zero_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s))))))) (HSMul.hSMul.{u2, u1, u1} R A A (instHSMul.{u2, u1} R A (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_2 _inst_3)) r (OfNat.ofNat.{u1} A 1 (One.toOfNat1.{u1} A (Semiring.toOne.{u1} A _inst_2)))) (Algebra.algebraMap_eq_smul_one.{u2, u1} R A _inst_1 _inst_2 _inst_3 r))) (Submodule.smul_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s (OfNat.ofNat.{u1} A 1 (One.toOfNat1.{u1} A (Semiring.toOne.{u1} A _inst_2))) r h0)))
 Case conversion may be inaccurate. Consider using '#align submodule.to_subalgebra_mk Submodule.toSubalgebra_mkₓ'. -/
 @[simp]
 theorem toSubalgebra_mk (s : Set A) (h0 hadd hsmul h1 hmul) :
@@ -1691,7 +1691,7 @@ instance : Inhabited (Subalgebra R A) :=
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {x : A}, Iff (Membership.Mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x (Bot.bot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toHasBot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) x (Set.range.{u2, succ u1} A R (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3))))
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {x : A}, Iff (Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x (Bot.bot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toBot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) x (Set.range.{u2, succ u1} A R (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3))))
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {x : A}, Iff (Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x (Bot.bot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toBot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) x (Set.range.{u2, succ u1} A R (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3))))
 Case conversion may be inaccurate. Consider using '#align algebra.mem_bot Algebra.mem_botₓ'. -/
 theorem mem_bot {x : A} : x ∈ (⊥ : Subalgebra R A) ↔ x ∈ Set.range (algebraMap R A) :=
   suffices (ofId R A).range = (⊥ : Subalgebra R A)
@@ -1717,7 +1717,7 @@ theorem toSubmodule_bot : (⊥ : Subalgebra R A).toSubmodule = R ∙ 1 :=
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], Eq.{succ u2} (Set.{u2} A) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Bot.bot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toHasBot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Set.range.{u2, succ u1} A R (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3)))
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], Eq.{succ u2} (Set.{u2} A) (SetLike.coe.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Bot.bot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toBot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Set.range.{u2, succ u1} A R (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3)))
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], Eq.{succ u2} (Set.{u2} A) (SetLike.coe.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Bot.bot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toBot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Set.range.{u2, succ u1} A R (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3)))
 Case conversion may be inaccurate. Consider using '#align algebra.coe_bot Algebra.coe_botₓ'. -/
 @[simp]
 theorem coe_bot : ((⊥ : Subalgebra R A) : Set A) = Set.range (algebraMap R A) := by
@@ -1806,7 +1806,7 @@ def toTop : A →ₐ[R] (⊤ : Subalgebra R A) :=
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], Iff (Function.Surjective.{succ u1, succ u2} R A (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Eq.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Top.top.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toHasTop.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Bot.bot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toHasBot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))))
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], Iff (Function.Surjective.{succ u1, succ u2} R A (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Eq.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Top.top.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toTop.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Bot.bot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toBot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))))
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], Iff (Function.Surjective.{succ u1, succ u2} R A (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Eq.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Top.top.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toTop.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Bot.bot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toBot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))))
 Case conversion may be inaccurate. Consider using '#align algebra.surjective_algebra_map_iff Algebra.surjective_algebraMap_iffₓ'. -/
 theorem surjective_algebraMap_iff :
     Function.Surjective (algebraMap R A) ↔ (⊤ : Subalgebra R A) = ⊥ :=
@@ -1821,7 +1821,7 @@ theorem surjective_algebraMap_iff :
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_6 : Field.{u1} R] [_inst_7 : Semiring.{u2} A] [_inst_8 : Nontrivial.{u2} A] [_inst_9 : Algebra.{u1, u2} R A (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_6)) _inst_7], Iff (Function.Bijective.{succ u1, succ u2} R A (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_6)))) (Semiring.toNonAssocSemiring.{u2} A _inst_7)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_6)))) (Semiring.toNonAssocSemiring.{u2} A _inst_7)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_6)))) (Semiring.toNonAssocSemiring.{u2} A _inst_7)) (algebraMap.{u1, u2} R A (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_6)) _inst_7 _inst_9))) (Eq.{succ u2} (Subalgebra.{u1, u2} R A (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_6)) _inst_7 _inst_9) (Top.top.{u2} (Subalgebra.{u1, u2} R A (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_6)) _inst_7 _inst_9) (CompleteLattice.toHasTop.{u2} (Subalgebra.{u1, u2} R A (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_6)) _inst_7 _inst_9) (Algebra.Subalgebra.completeLattice.{u1, u2} R A (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_6)) _inst_7 _inst_9))) (Bot.bot.{u2} (Subalgebra.{u1, u2} R A (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_6)) _inst_7 _inst_9) (CompleteLattice.toHasBot.{u2} (Subalgebra.{u1, u2} R A (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_6)) _inst_7 _inst_9) (Algebra.Subalgebra.completeLattice.{u1, u2} R A (Semifield.toCommSemiring.{u1} R (Field.toSemifield.{u1} R _inst_6)) _inst_7 _inst_9))))
 but is expected to have type
-  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_6 : Field.{u2} R] [_inst_7 : Semiring.{u1} A] [_inst_8 : Nontrivial.{u1} A] [_inst_9 : Algebra.{u2, u1} R A (Semifield.toCommSemiring.{u2} R (Field.toSemifield.{u2} R _inst_6)) _inst_7], Iff (Function.Bijective.{succ u2, succ u1} R A (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (Semifield.toCommSemiring.{u2} R (Field.toSemifield.{u2} R _inst_6)))) (Semiring.toNonAssocSemiring.{u1} A _inst_7)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => A) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (Semifield.toCommSemiring.{u2} R (Field.toSemifield.{u2} R _inst_6)))) (Semiring.toNonAssocSemiring.{u1} A _inst_7)) R A (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (Semifield.toCommSemiring.{u2} R (Field.toSemifield.{u2} R _inst_6)))))) (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_7))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (Semifield.toCommSemiring.{u2} R (Field.toSemifield.{u2} R _inst_6)))) (Semiring.toNonAssocSemiring.{u1} A _inst_7)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (Semifield.toCommSemiring.{u2} R (Field.toSemifield.{u2} R _inst_6))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_7)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (Semifield.toCommSemiring.{u2} R (Field.toSemifield.{u2} R _inst_6)))) (Semiring.toNonAssocSemiring.{u1} A _inst_7)) R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (Semifield.toCommSemiring.{u2} R (Field.toSemifield.{u2} R _inst_6)))) (Semiring.toNonAssocSemiring.{u1} A _inst_7) (RingHom.instRingHomClassRingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (Semifield.toCommSemiring.{u2} R (Field.toSemifield.{u2} R _inst_6)))) (Semiring.toNonAssocSemiring.{u1} A _inst_7))))) (algebraMap.{u2, u1} R A (Semifield.toCommSemiring.{u2} R (Field.toSemifield.{u2} R _inst_6)) _inst_7 _inst_9))) (Eq.{succ u1} (Subalgebra.{u2, u1} R A (Semifield.toCommSemiring.{u2} R (Field.toSemifield.{u2} R _inst_6)) _inst_7 _inst_9) (Top.top.{u1} (Subalgebra.{u2, u1} R A (Semifield.toCommSemiring.{u2} R (Field.toSemifield.{u2} R _inst_6)) _inst_7 _inst_9) (CompleteLattice.toTop.{u1} (Subalgebra.{u2, u1} R A (Semifield.toCommSemiring.{u2} R (Field.toSemifield.{u2} R _inst_6)) _inst_7 _inst_9) (Algebra.instCompleteLatticeSubalgebra.{u2, u1} R A (Semifield.toCommSemiring.{u2} R (Field.toSemifield.{u2} R _inst_6)) _inst_7 _inst_9))) (Bot.bot.{u1} (Subalgebra.{u2, u1} R A (Semifield.toCommSemiring.{u2} R (Field.toSemifield.{u2} R _inst_6)) _inst_7 _inst_9) (CompleteLattice.toBot.{u1} (Subalgebra.{u2, u1} R A (Semifield.toCommSemiring.{u2} R (Field.toSemifield.{u2} R _inst_6)) _inst_7 _inst_9) (Algebra.instCompleteLatticeSubalgebra.{u2, u1} R A (Semifield.toCommSemiring.{u2} R (Field.toSemifield.{u2} R _inst_6)) _inst_7 _inst_9))))
+  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_6 : Field.{u2} R] [_inst_7 : Semiring.{u1} A] [_inst_8 : Nontrivial.{u1} A] [_inst_9 : Algebra.{u2, u1} R A (Semifield.toCommSemiring.{u2} R (Field.toSemifield.{u2} R _inst_6)) _inst_7], Iff (Function.Bijective.{succ u2, succ u1} R A (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (Semifield.toCommSemiring.{u2} R (Field.toSemifield.{u2} R _inst_6)))) (Semiring.toNonAssocSemiring.{u1} A _inst_7)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (Semifield.toCommSemiring.{u2} R (Field.toSemifield.{u2} R _inst_6)))) (Semiring.toNonAssocSemiring.{u1} A _inst_7)) R A (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (Semifield.toCommSemiring.{u2} R (Field.toSemifield.{u2} R _inst_6)))))) (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_7))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (Semifield.toCommSemiring.{u2} R (Field.toSemifield.{u2} R _inst_6)))) (Semiring.toNonAssocSemiring.{u1} A _inst_7)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (Semifield.toCommSemiring.{u2} R (Field.toSemifield.{u2} R _inst_6))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_7)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (Semifield.toCommSemiring.{u2} R (Field.toSemifield.{u2} R _inst_6)))) (Semiring.toNonAssocSemiring.{u1} A _inst_7)) R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (Semifield.toCommSemiring.{u2} R (Field.toSemifield.{u2} R _inst_6)))) (Semiring.toNonAssocSemiring.{u1} A _inst_7) (RingHom.instRingHomClassRingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (Semifield.toCommSemiring.{u2} R (Field.toSemifield.{u2} R _inst_6)))) (Semiring.toNonAssocSemiring.{u1} A _inst_7))))) (algebraMap.{u2, u1} R A (Semifield.toCommSemiring.{u2} R (Field.toSemifield.{u2} R _inst_6)) _inst_7 _inst_9))) (Eq.{succ u1} (Subalgebra.{u2, u1} R A (Semifield.toCommSemiring.{u2} R (Field.toSemifield.{u2} R _inst_6)) _inst_7 _inst_9) (Top.top.{u1} (Subalgebra.{u2, u1} R A (Semifield.toCommSemiring.{u2} R (Field.toSemifield.{u2} R _inst_6)) _inst_7 _inst_9) (CompleteLattice.toTop.{u1} (Subalgebra.{u2, u1} R A (Semifield.toCommSemiring.{u2} R (Field.toSemifield.{u2} R _inst_6)) _inst_7 _inst_9) (Algebra.instCompleteLatticeSubalgebra.{u2, u1} R A (Semifield.toCommSemiring.{u2} R (Field.toSemifield.{u2} R _inst_6)) _inst_7 _inst_9))) (Bot.bot.{u1} (Subalgebra.{u2, u1} R A (Semifield.toCommSemiring.{u2} R (Field.toSemifield.{u2} R _inst_6)) _inst_7 _inst_9) (CompleteLattice.toBot.{u1} (Subalgebra.{u2, u1} R A (Semifield.toCommSemiring.{u2} R (Field.toSemifield.{u2} R _inst_6)) _inst_7 _inst_9) (Algebra.instCompleteLatticeSubalgebra.{u2, u1} R A (Semifield.toCommSemiring.{u2} R (Field.toSemifield.{u2} R _inst_6)) _inst_7 _inst_9))))
 Case conversion may be inaccurate. Consider using '#align algebra.bijective_algebra_map_iff Algebra.bijective_algebraMap_iffₓ'. -/
 theorem bijective_algebraMap_iff {R A : Type _} [Field R] [Semiring A] [Nontrivial A]
     [Algebra R A] : Function.Bijective (algebraMap R A) ↔ (⊤ : Subalgebra R A) = ⊥ :=
@@ -1833,7 +1833,7 @@ theorem bijective_algebraMap_iff {R A : Type _} [Field R] [Semiring A] [Nontrivi
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], (Function.Injective.{succ u1, succ u2} R A (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3))) -> (AlgEquiv.{u1, u2, u1} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Bot.bot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toHasBot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) R _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (Bot.bot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toHasBot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (CommSemiring.toSemiring.{u1} R _inst_1) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (Bot.bot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toHasBot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Algebra.id.{u1} R _inst_1))
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], (Function.Injective.{succ u1, succ u2} R A (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3))) -> (AlgEquiv.{u1, u2, u1} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x (Bot.bot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toBot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) R _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (Bot.bot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toBot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (CommSemiring.toSemiring.{u1} R _inst_1) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (Bot.bot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toBot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Algebra.id.{u1} R _inst_1))
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], (Function.Injective.{succ u1, succ u2} R A (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3))) -> (AlgEquiv.{u1, u2, u1} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x (Bot.bot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toBot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) R _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (Bot.bot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toBot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (CommSemiring.toSemiring.{u1} R _inst_1) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (Bot.bot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toBot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Algebra.id.{u1} R _inst_1))
 Case conversion may be inaccurate. Consider using '#align algebra.bot_equiv_of_injective Algebra.botEquivOfInjectiveₓ'. -/
 /-- The bottom subalgebra is isomorphic to the base ring. -/
 noncomputable def botEquivOfInjective (h : Function.Injective (algebraMap R A)) :
@@ -2164,7 +2164,7 @@ variable {ι : Type _}
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {ι : Type.{u3}} [_inst_6 : Nonempty.{succ u3} ι] {S : ι -> (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)}, (Directed.{u2, succ u3} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) ι (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) S) -> (Eq.{succ u2} (Set.{u2} A) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (supᵢ.{u2, succ u3} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))) ι S)) (Set.unionᵢ.{u2, succ u3} A ι (fun (i : ι) => (fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (S i))))
 but is expected to have type
-  forall {R : Type.{u2}} {A : Type.{u3}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u3} A] [_inst_3 : Algebra.{u2, u3} R A _inst_1 _inst_2] {ι : Type.{u1}} [_inst_6 : Nonempty.{succ u1} ι] {S : ι -> (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)}, (Directed.{u3, succ u1} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) ι (fun (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.12598 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.12600 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) => LE.le.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3))))) x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.12598 x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.12600) S) -> (Eq.{succ u3} (Set.{u3} A) (SetLike.coe.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (supᵢ.{u3, succ u1} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3))) ι S)) (Set.unionᵢ.{u3, succ u1} A ι (fun (i : ι) => SetLike.coe.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (S i))))
+  forall {R : Type.{u2}} {A : Type.{u3}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u3} A] [_inst_3 : Algebra.{u2, u3} R A _inst_1 _inst_2] {ι : Type.{u1}} [_inst_6 : Nonempty.{succ u1} ι] {S : ι -> (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)}, (Directed.{u3, succ u1} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) ι (fun (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.12698 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.12700 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) => LE.le.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3))))) x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.12698 x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.12700) S) -> (Eq.{succ u3} (Set.{u3} A) (SetLike.coe.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (supᵢ.{u3, succ u1} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3))) ι S)) (Set.unionᵢ.{u3, succ u1} A ι (fun (i : ι) => SetLike.coe.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (S i))))
 Case conversion may be inaccurate. Consider using '#align subalgebra.coe_supr_of_directed Subalgebra.coe_supᵢ_of_directedₓ'. -/
 theorem coe_supᵢ_of_directed [Nonempty ι] {S : ι → Subalgebra R A} (dir : Directed (· ≤ ·) S) :
     ↑(supᵢ S) = ⋃ i, (S i : Set A) :=
@@ -2193,7 +2193,7 @@ theorem coe_supᵢ_of_directed [Nonempty ι] {S : ι → Subalgebra R A} (dir :
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {ι : Type.{u4}} [_inst_6 : Nonempty.{succ u4} ι] (K : ι -> (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)), (Directed.{u2, succ u4} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) ι (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) K) -> (forall (f : forall (i : ι), AlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K i)) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5), (forall (i : ι) (j : ι) (h : LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (K i) (K j)), Eq.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K i)) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) (f i) (AlgHom.comp.{u1, u2, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K i)) (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K j)) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K j)) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K j)) _inst_5 (f j) (Subalgebra.inclusion.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i) (K j) h))) -> (forall (T : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), (Eq.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) T (supᵢ.{u2, succ u4} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))) ι K)) -> (AlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) _inst_5)))
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {ι : Type.{u4}} [_inst_6 : Nonempty.{succ u4} ι] (K : ι -> (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)), (Directed.{u2, succ u4} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) ι (fun (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.12981 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.12983 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.12981 x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.12983) K) -> (forall (f : forall (i : ι), AlgHom.{u1, u2, u3} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5), (forall (i : ι) (j : ι) (h : LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (K i) (K j)), Eq.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) (f i) (AlgHom.comp.{u1, u2, u2, u3} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x (K j))) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K j)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K j)) _inst_5 (f j) (Subalgebra.inclusion.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i) (K j) h))) -> (forall (T : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), (Eq.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) T (supᵢ.{u2, succ u4} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))) ι K)) -> (AlgHom.{u1, u2, u3} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T)) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) _inst_5)))
+  forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {ι : Type.{u4}} [_inst_6 : Nonempty.{succ u4} ι] (K : ι -> (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)), (Directed.{u2, succ u4} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) ι (fun (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13081 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13083 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13081 x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13083) K) -> (forall (f : forall (i : ι), AlgHom.{u1, u2, u3} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5), (forall (i : ι) (j : ι) (h : LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (K i) (K j)), Eq.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) (f i) (AlgHom.comp.{u1, u2, u2, u3} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x (K j))) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K j)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K j)) _inst_5 (f j) (Subalgebra.inclusion.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i) (K j) h))) -> (forall (T : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), (Eq.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) T (supᵢ.{u2, succ u4} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))) ι K)) -> (AlgHom.{u1, u2, u3} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T)) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) _inst_5)))
 Case conversion may be inaccurate. Consider using '#align subalgebra.supr_lift Subalgebra.supᵢLiftₓ'. -/
 /-- Define an algebra homomorphism on a directed supremum of subalgebras by defining
 it on each subalgebra, and proving that it agrees on the intersection of subalgebras. -/
@@ -2230,7 +2230,7 @@ variable [Nonempty ι] {K : ι → Subalgebra R A} {dir : Directed (· ≤ ·) K
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {ι : Type.{u4}} [_inst_6 : Nonempty.{succ u4} ι] {K : ι -> (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {dir : Directed.{u2, succ u4} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) ι (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) K} {f : forall (i : ι), AlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K i)) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5} {hf : forall (i : ι) (j : ι) (h : LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (K i) (K j)), Eq.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, 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 but is expected to have type
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+  forall {R : Type.{u2}} {A : Type.{u3}} {B : Type.{u4}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u3} A] [_inst_3 : Algebra.{u2, u3} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u4} B] [_inst_5 : Algebra.{u2, u4} R B _inst_1 _inst_4] {ι : Type.{u1}} [_inst_6 : Nonempty.{succ u1} ι] {K : ι -> (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)} {dir : Directed.{u3, succ u1} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) ι (fun (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13669 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13671 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) => LE.le.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) 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(Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)) (Module.toDistribMulAction.{u2, u3} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i))))) (Algebra.toModule.{u2, u3} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)))) (Module.toDistribMulAction.{u2, u4} R B (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u2, u4} R B _inst_1 _inst_4 _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u3, u4, max u3 u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5 (AlgHom.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) (AlgHom.algHomClass.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5))))) (f i) x)
 Case conversion may be inaccurate. Consider using '#align subalgebra.supr_lift_inclusion Subalgebra.supᵢLift_inclusionₓ'. -/
 @[simp]
 theorem supᵢLift_inclusion {i : ι} (x : K i) (h : K i ≤ T) :
@@ -2242,7 +2242,7 @@ theorem supᵢLift_inclusion {i : ι} (x : K i) (h : K i ≤ T) :
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {ι : Type.{u4}} [_inst_6 : Nonempty.{succ u4} ι] {K : ι -> (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {dir : Directed.{u2, succ u4} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) ι (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) K} {f : forall (i : ι), AlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K i)) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5} {hf : forall (i : ι) (j : ι) (h : LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (K i) (K j)), Eq.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K i)) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) (f i) (AlgHom.comp.{u1, u2, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K i)) (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K j)) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K j)) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K j)) _inst_5 (f j) (Subalgebra.inclusion.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i) (K j) h))} {T : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3} {hT : Eq.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) T (supᵢ.{u2, succ u4} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))) ι K)} {i : ι} (h : LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (K i) T), Eq.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K i)) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) (AlgHom.comp.{u1, u2, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K i)) (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) _inst_5 (Subalgebra.supᵢLift.{u1, u2, u3, u4} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 ι _inst_6 K dir f hf T hT) (Subalgebra.inclusion.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i) T h)) (f i)
 but is expected to have type
-  forall {R : Type.{u2}} {A : Type.{u3}} {B : Type.{u4}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u3} A] [_inst_3 : Algebra.{u2, u3} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u4} B] [_inst_5 : Algebra.{u2, u4} R B _inst_1 _inst_4] {ι : Type.{u1}} [_inst_6 : Nonempty.{succ u1} ι] {K : ι -> (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)} {dir : Directed.{u3, succ u1} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) ι (fun (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13719 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13721 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) => LE.le.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3))))) x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13719 x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13721) K} {f : forall (i : ι), AlgHom.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5} {hf : forall (i : ι) (j : ι) (h : LE.le.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3))))) (K i) (K j)), Eq.{max (succ u3) (succ u4)} (AlgHom.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) (f i) (AlgHom.comp.{u2, u3, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K j))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K j)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K j)) _inst_5 (f j) (Subalgebra.inclusion.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i) (K j) h))} {T : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3} {hT : Eq.{succ u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) T (supᵢ.{u3, succ u1} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3))) ι K)} {i : ι} (h : LE.le.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3))))) (K i) T), Eq.{max (succ u3) (succ u4)} (AlgHom.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) (AlgHom.comp.{u2, u3, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x T)) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 T) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 T) _inst_5 (Subalgebra.supᵢLift.{u2, u3, u4, u1} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 ι _inst_6 K dir f hf T hT) (Subalgebra.inclusion.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i) T h)) (f i)
+  forall {R : Type.{u2}} {A : Type.{u3}} {B : Type.{u4}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u3} A] [_inst_3 : Algebra.{u2, u3} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u4} B] [_inst_5 : Algebra.{u2, u4} R B _inst_1 _inst_4] {ι : Type.{u1}} [_inst_6 : Nonempty.{succ u1} ι] {K : ι -> (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)} {dir : Directed.{u3, succ u1} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) ι (fun (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13824 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13826 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) => LE.le.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3))))) x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13824 x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13826) K} {f : forall (i : ι), AlgHom.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5} {hf : forall (i : ι) (j : ι) (h : LE.le.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3))))) (K i) (K j)), Eq.{max (succ u3) (succ u4)} (AlgHom.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) (f i) (AlgHom.comp.{u2, u3, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K j))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K j)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K j)) _inst_5 (f j) (Subalgebra.inclusion.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i) (K j) h))} {T : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3} {hT : Eq.{succ u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) T (supᵢ.{u3, succ u1} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3))) ι K)} {i : ι} (h : LE.le.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3))))) (K i) T), Eq.{max (succ u3) (succ u4)} (AlgHom.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) (AlgHom.comp.{u2, u3, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x T)) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 T) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 T) _inst_5 (Subalgebra.supᵢLift.{u2, u3, u4, u1} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 ι _inst_6 K dir f hf T hT) (Subalgebra.inclusion.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i) T h)) (f i)
 Case conversion may be inaccurate. Consider using '#align subalgebra.supr_lift_comp_inclusion Subalgebra.supᵢLift_comp_inclusionₓ'. -/
 @[simp]
 theorem supᵢLift_comp_inclusion {i : ι} (h : K i ≤ T) :
@@ -2253,7 +2253,7 @@ theorem supᵢLift_comp_inclusion {i : ι} (h : K i ≤ T) :
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {ι : Type.{u4}} [_inst_6 : Nonempty.{succ u4} ι] {K : ι -> (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {dir : Directed.{u2, succ u4} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) ι (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) K} {f : forall (i : ι), AlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K i)) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5} {hf : forall (i : ι) (j : ι) (h : LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (K i) (K j)), Eq.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K i)) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) (f i) (AlgHom.comp.{u1, u2, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K i)) (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K j)) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 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_inst_4))))) (DistribSMul.toSMulZeroClass.{u2, u4} R B (AddMonoid.toAddZeroClass.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))))) (DistribMulAction.toDistribSMul.{u2, u4} R B (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)))) (Module.toDistribMulAction.{u2, u4} R B (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u2, u4} R B _inst_1 _inst_4 _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u4, u2, u3, u4} (AlgHom.{u2, u3, u4} R 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u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i))))) (Algebra.toModule.{u2, u3} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) 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u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)) (Module.toDistribMulAction.{u2, u3} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i))))) (Algebra.toModule.{u2, u3} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)))) (Module.toDistribMulAction.{u2, u4} R B (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u2, u4} R B _inst_1 _inst_4 _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u3, u4, max u3 u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5 (AlgHom.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) (AlgHom.algHomClass.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5))))) (f i) x)
+  forall {R : Type.{u2}} {A : Type.{u3}} {B : Type.{u4}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u3} A] [_inst_3 : Algebra.{u2, u3} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u4} B] [_inst_5 : Algebra.{u2, u4} R B _inst_1 _inst_4] {ι : Type.{u1}} [_inst_6 : Nonempty.{succ u1} ι] {K : ι -> (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)} {dir : Directed.{u3, succ u1} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) ι (fun (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13951 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13953 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) => LE.le.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3))))) x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13951 x._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.13953) K} {f : forall (i : ι), AlgHom.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5} {hf : forall (i : ι) (j : ι) (h : LE.le.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u3} (Subalgebra.{u2, u3} R A _inst_1 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A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5 (AlgHom.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) (AlgHom.algHomClass.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5))))) (f i) x)
 Case conversion may be inaccurate. Consider using '#align subalgebra.supr_lift_mk Subalgebra.supᵢLift_mkₓ'. -/
 @[simp]
 theorem supᵢLift_mk {i : ι} (x : K i) (hx : (x : A) ∈ T) :
@@ -2264,7 +2264,7 @@ theorem supᵢLift_mk {i : ι} (x : K i) (hx : (x : A) ∈ T) :
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {ι : Type.{u4}} [_inst_6 : Nonempty.{succ u4} ι] {K : ι -> (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {dir : Directed.{u2, succ u4} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) ι (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) K} {f : forall (i : ι), AlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K i)) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5} {hf : forall (i : ι) (j : ι) (h : LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (K i) (K j)), Eq.{max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, 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_inst_2 _inst_3 (K j)) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K j)) _inst_5 (f j) (Subalgebra.inclusion.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i) (K j) h))} {T : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3} {hT : Eq.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) T (supᵢ.{u2, succ u4} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))) ι K)} {i : ι} (x : coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T) (hx : Membership.Mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T) A (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T) A (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 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_inst_1 _inst_2 _inst_3 T) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) _inst_5) (fun (_x : AlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) _inst_5) => (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T) -> B) ([anonymous].{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 T) _inst_5) (Subalgebra.supᵢLift.{u1, u2, u3, u4} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 ι _inst_6 K dir f hf T hT) x) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K i)) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) (fun (_x : AlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K i)) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) => (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K i)) -> B) ([anonymous].{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (K i)) B _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) (f i) (Subtype.mk.{succ u2} A (fun (x : A) => Membership.Mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x (K i)) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T) A (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T) A (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T) A (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) T) A (coeSubtype.{succ u2} A (fun (x : A) => Membership.Mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T))))) x) hx))
 but is expected to have type
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A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i))))) (Algebra.toModule.{u2, u3} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)))) (Module.toDistribMulAction.{u2, u4} R B (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u2, u4} R B _inst_1 _inst_4 _inst_5)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u3 u4, u2, u3, u4} (AlgHom.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4)) (Module.toDistribMulAction.{u2, u3} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i))))) (Algebra.toModule.{u2, u3} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)))) (Module.toDistribMulAction.{u2, u4} R B (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_4))) (Algebra.toModule.{u2, u4} R B _inst_1 _inst_4 _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u3, u4, max u3 u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5 (AlgHom.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5) (AlgHom.algHomClass.{u2, u3, u4} R (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i))) B _inst_1 (Subalgebra.toSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_4 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u3} R A _inst_1 _inst_2 _inst_3 (K i)) _inst_5))))) (f i) (Subtype.mk.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (K i)) (Subtype.val.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Set.{u3} A) (Set.instMembershipSet.{u3} A) x (SetLike.coe.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) T)) x) hx))
 Case conversion may be inaccurate. Consider using '#align subalgebra.supr_lift_of_mem Subalgebra.supᵢLift_of_memₓ'. -/
 theorem supᵢLift_of_mem {i : ι} (x : T) (hx : (x : A) ∈ K i) :
     supᵢLift K dir f hf T hT x = f i ⟨x, hx⟩ := by subst hT <;> exact Set.unionᵢLift_of_mem x hx
@@ -2442,7 +2442,7 @@ section Center
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (r : R), Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) (Set.center.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (r : R), Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => A) r) (Set.{u2} A) (Set.instMembershipSet.{u2} A) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) (Set.center.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (r : R), Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) (Set.{u2} A) (Set.instMembershipSet.{u2} A) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) (Set.center.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))
 Case conversion may be inaccurate. Consider using '#align set.algebra_map_mem_center Set.algebraMap_mem_centerₓ'. -/
 theorem Set.algebraMap_mem_center (r : R) : algebraMap R A r ∈ Set.center A := by
   simp [Algebra.commutes, Set.mem_center_iff]
@@ -2524,7 +2524,7 @@ section Centralizer
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {s : Set.{u2} A} (r : R), Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) (Set.centralizer.{u2} A s (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {s : Set.{u2} A} (r : R), Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => A) r) (Set.{u2} A) (Set.instMembershipSet.{u2} A) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) (Set.centralizer.{u2} A s (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {s : Set.{u2} A} (r : R), Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) (Set.{u2} A) (Set.instMembershipSet.{u2} A) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) (Set.centralizer.{u2} A s (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))
 Case conversion may be inaccurate. Consider using '#align set.algebra_map_mem_centralizer Set.algebraMap_mem_centralizerₓ'. -/
 @[simp]
 theorem Set.algebraMap_mem_centralizer {s : Set A} (r : R) : algebraMap R A r ∈ s.centralizer :=
@@ -2625,7 +2625,7 @@ theorem mem_of_finset_sum_eq_one_of_pow_smul_mem {S : Type _} [CommRing S] [Alge
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {S : Type.{u2}} [_inst_6 : CommRing.{u2} S] [_inst_7 : Algebra.{u1, u2} R S _inst_1 (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6))] (S' : Subalgebra.{u1, u2} R S _inst_1 (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_7) (s : Set.{u2} S) (l : Finsupp.{u2, u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} S) Type.{u2} (Set.hasCoeToSort.{u2} S) s) S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} S (NonAssocRing.toNonUnitalNonAssocRing.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_6))))))), (Eq.{succ u2} S (coeFn.{succ u2, succ u2} (LinearMap.{u2, u2, u2, u2} S S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)))) (Finsupp.{u2, u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} S) Type.{u2} (Set.hasCoeToSort.{u2} S) s) S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6))))))) S (Finsupp.addCommMonoid.{u2, u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} S) Type.{u2} (Set.hasCoeToSort.{u2} S) s) S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)))))) (AddCommGroup.toAddCommMonoid.{u2} S (NonUnitalNonAssocRing.toAddCommGroup.{u2} S (NonAssocRing.toNonUnitalNonAssocRing.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_6))))) (Finsupp.module.{u2, u2, u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} S) Type.{u2} (Set.hasCoeToSort.{u2} S) s) S S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6))))) (Semiring.toModule.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)))) (Semiring.toModule.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)))) (fun (_x : LinearMap.{u2, u2, u2, u2} S S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)))) (Finsupp.{u2, u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} S) Type.{u2} (Set.hasCoeToSort.{u2} S) s) S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6))))))) S (Finsupp.addCommMonoid.{u2, u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} S) Type.{u2} (Set.hasCoeToSort.{u2} S) s) S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)))))) (AddCommGroup.toAddCommMonoid.{u2} S (NonUnitalNonAssocRing.toAddCommGroup.{u2} S (NonAssocRing.toNonUnitalNonAssocRing.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_6))))) (Finsupp.module.{u2, u2, u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} S) Type.{u2} (Set.hasCoeToSort.{u2} S) s) S S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6))))) (Semiring.toModule.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)))) (Semiring.toModule.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)))) => (Finsupp.{u2, u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} S) Type.{u2} (Set.hasCoeToSort.{u2} S) s) S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6))))))) -> S) (LinearMap.hasCoeToFun.{u2, u2, u2, u2} S S (Finsupp.{u2, u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} S) Type.{u2} (Set.hasCoeToSort.{u2} S) s) S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6))))))) S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) (Finsupp.addCommMonoid.{u2, u2} (coeSort.{succ u2, succ (succ 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 but is expected to have type
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(Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)))) (_private.Mathlib.RingTheory.Ideal.Operations.0.Ideal.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRing.{u1, u1} S S (CommRing.toCommSemiring.{u1} S _inst_6) _inst_6 (Algebra.id.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)))) (Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6))))) (fun (_x : Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6))))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6))))) => S) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} S S (Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6))))) S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) (Finsupp.addCommMonoid.{u1, u1} (Set.Elem.{u1} S s) S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_6))))) (Finsupp.module.{u1, u1, u1} (Set.Elem.{u1} S s) S S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6))))) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)))) (_private.Mathlib.RingTheory.Ideal.Operations.0.Ideal.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRing.{u1, u1} S S (CommRing.toCommSemiring.{u1} S _inst_6) _inst_6 (Algebra.id.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6))) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6))))) (Finsupp.total.{u1, u1, u1} (Set.Elem.{u1} S s) S S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_6))))) (_private.Mathlib.RingTheory.Ideal.Operations.0.Ideal.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRing.{u1, u1} S S (CommRing.toCommSemiring.{u1} S _inst_6) _inst_6 (Algebra.id.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6))) (Subtype.val.{succ u1} S (fun (x : S) => Membership.mem.{u1, u1} S (Set.{u1} S) (Set.instMembershipSet.{u1} S) x s))) l) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6))))) => S) l) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6))))) => S) l) (NonAssocRing.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6))))) => S) l) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6))))) => S) l) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6))))) => S) l) _inst_6)))))) -> (HasSubset.Subset.{u1} (Set.{u1} S) (Set.instHasSubsetSet.{u1} S) s (SetLike.coe.{u1, u1} (Subalgebra.{u2, u1} R S _inst_1 (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) _inst_7) S (Subalgebra.instSetLikeSubalgebra.{u2, u1} R S _inst_1 (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) _inst_7) S')) -> (forall (i : Set.Elem.{u1} S s), Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : Set.Elem.{u1} S s) => S) i) (Subalgebra.{u2, u1} R S _inst_1 (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) _inst_7) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R S _inst_1 (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) _inst_7) S (Subalgebra.instSetLikeSubalgebra.{u2, u1} R S _inst_1 (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) _inst_7)) (FunLike.coe.{succ u1, succ u1, succ u1} (Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (CommMonoidWithZero.toZero.{u1} S (CommSemiring.toCommMonoidWithZero.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)))) (Set.Elem.{u1} S s) (fun (_x : Set.Elem.{u1} S s) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : Set.Elem.{u1} S s) => S) _x) (Finsupp.funLike.{u1, u1} (Set.Elem.{u1} S s) S (CommMonoidWithZero.toZero.{u1} S (CommSemiring.toCommMonoidWithZero.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)))) l i) S') -> (forall (x : S), (forall (r : Set.Elem.{u1} S s), Exists.{1} Nat (fun (n : Nat) => Membership.mem.{u1, u1} S (Subalgebra.{u2, u1} R S _inst_1 (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) _inst_7) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R S _inst_1 (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) _inst_7) S (Subalgebra.instSetLikeSubalgebra.{u2, u1} R S _inst_1 (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) _inst_7)) (HSMul.hSMul.{u1, u1, u1} S S S (instHSMul.{u1, u1} S S (Algebra.toSMul.{u1, u1} S S (CommRing.toCommSemiring.{u1} S _inst_6) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) (Algebra.id.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)))) (HPow.hPow.{u1, 0, u1} S Nat S (instHPow.{u1, 0} S Nat (Monoid.Pow.{u1} S (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)))))) (Subtype.val.{succ u1} S (fun (x : S) => Membership.mem.{u1, u1} S (Set.{u1} S) (Set.instMembershipSet.{u1} S) x s) r) n) x) S')) -> (Membership.mem.{u1, u1} S (Subalgebra.{u2, u1} R S _inst_1 (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) _inst_7) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R S _inst_1 (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) _inst_7) S (Subalgebra.instSetLikeSubalgebra.{u2, u1} R S _inst_1 (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) _inst_7)) x S'))
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {S : Type.{u1}} [_inst_6 : CommRing.{u1} S] [_inst_7 : Algebra.{u2, u1} R S _inst_1 (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6))] (S' : Subalgebra.{u2, u1} R S _inst_1 (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) _inst_7) (s : Set.{u1} S) (l : Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (CommMonoidWithZero.toZero.{u1} S (CommSemiring.toCommMonoidWithZero.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)))), (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6))))) => S) l) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} S S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)))) (Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6))))) S (Finsupp.addCommMonoid.{u1, u1} (Set.Elem.{u1} S s) S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_6))))) (Finsupp.module.{u1, u1, u1} (Set.Elem.{u1} S s) S S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6))))) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)))) (_private.Mathlib.RingTheory.Ideal.Operations.0.Ideal.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRing.{u1, u1} S S (CommRing.toCommSemiring.{u1} S _inst_6) _inst_6 (Algebra.id.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)))) (Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6))))) (fun (_x : Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6))))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6))))) => S) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} S S (Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6))))) S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) (Finsupp.addCommMonoid.{u1, u1} (Set.Elem.{u1} S s) S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_6))))) (Finsupp.module.{u1, u1, u1} (Set.Elem.{u1} S s) S S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6))))) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)))) (_private.Mathlib.RingTheory.Ideal.Operations.0.Ideal.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRing.{u1, u1} S S (CommRing.toCommSemiring.{u1} S _inst_6) _inst_6 (Algebra.id.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6))) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6))))) (Finsupp.total.{u1, u1, u1} (Set.Elem.{u1} S s) S S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_6))))) 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_inst_6)) _inst_7) S')) -> (forall (i : Set.Elem.{u1} S s), Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : Set.Elem.{u1} S s) => S) i) (Subalgebra.{u2, u1} R S _inst_1 (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) _inst_7) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R S _inst_1 (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) _inst_7) S (Subalgebra.instSetLikeSubalgebra.{u2, u1} R S _inst_1 (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) _inst_7)) (FunLike.coe.{succ u1, succ u1, succ u1} (Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (CommMonoidWithZero.toZero.{u1} S (CommSemiring.toCommMonoidWithZero.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)))) (Set.Elem.{u1} S s) (fun (_x : Set.Elem.{u1} S s) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : Set.Elem.{u1} S s) => S) _x) (Finsupp.funLike.{u1, u1} (Set.Elem.{u1} S s) S (CommMonoidWithZero.toZero.{u1} S (CommSemiring.toCommMonoidWithZero.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)))) l i) S') -> (forall (x : S), (forall (r : Set.Elem.{u1} S s), Exists.{1} Nat (fun (n : Nat) => Membership.mem.{u1, u1} S (Subalgebra.{u2, u1} R S _inst_1 (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) _inst_7) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R S _inst_1 (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) _inst_7) S (Subalgebra.instSetLikeSubalgebra.{u2, u1} R S _inst_1 (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) _inst_7)) (HSMul.hSMul.{u1, u1, u1} S S S (instHSMul.{u1, u1} S S (Algebra.toSMul.{u1, u1} S S (CommRing.toCommSemiring.{u1} S _inst_6) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) (Algebra.id.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)))) (HPow.hPow.{u1, 0, u1} S Nat S (instHPow.{u1, 0} S Nat (Monoid.Pow.{u1} S (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)))))) (Subtype.val.{succ u1} S (fun (x : S) => Membership.mem.{u1, u1} S (Set.{u1} S) (Set.instMembershipSet.{u1} S) x s) r) n) x) S')) -> (Membership.mem.{u1, u1} S (Subalgebra.{u2, u1} R S _inst_1 (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) _inst_7) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R S _inst_1 (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) _inst_7) S (Subalgebra.instSetLikeSubalgebra.{u2, u1} R S _inst_1 (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) _inst_7)) x S'))
 Case conversion may be inaccurate. Consider using '#align subalgebra.mem_of_span_eq_top_of_smul_pow_mem Subalgebra.mem_of_span_eq_top_of_smul_pow_memₓ'. -/
 theorem mem_of_span_eq_top_of_smul_pow_mem {S : Type _} [CommRing S] [Algebra R S]
     (S' : Subalgebra R S) (s : Set S) (l : s →₀ S) (hs : Finsupp.total s S S coe l = 1)

bump to nightly-2023-03-10-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/ddec54a71a0dd025c05445d467f1a2b7d586a3ba

241c8ba6

Diff

@@ -26,6 +26,7 @@ universe u u' v w w'
 
 open BigOperators
 
+#print Subalgebra /-
 /-- A subalgebra is a sub(semi)ring that includes the range of `algebra_map`. -/
 structure Subalgebra (R : Type u) (A : Type v) [CommSemiring R] [Semiring A] [Algebra R A] extends
   Subsemiring A : Type v where
@@ -33,6 +34,7 @@ structure Subalgebra (R : Type u) (A : Type v) [CommSemiring R] [Semiring A] [Al
   zero_mem' := (algebraMap R A).map_zero ▸ algebra_map_mem' 0
   one_mem' := (algebraMap R A).map_one ▸ algebra_map_mem' 1
 #align subalgebra Subalgebra
+-/
 
 /-- Reinterpret a `subalgebra` as a `subsemiring`. -/
 add_decl_doc Subalgebra.toSubsemiring
@@ -59,35 +61,69 @@ instance : SubsemiringClass (Subalgebra R A) A
   one_mem := one_mem'
   zero_mem := zero_mem'
 
+/- warning: subalgebra.mem_carrier -> Subalgebra.mem_carrier is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {s : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3} {x : A}, Iff (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) x (Subalgebra.carrier.{u1, u2} R A _inst_1 _inst_2 _inst_3 s)) (Membership.Mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x s)
+but is expected to have type
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {s : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3} {x : A}, Iff (Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) x (Subsemigroup.carrier.{u2} A (MulOneClass.toMul.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Submonoid.toSubsemigroup.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Subsemiring.toSubmonoid.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2) (Subalgebra.toSubsemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 s))))) (Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x s)
+Case conversion may be inaccurate. Consider using '#align subalgebra.mem_carrier Subalgebra.mem_carrierₓ'. -/
 @[simp]
 theorem mem_carrier {s : Subalgebra R A} {x : A} : x ∈ s.carrier ↔ x ∈ s :=
   Iff.rfl
 #align subalgebra.mem_carrier Subalgebra.mem_carrier
 
+/- warning: subalgebra.ext -> Subalgebra.ext is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align subalgebra.ext Subalgebra.extₓ'. -/
 @[ext]
 theorem ext {S T : Subalgebra R A} (h : ∀ x : A, x ∈ S ↔ x ∈ T) : S = T :=
   SetLike.ext h
 #align subalgebra.ext Subalgebra.ext
 
+/- warning: subalgebra.mem_to_subsemiring -> Subalgebra.mem_toSubsemiring is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3} {x : A}, Iff (Membership.mem.{u2, u2} A (Subsemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (SetLike.instMembership.{u2, u2} (Subsemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) A (Subsemiring.instSetLikeSubsemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) x (Subalgebra.toSubsemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S)) (Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)
+Case conversion may be inaccurate. Consider using '#align subalgebra.mem_to_subsemiring Subalgebra.mem_toSubsemiringₓ'. -/
 @[simp]
 theorem mem_toSubsemiring {S : Subalgebra R A} {x} : x ∈ S.toSubsemiring ↔ x ∈ S :=
   Iff.rfl
 #align subalgebra.mem_to_subsemiring Subalgebra.mem_toSubsemiring
 
+/- warning: subalgebra.coe_to_subsemiring -> Subalgebra.coe_toSubsemiring is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align subalgebra.coe_to_subsemiring Subalgebra.coe_toSubsemiringₓ'. -/
 @[simp]
 theorem coe_toSubsemiring (S : Subalgebra R A) : (↑S.toSubsemiring : Set A) = S :=
   rfl
 #align subalgebra.coe_to_subsemiring Subalgebra.coe_toSubsemiring
 
+#print Subalgebra.toSubsemiring_injective /-
 theorem toSubsemiring_injective :
     Function.Injective (toSubsemiring : Subalgebra R A → Subsemiring A) := fun S T h =>
   ext fun x => by rw [← mem_to_subsemiring, ← mem_to_subsemiring, h]
 #align subalgebra.to_subsemiring_injective Subalgebra.toSubsemiring_injective
+-/
 
+#print Subalgebra.toSubsemiring_inj /-
 theorem toSubsemiring_inj {S U : Subalgebra R A} : S.toSubsemiring = U.toSubsemiring ↔ S = U :=
   toSubsemiring_injective.eq_iff
 #align subalgebra.to_subsemiring_inj Subalgebra.toSubsemiring_inj
+-/
 
+/- warning: subalgebra.copy -> Subalgebra.copy is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align subalgebra.copy Subalgebra.copyₓ'. -/
 /-- Copy of a subalgebra with a new `carrier` equal to the old one. Useful to fix definitional
 equalities. -/
 protected def copy (S : Subalgebra R A) (s : Set A) (hs : s = ↑S) : Subalgebra R A
@@ -98,86 +134,206 @@ protected def copy (S : Subalgebra R A) (s : Set A) (hs : s = ↑S) : Subalgebra
   algebraMap_mem' := hs.symm ▸ S.algebraMap_mem'
 #align subalgebra.copy Subalgebra.copy
 
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 @[simp]
 theorem coe_copy (S : Subalgebra R A) (s : Set A) (hs : s = ↑S) : (S.copy s hs : Set A) = s :=
   rfl
 #align subalgebra.coe_copy Subalgebra.coe_copy
 
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 theorem copy_eq (S : Subalgebra R A) (s : Set A) (hs : s = ↑S) : S.copy s hs = S :=
   SetLike.coe_injective hs
 #align subalgebra.copy_eq Subalgebra.copy_eq
 
 variable (S : Subalgebra R A)
 
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 theorem algebraMap_mem (r : R) : algebraMap R A r ∈ S :=
   S.algebraMap_mem' r
 #align subalgebra.algebra_map_mem Subalgebra.algebraMap_mem
 
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 theorem rangeS_le : (algebraMap R A).srange ≤ S.toSubsemiring := fun x ⟨r, hr⟩ =>
   hr ▸ S.algebraMap_mem r
 #align subalgebra.srange_le Subalgebra.rangeS_le
 
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 theorem range_subset : Set.range (algebraMap R A) ⊆ S := fun x ⟨r, hr⟩ => hr ▸ S.algebraMap_mem r
 #align subalgebra.range_subset Subalgebra.range_subset
 
+/- warning: subalgebra.range_le -> Subalgebra.range_le is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align subalgebra.range_le Subalgebra.range_leₓ'. -/
 theorem range_le : Set.range (algebraMap R A) ≤ S :=
   S.range_subset
 #align subalgebra.range_le Subalgebra.range_le
 
+/- warning: subalgebra.smul_mem -> Subalgebra.smul_mem is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align subalgebra.smul_mem Subalgebra.smul_memₓ'. -/
 theorem smul_mem {x : A} (hx : x ∈ S) (r : R) : r • x ∈ S :=
   (Algebra.smul_def r x).symm ▸ mul_mem (S.algebraMap_mem r) hx
 #align subalgebra.smul_mem Subalgebra.smul_mem
 
+/- warning: subalgebra.one_mem -> Subalgebra.one_mem is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align subalgebra.one_mem Subalgebra.one_memₓ'. -/
 protected theorem one_mem : (1 : A) ∈ S :=
   one_mem S
 #align subalgebra.one_mem Subalgebra.one_mem
 
+/- warning: subalgebra.mul_mem -> Subalgebra.mul_mem is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align subalgebra.mul_mem Subalgebra.mul_memₓ'. -/
 protected theorem mul_mem {x y : A} (hx : x ∈ S) (hy : y ∈ S) : x * y ∈ S :=
   mul_mem hx hy
 #align subalgebra.mul_mem Subalgebra.mul_mem
 
+/- warning: subalgebra.pow_mem -> Subalgebra.pow_mem is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align subalgebra.pow_mem Subalgebra.pow_memₓ'. -/
 protected theorem pow_mem {x : A} (hx : x ∈ S) (n : ℕ) : x ^ n ∈ S :=
   pow_mem hx n
 #align subalgebra.pow_mem Subalgebra.pow_mem
 
+/- warning: subalgebra.zero_mem -> Subalgebra.zero_mem is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align subalgebra.zero_mem Subalgebra.zero_memₓ'. -/
 protected theorem zero_mem : (0 : A) ∈ S :=
   zero_mem S
 #align subalgebra.zero_mem Subalgebra.zero_mem
 
+/- warning: subalgebra.add_mem -> Subalgebra.add_mem is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) {x : A} {y : A}, (Membership.Mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S) -> (Membership.Mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) y S) -> (Membership.Mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y) S)
+but is expected to have type
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) {x : A} {y : A}, (Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S) -> (Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) y S) -> (Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y) S)
+Case conversion may be inaccurate. Consider using '#align subalgebra.add_mem Subalgebra.add_memₓ'. -/
 protected theorem add_mem {x y : A} (hx : x ∈ S) (hy : y ∈ S) : x + y ∈ S :=
   add_mem hx hy
 #align subalgebra.add_mem Subalgebra.add_mem
 
+/- warning: subalgebra.nsmul_mem -> Subalgebra.nsmul_mem is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) {x : A}, (Membership.Mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S) -> (forall (n : Nat), Membership.Mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SMul.smul.{0, u2} Nat A (AddMonoid.SMul.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) n x) S)
+but is expected to have type
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) {x : A}, (Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S) -> (forall (n : Nat), Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HSMul.hSMul.{0, u2, u2} Nat A A (instHSMul.{0, u2} Nat A (AddMonoid.SMul.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) n x) S)
+Case conversion may be inaccurate. Consider using '#align subalgebra.nsmul_mem Subalgebra.nsmul_memₓ'. -/
 protected theorem nsmul_mem {x : A} (hx : x ∈ S) (n : ℕ) : n • x ∈ S :=
   nsmul_mem hx n
 #align subalgebra.nsmul_mem Subalgebra.nsmul_mem
 
+/- warning: subalgebra.coe_nat_mem -> Subalgebra.coe_nat_mem is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (n : Nat), Membership.Mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) ((fun (a : Type) (b : Type.{u2}) [self : HasLiftT.{1, succ u2} a b] => self.0) Nat A (HasLiftT.mk.{1, succ u2} Nat A (CoeTCₓ.coe.{1, succ u2} Nat A (Nat.castCoe.{u2} A (AddMonoidWithOne.toNatCast.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))))) n) S
+but is expected to have type
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (n : Nat), Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Nat.cast.{u2} A (Semiring.toNatCast.{u2} A _inst_2) n) S
+Case conversion may be inaccurate. Consider using '#align subalgebra.coe_nat_mem Subalgebra.coe_nat_memₓ'. -/
 protected theorem coe_nat_mem (n : ℕ) : (n : A) ∈ S :=
   coe_nat_mem S n
 #align subalgebra.coe_nat_mem Subalgebra.coe_nat_mem
 
+/- warning: subalgebra.list_prod_mem -> Subalgebra.list_prod_mem is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) {L : List.{u2} A}, (forall (x : A), (Membership.Mem.{u2, u2} A (List.{u2} A) (List.hasMem.{u2} A) x L) -> (Membership.Mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) -> (Membership.Mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (List.prod.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (AddMonoidWithOne.toOne.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) L) S)
+but is expected to have type
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) {L : List.{u2} A}, (forall (x : A), (Membership.mem.{u2, u2} A (List.{u2} A) (List.instMembershipList.{u2} A) x L) -> (Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) -> (Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (List.prod.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Semiring.toOne.{u2} A _inst_2) L) S)
+Case conversion may be inaccurate. Consider using '#align subalgebra.list_prod_mem Subalgebra.list_prod_memₓ'. -/
 protected theorem list_prod_mem {L : List A} (h : ∀ x ∈ L, x ∈ S) : L.Prod ∈ S :=
   list_prod_mem h
 #align subalgebra.list_prod_mem Subalgebra.list_prod_mem
 
+/- warning: subalgebra.list_sum_mem -> Subalgebra.list_sum_mem is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) {L : List.{u2} A}, (forall (x : A), (Membership.Mem.{u2, u2} A (List.{u2} A) (List.hasMem.{u2} A) x L) -> (Membership.Mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) -> (Membership.Mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (List.sum.{u2} A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulZeroClass.toHasZero.{u2} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) L) S)
+but is expected to have type
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) {L : List.{u2} A}, (forall (x : A), (Membership.mem.{u2, u2} A (List.{u2} A) (List.instMembershipList.{u2} A) x L) -> (Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) -> (Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (List.sum.{u2} A (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) L) S)
+Case conversion may be inaccurate. Consider using '#align subalgebra.list_sum_mem Subalgebra.list_sum_memₓ'. -/
 protected theorem list_sum_mem {L : List A} (h : ∀ x ∈ L, x ∈ S) : L.Sum ∈ S :=
   list_sum_mem h
 #align subalgebra.list_sum_mem Subalgebra.list_sum_mem
 
+/- warning: subalgebra.multiset_sum_mem -> Subalgebra.multiset_sum_mem is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) {m : Multiset.{u2} A}, (forall (x : A), (Membership.mem.{u2, u2} A (Multiset.{u2} A) (Multiset.instMembershipMultiset.{u2} A) x m) -> (Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) -> (Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Multiset.sum.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) m) S)
+Case conversion may be inaccurate. Consider using '#align subalgebra.multiset_sum_mem Subalgebra.multiset_sum_memₓ'. -/
 protected theorem multiset_sum_mem {m : Multiset A} (h : ∀ x ∈ m, x ∈ S) : m.Sum ∈ S :=
   multiset_sum_mem m h
 #align subalgebra.multiset_sum_mem Subalgebra.multiset_sum_mem
 
+/- warning: subalgebra.sum_mem -> Subalgebra.sum_mem is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) {ι : Type.{u3}} {t : Finset.{u3} ι} {f : ι -> A}, (forall (x : ι), (Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) x t) -> (Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (f x) S)) -> (Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Finset.sum.{u2, u3} A ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) t (fun (x : ι) => f x)) S)
+Case conversion may be inaccurate. Consider using '#align subalgebra.sum_mem Subalgebra.sum_memₓ'. -/
 protected theorem sum_mem {ι : Type w} {t : Finset ι} {f : ι → A} (h : ∀ x ∈ t, f x ∈ S) :
     (∑ x in t, f x) ∈ S :=
   sum_mem h
 #align subalgebra.sum_mem Subalgebra.sum_mem
 
+/- warning: subalgebra.multiset_prod_mem -> Subalgebra.multiset_prod_mem is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_8 : CommSemiring.{u1} R] [_inst_9 : CommSemiring.{u2} A] [_inst_10 : Algebra.{u1, u2} R A _inst_8 (CommSemiring.toSemiring.{u2} A _inst_9)] (S : Subalgebra.{u1, u2} R A _inst_8 (CommSemiring.toSemiring.{u2} A _inst_9) _inst_10) {m : Multiset.{u2} A}, (forall (x : A), (Membership.Mem.{u2, u2} A (Multiset.{u2} A) (Multiset.hasMem.{u2} A) x m) -> (Membership.Mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_8 (CommSemiring.toSemiring.{u2} A _inst_9) _inst_10) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R A _inst_8 (CommSemiring.toSemiring.{u2} A _inst_9) _inst_10) A (Subalgebra.setLike.{u1, u2} R A _inst_8 (CommSemiring.toSemiring.{u2} A _inst_9) _inst_10)) x S)) -> (Membership.Mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_8 (CommSemiring.toSemiring.{u2} A _inst_9) _inst_10) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R A _inst_8 (CommSemiring.toSemiring.{u2} A _inst_9) _inst_10) A (Subalgebra.setLike.{u1, u2} R A _inst_8 (CommSemiring.toSemiring.{u2} A _inst_9) _inst_10)) (Multiset.prod.{u2} A (CommSemiring.toCommMonoid.{u2} A _inst_9) m) S)
+but is expected to have type
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_8 : CommSemiring.{u1} R] [_inst_9 : CommSemiring.{u2} A] [_inst_10 : Algebra.{u1, u2} R A _inst_8 (CommSemiring.toSemiring.{u2} A _inst_9)] (S : Subalgebra.{u1, u2} R A _inst_8 (CommSemiring.toSemiring.{u2} A _inst_9) _inst_10) {m : Multiset.{u2} A}, (forall (x : A), (Membership.mem.{u2, u2} A (Multiset.{u2} A) (Multiset.instMembershipMultiset.{u2} A) x m) -> (Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_8 (CommSemiring.toSemiring.{u2} A _inst_9) _inst_10) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_8 (CommSemiring.toSemiring.{u2} A _inst_9) _inst_10) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_8 (CommSemiring.toSemiring.{u2} A _inst_9) _inst_10)) x S)) -> (Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_8 (CommSemiring.toSemiring.{u2} A _inst_9) _inst_10) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_8 (CommSemiring.toSemiring.{u2} A _inst_9) _inst_10) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_8 (CommSemiring.toSemiring.{u2} A _inst_9) _inst_10)) (Multiset.prod.{u2} A (CommSemiring.toCommMonoid.{u2} A _inst_9) m) S)
+Case conversion may be inaccurate. Consider using '#align subalgebra.multiset_prod_mem Subalgebra.multiset_prod_memₓ'. -/
 protected theorem multiset_prod_mem {R : Type u} {A : Type v} [CommSemiring R] [CommSemiring A]
     [Algebra R A] (S : Subalgebra R A) {m : Multiset A} (h : ∀ x ∈ m, x ∈ S) : m.Prod ∈ S :=
   multiset_prod_mem m h
 #align subalgebra.multiset_prod_mem Subalgebra.multiset_prod_mem
 
+/- warning: subalgebra.prod_mem -> Subalgebra.prod_mem is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_8 : CommSemiring.{u1} R] [_inst_9 : CommSemiring.{u2} A] [_inst_10 : Algebra.{u1, u2} R A _inst_8 (CommSemiring.toSemiring.{u2} A _inst_9)] (S : Subalgebra.{u1, u2} R A _inst_8 (CommSemiring.toSemiring.{u2} A _inst_9) _inst_10) {ι : Type.{u3}} {t : Finset.{u3} ι} {f : ι -> A}, (forall (x : ι), (Membership.Mem.{u3, u3} ι (Finset.{u3} ι) (Finset.hasMem.{u3} ι) x t) -> (Membership.Mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_8 (CommSemiring.toSemiring.{u2} A _inst_9) _inst_10) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R A _inst_8 (CommSemiring.toSemiring.{u2} A _inst_9) _inst_10) A (Subalgebra.setLike.{u1, u2} R A _inst_8 (CommSemiring.toSemiring.{u2} A _inst_9) _inst_10)) (f x) S)) -> (Membership.Mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_8 (CommSemiring.toSemiring.{u2} A _inst_9) _inst_10) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R A _inst_8 (CommSemiring.toSemiring.{u2} A _inst_9) _inst_10) A (Subalgebra.setLike.{u1, u2} R A _inst_8 (CommSemiring.toSemiring.{u2} A _inst_9) _inst_10)) (Finset.prod.{u2, u3} A ι (CommSemiring.toCommMonoid.{u2} A _inst_9) t (fun (x : ι) => f x)) S)
+but is expected to have type
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_8 : CommSemiring.{u1} R] [_inst_9 : CommSemiring.{u2} A] [_inst_10 : Algebra.{u1, u2} R A _inst_8 (CommSemiring.toSemiring.{u2} A _inst_9)] (S : Subalgebra.{u1, u2} R A _inst_8 (CommSemiring.toSemiring.{u2} A _inst_9) _inst_10) {ι : Type.{u3}} {t : Finset.{u3} ι} {f : ι -> A}, (forall (x : ι), (Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) x t) -> (Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_8 (CommSemiring.toSemiring.{u2} A _inst_9) _inst_10) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_8 (CommSemiring.toSemiring.{u2} A _inst_9) _inst_10) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_8 (CommSemiring.toSemiring.{u2} A _inst_9) _inst_10)) (f x) S)) -> (Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_8 (CommSemiring.toSemiring.{u2} A _inst_9) _inst_10) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_8 (CommSemiring.toSemiring.{u2} A _inst_9) _inst_10) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_8 (CommSemiring.toSemiring.{u2} A _inst_9) _inst_10)) (Finset.prod.{u2, u3} A ι (CommSemiring.toCommMonoid.{u2} A _inst_9) t (fun (x : ι) => f x)) S)
+Case conversion may be inaccurate. Consider using '#align subalgebra.prod_mem Subalgebra.prod_memₓ'. -/
 protected theorem prod_mem {R : Type u} {A : Type v} [CommSemiring R] [CommSemiring A] [Algebra R A]
     (S : Subalgebra R A) {ι : Type w} {t : Finset ι} {f : ι → A} (h : ∀ x ∈ t, f x ∈ S) :
     (∏ x in t, f x) ∈ S :=
@@ -187,31 +343,57 @@ protected theorem prod_mem {R : Type u} {A : Type v} [CommSemiring R] [CommSemir
 instance {R A : Type _} [CommRing R] [Ring A] [Algebra R A] : SubringClass (Subalgebra R A) A :=
   { Subalgebra.subsemiringClass with neg_mem := fun S x hx => neg_one_smul R x ▸ S.smul_mem hx _ }
 
+/- warning: subalgebra.neg_mem -> Subalgebra.neg_mem is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_8 : CommRing.{u1} R] [_inst_9 : Ring.{u2} A] [_inst_10 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9)] (S : Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) {x : A}, (Membership.Mem.{u2, u2} A (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) A (Subalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10)) x S) -> (Membership.Mem.{u2, u2} A (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) A (Subalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10)) (Neg.neg.{u2} A (SubNegMonoid.toHasNeg.{u2} A (AddGroup.toSubNegMonoid.{u2} A (AddGroupWithOne.toAddGroup.{u2} A (NonAssocRing.toAddGroupWithOne.{u2} A (Ring.toNonAssocRing.{u2} A _inst_9))))) x) S)
+but is expected to have type
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_8 : CommRing.{u1} R] [_inst_9 : Ring.{u2} A] [_inst_10 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9)] (S : Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) {x : A}, (Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10)) x S) -> (Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10)) (Neg.neg.{u2} A (Ring.toNeg.{u2} A _inst_9) x) S)
+Case conversion may be inaccurate. Consider using '#align subalgebra.neg_mem Subalgebra.neg_memₓ'. -/
 protected theorem neg_mem {R : Type u} {A : Type v} [CommRing R] [Ring A] [Algebra R A]
     (S : Subalgebra R A) {x : A} (hx : x ∈ S) : -x ∈ S :=
   neg_mem hx
 #align subalgebra.neg_mem Subalgebra.neg_mem
 
+/- warning: subalgebra.sub_mem -> Subalgebra.sub_mem is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_8 : CommRing.{u1} R] [_inst_9 : Ring.{u2} A] [_inst_10 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9)] (S : Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) {x : A} {y : A}, (Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10)) x S) -> (Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10)) y S) -> (Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10)) (HSub.hSub.{u2, u2, u2} A A A (instHSub.{u2} A (Ring.toSub.{u2} A _inst_9)) x y) S)
+Case conversion may be inaccurate. Consider using '#align subalgebra.sub_mem Subalgebra.sub_memₓ'. -/
 protected theorem sub_mem {R : Type u} {A : Type v} [CommRing R] [Ring A] [Algebra R A]
     (S : Subalgebra R A) {x y : A} (hx : x ∈ S) (hy : y ∈ S) : x - y ∈ S :=
   sub_mem hx hy
 #align subalgebra.sub_mem Subalgebra.sub_mem
 
+/- warning: subalgebra.zsmul_mem -> Subalgebra.zsmul_mem is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_8 : CommRing.{u1} R] [_inst_9 : Ring.{u2} A] [_inst_10 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9)] (S : Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) {x : A}, (Membership.Mem.{u2, u2} A (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) A (Subalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10)) x S) -> (forall (n : Int), Membership.Mem.{u2, u2} A (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) A (Subalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10)) (SMul.smul.{0, u2} Int A (SubNegMonoid.SMulInt.{u2} A (AddGroup.toSubNegMonoid.{u2} A (AddGroupWithOne.toAddGroup.{u2} A (NonAssocRing.toAddGroupWithOne.{u2} A (Ring.toNonAssocRing.{u2} A _inst_9))))) n x) S)
+but is expected to have type
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_8 : CommRing.{u1} R] [_inst_9 : Ring.{u2} A] [_inst_10 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9)] (S : Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) {x : A}, (Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10)) x S) -> (forall (n : Int), Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10)) (HSMul.hSMul.{0, u2, u2} Int A A (instHSMul.{0, u2} Int A (SubNegMonoid.SMulInt.{u2} A (AddGroup.toSubNegMonoid.{u2} A (AddGroupWithOne.toAddGroup.{u2} A (Ring.toAddGroupWithOne.{u2} A _inst_9))))) n x) S)
+Case conversion may be inaccurate. Consider using '#align subalgebra.zsmul_mem Subalgebra.zsmul_memₓ'. -/
 protected theorem zsmul_mem {R : Type u} {A : Type v} [CommRing R] [Ring A] [Algebra R A]
     (S : Subalgebra R A) {x : A} (hx : x ∈ S) (n : ℤ) : n • x ∈ S :=
   zsmul_mem hx n
 #align subalgebra.zsmul_mem Subalgebra.zsmul_mem
 
+/- warning: subalgebra.coe_int_mem -> Subalgebra.coe_int_mem is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_8 : CommRing.{u1} R] [_inst_9 : Ring.{u2} A] [_inst_10 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9)] (S : Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) (n : Int), Membership.Mem.{u2, u2} A (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) A (Subalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10)) ((fun (a : Type) (b : Type.{u2}) [self : HasLiftT.{1, succ u2} a b] => self.0) Int A (HasLiftT.mk.{1, succ u2} Int A (CoeTCₓ.coe.{1, succ u2} Int A (Int.castCoe.{u2} A (AddGroupWithOne.toHasIntCast.{u2} A (NonAssocRing.toAddGroupWithOne.{u2} A (Ring.toNonAssocRing.{u2} A _inst_9)))))) n) S
+but is expected to have type
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_8 : CommRing.{u1} R] [_inst_9 : Ring.{u2} A] [_inst_10 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9)] (S : Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) (n : Int), Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10)) (Int.cast.{u2} A (Ring.toIntCast.{u2} A _inst_9) n) S
+Case conversion may be inaccurate. Consider using '#align subalgebra.coe_int_mem Subalgebra.coe_int_memₓ'. -/
 protected theorem coe_int_mem {R : Type u} {A : Type v} [CommRing R] [Ring A] [Algebra R A]
     (S : Subalgebra R A) (n : ℤ) : (n : A) ∈ S :=
   coe_int_mem S n
 #align subalgebra.coe_int_mem Subalgebra.coe_int_mem
 
+#print Subalgebra.toAddSubmonoid /-
 /-- The projection from a subalgebra of `A` to an additive submonoid of `A`. -/
 def toAddSubmonoid {R : Type u} {A : Type v} [CommSemiring R] [Semiring A] [Algebra R A]
     (S : Subalgebra R A) : AddSubmonoid A :=
   S.toSubsemiring.toAddSubmonoid
 #align subalgebra.to_add_submonoid Subalgebra.toAddSubmonoid
+-/
 
 /-- The projection from a subalgebra of `A` to a submonoid of `A`. -/
 def toSubmonoid {R : Type u} {A : Type v} [CommSemiring R] [Semiring A] [Algebra R A]
@@ -219,33 +401,51 @@ def toSubmonoid {R : Type u} {A : Type v} [CommSemiring R] [Semiring A] [Algebra
   S.toSubsemiring.toSubmonoid
 #align subalgebra.to_submonoid Subalgebra.toSubmonoid
 
+#print Subalgebra.toSubring /-
 /-- A subalgebra over a ring is also a `subring`. -/
 def toSubring {R : Type u} {A : Type v} [CommRing R] [Ring A] [Algebra R A] (S : Subalgebra R A) :
     Subring A :=
   { S.toSubsemiring with neg_mem' := fun _ => S.neg_mem }
 #align subalgebra.to_subring Subalgebra.toSubring
+-/
 
+/- warning: subalgebra.mem_to_subring -> Subalgebra.mem_toSubring is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_8 : CommRing.{u1} R] [_inst_9 : Ring.{u2} A] [_inst_10 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9)] {S : Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10} {x : A}, Iff (Membership.Mem.{u2, u2} A (Subring.{u2} A _inst_9) (SetLike.hasMem.{u2, u2} (Subring.{u2} A _inst_9) A (Subring.setLike.{u2} A _inst_9)) x (Subalgebra.toSubring.{u1, u2} R A _inst_8 _inst_9 _inst_10 S)) (Membership.Mem.{u2, u2} A (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) A (Subalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10)) x S)
+but is expected to have type
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_8 : CommRing.{u1} R] [_inst_9 : Ring.{u2} A] [_inst_10 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9)] {S : Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10} {x : A}, Iff (Membership.mem.{u2, u2} A (Subring.{u2} A _inst_9) (SetLike.instMembership.{u2, u2} (Subring.{u2} A _inst_9) A (Subring.instSetLikeSubring.{u2} A _inst_9)) x (Subalgebra.toSubring.{u1, u2} R A _inst_8 _inst_9 _inst_10 S)) (Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10)) x S)
+Case conversion may be inaccurate. Consider using '#align subalgebra.mem_to_subring Subalgebra.mem_toSubringₓ'. -/
 @[simp]
 theorem mem_toSubring {R : Type u} {A : Type v} [CommRing R] [Ring A] [Algebra R A]
     {S : Subalgebra R A} {x} : x ∈ S.toSubring ↔ x ∈ S :=
   Iff.rfl
 #align subalgebra.mem_to_subring Subalgebra.mem_toSubring
 
+/- warning: subalgebra.coe_to_subring -> Subalgebra.coe_toSubring is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_8 : CommRing.{u1} R] [_inst_9 : Ring.{u2} A] [_inst_10 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9)] (S : Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10), Eq.{succ u2} (Set.{u2} A) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Subring.{u2} A _inst_9) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Subring.{u2} A _inst_9) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Subring.{u2} A _inst_9) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (Subring.{u2} A _inst_9) A (Subring.setLike.{u2} A _inst_9)))) (Subalgebra.toSubring.{u1, u2} R A _inst_8 _inst_9 _inst_10 S)) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) A (Subalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10)))) S)
+but is expected to have type
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_8 : CommRing.{u1} R] [_inst_9 : Ring.{u2} A] [_inst_10 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9)] (S : Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10), Eq.{succ u2} (Set.{u2} A) (SetLike.coe.{u2, u2} (Subring.{u2} A _inst_9) A (Subring.instSetLikeSubring.{u2} A _inst_9) (Subalgebra.toSubring.{u1, u2} R A _inst_8 _inst_9 _inst_10 S)) (SetLike.coe.{u2, u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_10) S)
+Case conversion may be inaccurate. Consider using '#align subalgebra.coe_to_subring Subalgebra.coe_toSubringₓ'. -/
 @[simp]
 theorem coe_toSubring {R : Type u} {A : Type v} [CommRing R] [Ring A] [Algebra R A]
     (S : Subalgebra R A) : (↑S.toSubring : Set A) = S :=
   rfl
 #align subalgebra.coe_to_subring Subalgebra.coe_toSubring
 
+#print Subalgebra.toSubring_injective /-
 theorem toSubring_injective {R : Type u} {A : Type v} [CommRing R] [Ring A] [Algebra R A] :
     Function.Injective (toSubring : Subalgebra R A → Subring A) := fun S T h =>
   ext fun x => by rw [← mem_to_subring, ← mem_to_subring, h]
 #align subalgebra.to_subring_injective Subalgebra.toSubring_injective
+-/
 
+#print Subalgebra.toSubring_inj /-
 theorem toSubring_inj {R : Type u} {A : Type v} [CommRing R] [Ring A] [Algebra R A]
     {S U : Subalgebra R A} : S.toSubring = U.toSubring ↔ S = U :=
   toSubring_injective.eq_iff
 #align subalgebra.to_subring_inj Subalgebra.toSubring_inj
+-/
 
 instance : Inhabited S :=
   ⟨(0 : S.toSubsemiring)⟩
@@ -255,70 +455,154 @@ section
 /-! `subalgebra`s inherit structure from their `subsemiring` / `semiring` coercions. -/
 
 
+/- warning: subalgebra.to_semiring -> Subalgebra.toSemiring is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align subalgebra.to_semiring Subalgebra.toSemiringₓ'. -/
 instance toSemiring {R A} [CommSemiring R] [Semiring A] [Algebra R A] (S : Subalgebra R A) :
     Semiring S :=
   S.toSubsemiring.toSemiring
 #align subalgebra.to_semiring Subalgebra.toSemiring
 
+/- warning: subalgebra.to_comm_semiring -> Subalgebra.toCommSemiring is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align subalgebra.to_comm_semiring Subalgebra.toCommSemiringₓ'. -/
 instance toCommSemiring {R A} [CommSemiring R] [CommSemiring A] [Algebra R A] (S : Subalgebra R A) :
     CommSemiring S :=
   S.toSubsemiring.toCommSemiring
 #align subalgebra.to_comm_semiring Subalgebra.toCommSemiring
 
+/- warning: subalgebra.to_ring -> Subalgebra.toRing is a dubious translation:
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 instance toRing {R A} [CommRing R] [Ring A] [Algebra R A] (S : Subalgebra R A) : Ring S :=
   S.toSubring.toRing
 #align subalgebra.to_ring Subalgebra.toRing
 
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 instance toCommRing {R A} [CommRing R] [CommRing A] [Algebra R A] (S : Subalgebra R A) :
     CommRing S :=
   S.toSubring.toCommRing
 #align subalgebra.to_comm_ring Subalgebra.toCommRing
 
+/- warning: subalgebra.to_ordered_semiring -> Subalgebra.toOrderedSemiring is a dubious translation:
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+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_8 : CommSemiring.{u1} R] [_inst_9 : OrderedSemiring.{u2} A] [_inst_10 : Algebra.{u1, u2} R A _inst_8 (OrderedSemiring.toSemiring.{u2} A _inst_9)] (S : Subalgebra.{u1, u2} R A _inst_8 (OrderedSemiring.toSemiring.{u2} A _inst_9) _inst_10), OrderedSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_8 (OrderedSemiring.toSemiring.{u2} A _inst_9) _inst_10) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_8 (OrderedSemiring.toSemiring.{u2} A _inst_9) _inst_10) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_8 (OrderedSemiring.toSemiring.{u2} A _inst_9) _inst_10)) x S))
+Case conversion may be inaccurate. Consider using '#align subalgebra.to_ordered_semiring Subalgebra.toOrderedSemiringₓ'. -/
 instance toOrderedSemiring {R A} [CommSemiring R] [OrderedSemiring A] [Algebra R A]
     (S : Subalgebra R A) : OrderedSemiring S :=
   S.toSubsemiring.toOrderedSemiring
 #align subalgebra.to_ordered_semiring Subalgebra.toOrderedSemiring
 
+/- warning: subalgebra.to_strict_ordered_semiring -> Subalgebra.toStrictOrderedSemiring is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_8 : CommSemiring.{u1} R] [_inst_9 : StrictOrderedSemiring.{u2} A] [_inst_10 : Algebra.{u1, u2} R A _inst_8 (StrictOrderedSemiring.toSemiring.{u2} A _inst_9)] (S : Subalgebra.{u1, u2} R A _inst_8 (StrictOrderedSemiring.toSemiring.{u2} A _inst_9) _inst_10), StrictOrderedSemiring.{u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_8 (StrictOrderedSemiring.toSemiring.{u2} A _inst_9) _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_8 (StrictOrderedSemiring.toSemiring.{u2} A _inst_9) _inst_10) A (Subalgebra.setLike.{u1, u2} R A _inst_8 (StrictOrderedSemiring.toSemiring.{u2} A _inst_9) _inst_10)) S)
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align subalgebra.to_strict_ordered_semiring Subalgebra.toStrictOrderedSemiringₓ'. -/
 instance toStrictOrderedSemiring {R A} [CommSemiring R] [StrictOrderedSemiring A] [Algebra R A]
     (S : Subalgebra R A) : StrictOrderedSemiring S :=
   S.toSubsemiring.toStrictOrderedSemiring
 #align subalgebra.to_strict_ordered_semiring Subalgebra.toStrictOrderedSemiring
 
+/- warning: subalgebra.to_ordered_comm_semiring -> Subalgebra.toOrderedCommSemiring is a dubious translation:
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+but is expected to have type
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_8 : CommSemiring.{u1} R] [_inst_9 : OrderedCommSemiring.{u2} A] [_inst_10 : Algebra.{u1, u2} R A _inst_8 (OrderedSemiring.toSemiring.{u2} A (OrderedCommSemiring.toOrderedSemiring.{u2} A _inst_9))] (S : Subalgebra.{u1, u2} R A _inst_8 (OrderedSemiring.toSemiring.{u2} A (OrderedCommSemiring.toOrderedSemiring.{u2} A _inst_9)) _inst_10), OrderedCommSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_8 (OrderedSemiring.toSemiring.{u2} A (OrderedCommSemiring.toOrderedSemiring.{u2} A _inst_9)) _inst_10) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_8 (OrderedSemiring.toSemiring.{u2} A (OrderedCommSemiring.toOrderedSemiring.{u2} A _inst_9)) _inst_10) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_8 (OrderedSemiring.toSemiring.{u2} A (OrderedCommSemiring.toOrderedSemiring.{u2} A _inst_9)) _inst_10)) x S))
+Case conversion may be inaccurate. Consider using '#align subalgebra.to_ordered_comm_semiring Subalgebra.toOrderedCommSemiringₓ'. -/
 instance toOrderedCommSemiring {R A} [CommSemiring R] [OrderedCommSemiring A] [Algebra R A]
     (S : Subalgebra R A) : OrderedCommSemiring S :=
   S.toSubsemiring.toOrderedCommSemiring
 #align subalgebra.to_ordered_comm_semiring Subalgebra.toOrderedCommSemiring
 
+/- warning: subalgebra.to_strict_ordered_comm_semiring -> Subalgebra.toStrictOrderedCommSemiring is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align subalgebra.to_strict_ordered_comm_semiring Subalgebra.toStrictOrderedCommSemiringₓ'. -/
 instance toStrictOrderedCommSemiring {R A} [CommSemiring R] [StrictOrderedCommSemiring A]
     [Algebra R A] (S : Subalgebra R A) : StrictOrderedCommSemiring S :=
   S.toSubsemiring.toStrictOrderedCommSemiring
 #align subalgebra.to_strict_ordered_comm_semiring Subalgebra.toStrictOrderedCommSemiring
 
+/- warning: subalgebra.to_ordered_ring -> Subalgebra.toOrderedRing is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align subalgebra.to_ordered_ring Subalgebra.toOrderedRingₓ'. -/
 instance toOrderedRing {R A} [CommRing R] [OrderedRing A] [Algebra R A] (S : Subalgebra R A) :
     OrderedRing S :=
   S.toSubring.toOrderedRing
 #align subalgebra.to_ordered_ring Subalgebra.toOrderedRing
 
+/- warning: subalgebra.to_ordered_comm_ring -> Subalgebra.toOrderedCommRing is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align subalgebra.to_ordered_comm_ring Subalgebra.toOrderedCommRingₓ'. -/
 instance toOrderedCommRing {R A} [CommRing R] [OrderedCommRing A] [Algebra R A]
     (S : Subalgebra R A) : OrderedCommRing S :=
   S.toSubring.toOrderedCommRing
 #align subalgebra.to_ordered_comm_ring Subalgebra.toOrderedCommRing
 
+/- warning: subalgebra.to_linear_ordered_semiring -> Subalgebra.toLinearOrderedSemiring is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align subalgebra.to_linear_ordered_semiring Subalgebra.toLinearOrderedSemiringₓ'. -/
 instance toLinearOrderedSemiring {R A} [CommSemiring R] [LinearOrderedSemiring A] [Algebra R A]
     (S : Subalgebra R A) : LinearOrderedSemiring S :=
   S.toSubsemiring.toLinearOrderedSemiring
 #align subalgebra.to_linear_ordered_semiring Subalgebra.toLinearOrderedSemiring
 
+/- warning: subalgebra.to_linear_ordered_comm_semiring -> Subalgebra.toLinearOrderedCommSemiring is a dubious translation:
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+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_8 : CommSemiring.{u1} R] [_inst_9 : LinearOrderedCommSemiring.{u2} A] [_inst_10 : Algebra.{u1, u2} R A _inst_8 (StrictOrderedSemiring.toSemiring.{u2} A (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} A (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} A _inst_9)))] (S : Subalgebra.{u1, u2} R A _inst_8 (StrictOrderedSemiring.toSemiring.{u2} A (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} A (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} A _inst_9))) _inst_10), LinearOrderedCommSemiring.{u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_8 (StrictOrderedSemiring.toSemiring.{u2} A (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} A (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} A _inst_9))) _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_8 (StrictOrderedSemiring.toSemiring.{u2} A (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} A (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} A _inst_9))) _inst_10) A (Subalgebra.setLike.{u1, u2} R A _inst_8 (StrictOrderedSemiring.toSemiring.{u2} A (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} A (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} A _inst_9))) _inst_10)) S)
+but is expected to have type
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_8 : CommSemiring.{u1} R] [_inst_9 : LinearOrderedCommSemiring.{u2} A] [_inst_10 : Algebra.{u1, u2} R A _inst_8 (StrictOrderedSemiring.toSemiring.{u2} A (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} A (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} A _inst_9)))] (S : Subalgebra.{u1, u2} R A _inst_8 (StrictOrderedSemiring.toSemiring.{u2} A (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} A (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} A _inst_9))) _inst_10), LinearOrderedCommSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_8 (StrictOrderedSemiring.toSemiring.{u2} A (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} A (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} A _inst_9))) _inst_10) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_8 (StrictOrderedSemiring.toSemiring.{u2} A (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} A (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} A _inst_9))) _inst_10) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_8 (StrictOrderedSemiring.toSemiring.{u2} A (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} A (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} A _inst_9))) _inst_10)) x S))
+Case conversion may be inaccurate. Consider using '#align subalgebra.to_linear_ordered_comm_semiring Subalgebra.toLinearOrderedCommSemiringₓ'. -/
 instance toLinearOrderedCommSemiring {R A} [CommSemiring R] [LinearOrderedCommSemiring A]
     [Algebra R A] (S : Subalgebra R A) : LinearOrderedCommSemiring S :=
   S.toSubsemiring.toLinearOrderedCommSemiring
 #align subalgebra.to_linear_ordered_comm_semiring Subalgebra.toLinearOrderedCommSemiring
 
+/- warning: subalgebra.to_linear_ordered_ring -> Subalgebra.toLinearOrderedRing is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_8 : CommRing.{u1} R] [_inst_9 : LinearOrderedRing.{u2} A] [_inst_10 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A (StrictOrderedRing.toRing.{u2} A (LinearOrderedRing.toStrictOrderedRing.{u2} A _inst_9)))] (S : Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A (StrictOrderedRing.toRing.{u2} A (LinearOrderedRing.toStrictOrderedRing.{u2} A _inst_9))) _inst_10), LinearOrderedRing.{u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A (StrictOrderedRing.toRing.{u2} A (LinearOrderedRing.toStrictOrderedRing.{u2} A _inst_9))) _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A (StrictOrderedRing.toRing.{u2} A (LinearOrderedRing.toStrictOrderedRing.{u2} A _inst_9))) _inst_10) A (Subalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A (StrictOrderedRing.toRing.{u2} A (LinearOrderedRing.toStrictOrderedRing.{u2} A _inst_9))) _inst_10)) S)
+but is expected to have type
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_8 : CommRing.{u1} R] [_inst_9 : LinearOrderedRing.{u2} A] [_inst_10 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (StrictOrderedSemiring.toSemiring.{u2} A (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} A (LinearOrderedRing.toLinearOrderedSemiring.{u2} A _inst_9)))] (S : Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (StrictOrderedSemiring.toSemiring.{u2} A (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} A (LinearOrderedRing.toLinearOrderedSemiring.{u2} A _inst_9))) _inst_10), LinearOrderedRing.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (StrictOrderedSemiring.toSemiring.{u2} A (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} A (LinearOrderedRing.toLinearOrderedSemiring.{u2} A _inst_9))) _inst_10) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (StrictOrderedSemiring.toSemiring.{u2} A (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} A (LinearOrderedRing.toLinearOrderedSemiring.{u2} A _inst_9))) _inst_10) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (StrictOrderedSemiring.toSemiring.{u2} A (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} A (LinearOrderedRing.toLinearOrderedSemiring.{u2} A _inst_9))) _inst_10)) x S))
+Case conversion may be inaccurate. Consider using '#align subalgebra.to_linear_ordered_ring Subalgebra.toLinearOrderedRingₓ'. -/
 instance toLinearOrderedRing {R A} [CommRing R] [LinearOrderedRing A] [Algebra R A]
     (S : Subalgebra R A) : LinearOrderedRing S :=
   S.toSubring.toLinearOrderedRing
 #align subalgebra.to_linear_ordered_ring Subalgebra.toLinearOrderedRing
 
+/- warning: subalgebra.to_linear_ordered_comm_ring -> Subalgebra.toLinearOrderedCommRing is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_8 : CommRing.{u1} R] [_inst_9 : LinearOrderedCommRing.{u2} A] [_inst_10 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A (StrictOrderedRing.toRing.{u2} A (LinearOrderedRing.toStrictOrderedRing.{u2} A (LinearOrderedCommRing.toLinearOrderedRing.{u2} A _inst_9))))] (S : Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A (StrictOrderedRing.toRing.{u2} A (LinearOrderedRing.toStrictOrderedRing.{u2} A (LinearOrderedCommRing.toLinearOrderedRing.{u2} A _inst_9)))) _inst_10), LinearOrderedCommRing.{u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A (StrictOrderedRing.toRing.{u2} A (LinearOrderedRing.toStrictOrderedRing.{u2} A (LinearOrderedCommRing.toLinearOrderedRing.{u2} A _inst_9)))) _inst_10) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A (StrictOrderedRing.toRing.{u2} A (LinearOrderedRing.toStrictOrderedRing.{u2} A (LinearOrderedCommRing.toLinearOrderedRing.{u2} A _inst_9)))) _inst_10) A (Subalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A (StrictOrderedRing.toRing.{u2} A (LinearOrderedRing.toStrictOrderedRing.{u2} A (LinearOrderedCommRing.toLinearOrderedRing.{u2} A _inst_9)))) _inst_10)) S)
+but is expected to have type
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_8 : CommRing.{u1} R] [_inst_9 : LinearOrderedCommRing.{u2} A] [_inst_10 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (StrictOrderedSemiring.toSemiring.{u2} A (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} A (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} A (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} A _inst_9))))] (S : Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (StrictOrderedSemiring.toSemiring.{u2} A (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} A (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} A (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} A _inst_9)))) _inst_10), LinearOrderedCommRing.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (StrictOrderedSemiring.toSemiring.{u2} A (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} A (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} A (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} A _inst_9)))) _inst_10) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (StrictOrderedSemiring.toSemiring.{u2} A (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} A (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} A (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} A _inst_9)))) _inst_10) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (StrictOrderedSemiring.toSemiring.{u2} A (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} A (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} A (LinearOrderedCommRing.toLinearOrderedCommSemiring.{u2} A _inst_9)))) _inst_10)) x S))
+Case conversion may be inaccurate. Consider using '#align subalgebra.to_linear_ordered_comm_ring Subalgebra.toLinearOrderedCommRingₓ'. -/
 instance toLinearOrderedCommRing {R A} [CommRing R] [LinearOrderedCommRing A] [Algebra R A]
     (S : Subalgebra R A) : LinearOrderedCommRing S :=
   S.toSubring.toLinearOrderedCommRing
@@ -326,6 +610,12 @@ instance toLinearOrderedCommRing {R A} [CommRing R] [LinearOrderedCommRing A] [A
 
 end
 
+/- warning: subalgebra.to_submodule -> Subalgebra.toSubmodule is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))
+but is expected to have type
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))
+Case conversion may be inaccurate. Consider using '#align subalgebra.to_submodule Subalgebra.toSubmoduleₓ'. -/
 /-- The forgetful map from `subalgebra` to `submodule` as an `order_embedding` -/
 def toSubmodule : Subalgebra R A ↪o Submodule R A
     where
@@ -341,6 +631,12 @@ def toSubmodule : Subalgebra R A ↪o Submodule R A
   map_rel_iff' S T := SetLike.coe_subset_coe.symm.trans SetLike.coe_subset_coe
 #align subalgebra.to_submodule Subalgebra.toSubmodule
 
+/- warning: subalgebra.mem_to_submodule -> Subalgebra.mem_toSubmodule is a dubious translation:
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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) S)) (Membership.Mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)
+but is expected to have type
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) {x : A}, Iff (Membership.mem.{u2, u2} A ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) (SetLike.instMembership.{u2, u2} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (FunLike.coe.{succ u2, succ u2, succ u2} (Function.Embedding.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (fun (_x : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) _x) (EmbeddingLike.toFunLike.{succ u2, succ u2, succ u2} (Function.Embedding.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Function.instEmbeddingLikeEmbedding.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (RelEmbedding.toEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S)) (Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)
+Case conversion may be inaccurate. Consider using '#align subalgebra.mem_to_submodule Subalgebra.mem_toSubmoduleₓ'. -/
 /- TODO: bundle other forgetful maps between algebraic substructures, e.g.
   `to_subsemiring` and `to_subring` in this file. -/
 @[simp]
@@ -348,6 +644,12 @@ theorem mem_toSubmodule {x} : x ∈ S.toSubmodule ↔ x ∈ S :=
   Iff.rfl
 #align subalgebra.mem_to_submodule Subalgebra.mem_toSubmodule
 
+/- warning: subalgebra.coe_to_submodule -> Subalgebra.coe_toSubmodule is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), Eq.{succ u2} (Set.{u2} A) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R A 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(CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A 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_inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) => (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) -> (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (RelEmbedding.hasCoeToFun.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) S)) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) S)
+but is expected to have type
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), Eq.{succ u2} (Set.{u2} A) (SetLike.coe.{u2, u2} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (FunLike.coe.{succ u2, succ u2, succ u2} (Function.Embedding.{succ u2, 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(CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Function.instEmbeddingLikeEmbedding.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (RelEmbedding.toEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S)) (SetLike.coe.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) S)
+Case conversion may be inaccurate. Consider using '#align subalgebra.coe_to_submodule Subalgebra.coe_toSubmoduleₓ'. -/
 @[simp]
 theorem coe_toSubmodule (S : Subalgebra R A) : (↑S.toSubmodule : Set A) = S :=
   rfl
@@ -358,6 +660,12 @@ section
 /-! `subalgebra`s inherit structure from their `submodule` coercions. -/
 
 
+/- warning: subalgebra.module' -> Subalgebra.module' is a dubious translation:
+lean 3 declaration is
+  forall {R' : Type.{u2}} {R : Type.{u1}} {A : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u3} A] [_inst_3 : Algebra.{u1, u3} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) [_inst_8 : Semiring.{u2} R'] [_inst_9 : SMul.{u2, u1} R' R] [_inst_10 : Module.{u2, u3} R' A _inst_8 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2)))] [_inst_11 : IsScalarTower.{u2, u1, u3} R' R A _inst_9 (SMulZeroClass.toHasSmul.{u1, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u1, u3} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toHasSmul.{u2, u3} R' A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} R' A (MulZeroClass.toHasZero.{u2} R' (MulZeroOneClass.toMulZeroClass.{u2} R' (MonoidWithZero.toMulZeroOneClass.{u2} R' (Semiring.toMonoidWithZero.{u2} R' _inst_8)))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} R' A (Semiring.toMonoidWithZero.{u2} R' _inst_8) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2)))))) (Module.toMulActionWithZero.{u2, u3} R' A _inst_8 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) _inst_10))))], Module.{u2, u3} R' (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u3} R A _inst_1 _inst_2 _inst_3)) S) _inst_8 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u3} R A _inst_1 _inst_2 _inst_3)) S) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u3} R A _inst_1 _inst_2 _inst_3)) S) (Semiring.toNonAssocSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u3} R A _inst_1 _inst_2 _inst_3)) S) (Subalgebra.toSemiring.{u1, u3} R A _inst_1 _inst_2 _inst_3 S))))
+but is expected to have type
+  forall {R' : Type.{u2}} {R : Type.{u1}} {A : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u3} A] [_inst_3 : Algebra.{u1, u3} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) [_inst_8 : Semiring.{u2} R'] [_inst_9 : SMul.{u2, u1} R' R] [_inst_10 : Module.{u2, u3} R' A _inst_8 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2)))] [_inst_11 : IsScalarTower.{u2, u1, u3} R' R A _inst_9 (Algebra.toSMul.{u1, u3} R A _inst_1 _inst_2 _inst_3) (SMulZeroClass.toSMul.{u2, u3} R' A (MonoidWithZero.toZero.{u3} A (Semiring.toMonoidWithZero.{u3} A _inst_2)) (SMulWithZero.toSMulZeroClass.{u2, u3} R' A (MonoidWithZero.toZero.{u2} R' (Semiring.toMonoidWithZero.{u2} R' _inst_8)) (MonoidWithZero.toZero.{u3} A (Semiring.toMonoidWithZero.{u3} A _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u3} R' A (Semiring.toMonoidWithZero.{u2} R' _inst_8) (MonoidWithZero.toZero.{u3} A (Semiring.toMonoidWithZero.{u3} A _inst_2)) (Module.toMulActionWithZero.{u2, u3} R' A _inst_8 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) _inst_10))))], Module.{u2, u3} R' (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3)) x S)) _inst_8 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3)) x S)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3)) x S)) (Subsemiring.toNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2) (Subalgebra.toSubsemiring.{u1, u3} R A _inst_1 _inst_2 _inst_3 S))))
+Case conversion may be inaccurate. Consider using '#align subalgebra.module' Subalgebra.module'ₓ'. -/
 instance module' [Semiring R'] [SMul R' R] [Module R' A] [IsScalarTower R' R A] : Module R' S :=
   S.toSubmodule.module'
 #align subalgebra.module' Subalgebra.module'
@@ -368,6 +676,12 @@ instance : Module R S :=
 instance [Semiring R'] [SMul R' R] [Module R' A] [IsScalarTower R' R A] : IsScalarTower R' R S :=
   S.toSubmodule.IsScalarTower
 
+/- warning: subalgebra.algebra' -> Subalgebra.algebra' is a dubious translation:
+lean 3 declaration is
+  forall {R' : Type.{u2}} {R : Type.{u1}} {A : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u3} A] [_inst_3 : Algebra.{u1, u3} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) [_inst_8 : CommSemiring.{u2} R'] [_inst_9 : SMul.{u2, u1} R' R] [_inst_10 : Algebra.{u2, u3} R' A _inst_8 _inst_2] [_inst_11 : IsScalarTower.{u2, u1, u3} R' R A _inst_9 (SMulZeroClass.toHasSmul.{u1, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u1, u3} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toHasSmul.{u2, u3} R' A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} R' A (MulZeroClass.toHasZero.{u2} R' (MulZeroOneClass.toMulZeroClass.{u2} R' (MonoidWithZero.toMulZeroOneClass.{u2} R' (Semiring.toMonoidWithZero.{u2} R' (CommSemiring.toSemiring.{u2} R' _inst_8))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} R' A (Semiring.toMonoidWithZero.{u2} R' (CommSemiring.toSemiring.{u2} R' _inst_8)) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2)))))) (Module.toMulActionWithZero.{u2, u3} R' A (CommSemiring.toSemiring.{u2} R' _inst_8) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R' A _inst_8 _inst_2 _inst_10)))))], Algebra.{u2, u3} R' (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u3} R A _inst_1 _inst_2 _inst_3)) S) _inst_8 (Subalgebra.toSemiring.{u1, u3} R A _inst_1 _inst_2 _inst_3 S)
+but is expected to have type
+  forall {R' : Type.{u2}} {R : Type.{u1}} {A : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u3} A] [_inst_3 : Algebra.{u1, u3} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) [_inst_8 : CommSemiring.{u2} R'] [_inst_9 : SMul.{u2, u1} R' R] [_inst_10 : Algebra.{u2, u3} R' A _inst_8 _inst_2] [_inst_11 : IsScalarTower.{u2, u1, u3} R' R A _inst_9 (Algebra.toSMul.{u1, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.toSMul.{u2, u3} R' A _inst_8 _inst_2 _inst_10)], Algebra.{u2, u3} R' (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3)) x S)) _inst_8 (Subalgebra.toSemiring.{u1, u3} R A _inst_1 _inst_2 _inst_3 S)
+Case conversion may be inaccurate. Consider using '#align subalgebra.algebra' Subalgebra.algebra'ₓ'. -/
 instance algebra' [CommSemiring R'] [SMul R' R] [Algebra R' A] [IsScalarTower R' R A] :
     Algebra R' S :=
   {
@@ -387,168 +701,344 @@ instance : Algebra R S :=
 
 end
 
+/- warning: subalgebra.no_zero_smul_divisors_bot -> Subalgebra.noZeroSMulDivisors_bot is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) [_inst_8 : NoZeroSMulDivisors.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (MulZeroClass.toHasZero.{u2} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A 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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align subalgebra.no_zero_smul_divisors_bot Subalgebra.noZeroSMulDivisors_botₓ'. -/
 instance noZeroSMulDivisors_bot [NoZeroSMulDivisors R A] : NoZeroSMulDivisors R S :=
   ⟨fun c x h =>
     have : c = 0 ∨ (x : A) = 0 := eq_zero_or_eq_zero_of_smul_eq_zero (congr_arg coe h)
     this.imp_right (@Subtype.ext_iff _ _ x 0).mpr⟩
 #align subalgebra.no_zero_smul_divisors_bot Subalgebra.noZeroSMulDivisors_bot
 
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 protected theorem coe_add (x y : S) : (↑(x + y) : A) = ↑x + ↑y :=
   rfl
 #align subalgebra.coe_add Subalgebra.coe_add
 
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 protected theorem coe_mul (x y : S) : (↑(x * y) : A) = ↑x * ↑y :=
   rfl
 #align subalgebra.coe_mul Subalgebra.coe_mul
 
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 protected theorem coe_zero : ((0 : S) : A) = 0 :=
   rfl
 #align subalgebra.coe_zero Subalgebra.coe_zero
 
+#print Subalgebra.coe_one /-
 protected theorem coe_one : ((1 : S) : A) = 1 :=
   rfl
 #align subalgebra.coe_one Subalgebra.coe_one
+-/
 
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+Case conversion may be inaccurate. Consider using '#align subalgebra.coe_neg Subalgebra.coe_negₓ'. -/
 protected theorem coe_neg {R : Type u} {A : Type v} [CommRing R] [Ring A] [Algebra R A]
     {S : Subalgebra R A} (x : S) : (↑(-x) : A) = -↑x :=
   rfl
 #align subalgebra.coe_neg Subalgebra.coe_neg
 
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+Case conversion may be inaccurate. Consider using '#align subalgebra.coe_sub Subalgebra.coe_subₓ'. -/
 protected theorem coe_sub {R : Type u} {A : Type v} [CommRing R] [Ring A] [Algebra R A]
     {S : Subalgebra R A} (x y : S) : (↑(x - y) : A) = ↑x - ↑y :=
   rfl
 #align subalgebra.coe_sub Subalgebra.coe_sub
 
+/- warning: subalgebra.coe_smul -> Subalgebra.coe_smul is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {R' : Type.{u2}} {R : Type.{u1}} {A : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u3} A] [_inst_3 : Algebra.{u1, u3} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) [_inst_8 : Semiring.{u2} R'] [_inst_9 : SMul.{u2, u1} R' R] [_inst_10 : Module.{u2, u3} R' A _inst_8 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2)))] [_inst_11 : IsScalarTower.{u2, u1, u3} R' R A _inst_9 (Algebra.toSMul.{u1, u3} R A _inst_1 _inst_2 _inst_3) (SMulZeroClass.toSMul.{u2, u3} R' A (MonoidWithZero.toZero.{u3} A (Semiring.toMonoidWithZero.{u3} A _inst_2)) (SMulWithZero.toSMulZeroClass.{u2, u3} R' A (MonoidWithZero.toZero.{u2} R' (Semiring.toMonoidWithZero.{u2} R' _inst_8)) (MonoidWithZero.toZero.{u3} A (Semiring.toMonoidWithZero.{u3} A _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u3} R' A (Semiring.toMonoidWithZero.{u2} R' _inst_8) 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(SMulWithZero.toSMulZeroClass.{u2, u3} R' A (MonoidWithZero.toZero.{u2} R' (Semiring.toMonoidWithZero.{u2} R' _inst_8)) (MonoidWithZero.toZero.{u3} A (Semiring.toMonoidWithZero.{u3} A _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u3} R' A (Semiring.toMonoidWithZero.{u2} R' _inst_8) (MonoidWithZero.toZero.{u3} A (Semiring.toMonoidWithZero.{u3} A _inst_2)) (Module.toMulActionWithZero.{u2, u3} R' A _inst_8 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) _inst_10))))) r (Subtype.val.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Set.{u3} A) (Set.instMembershipSet.{u3} A) x (SetLike.coe.{u3, u3} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) S)) x))
+Case conversion may be inaccurate. Consider using '#align subalgebra.coe_smul Subalgebra.coe_smulₓ'. -/
 @[simp, norm_cast]
 theorem coe_smul [Semiring R'] [SMul R' R] [Module R' A] [IsScalarTower R' R A] (r : R') (x : S) :
     (↑(r • x) : A) = r • ↑x :=
   rfl
 #align subalgebra.coe_smul Subalgebra.coe_smul
 
+/- warning: subalgebra.coe_algebra_map -> Subalgebra.coe_algebraMap is a dubious translation:
+lean 3 declaration is
+  forall {R' : Type.{u2}} {R : Type.{u1}} {A : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u3} A] [_inst_3 : Algebra.{u1, u3} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) [_inst_8 : CommSemiring.{u2} R'] [_inst_9 : SMul.{u2, u1} R' R] [_inst_10 : Algebra.{u2, u3} R' A _inst_8 _inst_2] [_inst_11 : IsScalarTower.{u2, u1, u3} R' R A _inst_9 (SMulZeroClass.toHasSmul.{u1, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} R' A (MulZeroClass.toHasZero.{u2} R' (MulZeroOneClass.toMulZeroClass.{u2} R' (MonoidWithZero.toMulZeroOneClass.{u2} R' (Semiring.toMonoidWithZero.{u2} R' (CommSemiring.toSemiring.{u2} R' _inst_8))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} R' A (Semiring.toMonoidWithZero.{u2} R' (CommSemiring.toSemiring.{u2} R' _inst_8)) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A 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+but is expected to have type
+  forall {R' : Type.{u2}} {R : Type.{u1}} {A : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u3} A] [_inst_3 : Algebra.{u1, u3} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) [_inst_8 : CommSemiring.{u2} R'] [_inst_9 : SMul.{u2, u1} R' R] [_inst_10 : Algebra.{u2, u3} R' A _inst_8 _inst_2] [_inst_11 : IsScalarTower.{u2, u1, u3} R' R A _inst_9 (Algebra.toSMul.{u1, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.toSMul.{u2, u3} R' A _inst_8 _inst_2 _inst_10)] (r : R'), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R') => A) r) (Subtype.val.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Set.{u3} A) (Set.instMembershipSet.{u3} A) x (SetLike.coe.{u3, u3} (Subalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u3} R A _inst_1 _inst_2 _inst_3) S)) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RingHom.{u2, u3} R' (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A 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 @[simp, norm_cast]
 theorem coe_algebraMap [CommSemiring R'] [SMul R' R] [Algebra R' A] [IsScalarTower R' R A]
     (r : R') : ↑(algebraMap R' S r) = algebraMap R' A r :=
   rfl
 #align subalgebra.coe_algebra_map Subalgebra.coe_algebraMap
 
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 protected theorem coe_pow (x : S) (n : ℕ) : (↑(x ^ n) : A) = ↑x ^ n :=
   SubmonoidClass.coe_pow x n
 #align subalgebra.coe_pow Subalgebra.coe_pow
 
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 protected theorem coe_eq_zero {x : S} : (x : A) = 0 ↔ x = 0 :=
   ZeroMemClass.coe_eq_zero
 #align subalgebra.coe_eq_zero Subalgebra.coe_eq_zero
 
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 protected theorem coe_eq_one {x : S} : (x : A) = 1 ↔ x = 1 :=
   OneMemClass.coe_eq_one
 #align subalgebra.coe_eq_one Subalgebra.coe_eq_one
 
+/- warning: subalgebra.val -> Subalgebra.val is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align subalgebra.val Subalgebra.valₓ'. -/
 -- todo: standardize on the names these morphisms
 -- compare with submodule.subtype
 /-- Embedding of a subalgebra into the algebra. -/
 def val : S →ₐ[R] A := by refine_struct { toFun := (coe : S → A) } <;> intros <;> rfl
 #align subalgebra.val Subalgebra.val
 
+/- warning: subalgebra.coe_val -> Subalgebra.coe_val is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align subalgebra.coe_val Subalgebra.coe_valₓ'. -/
 @[simp]
 theorem coe_val : (S.val : S → A) = coe :=
   rfl
 #align subalgebra.coe_val Subalgebra.coe_val
 
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+but is expected to have type
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_inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_2 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_3) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (fun (_x : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) => A) _x) (SMulHomClass.toFunLike.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_2 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_3) R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 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(Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S)))))) (DistribSMul.toSMulZeroClass.{u1, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (AddMonoid.toAddZeroClass.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A 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(DistribMulActionHomClass.toSMulHomClass.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_2 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) _inst_3) R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S)) A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} 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+Case conversion may be inaccurate. Consider using '#align subalgebra.val_apply Subalgebra.val_applyₓ'. -/
 theorem val_apply (x : S) : S.val x = (x : A) :=
   rfl
 #align subalgebra.val_apply Subalgebra.val_apply
 
+/- warning: subalgebra.to_subsemiring_subtype -> Subalgebra.toSubsemiring_subtype is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align subalgebra.to_subsemiring_subtype Subalgebra.toSubsemiring_subtypeₓ'. -/
 @[simp]
 theorem toSubsemiring_subtype : S.toSubsemiring.Subtype = (S.val : S →+* A) :=
   rfl
 #align subalgebra.to_subsemiring_subtype Subalgebra.toSubsemiring_subtype
 
+/- warning: subalgebra.to_subring_subtype -> Subalgebra.toSubring_subtype is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align subalgebra.to_subring_subtype Subalgebra.toSubring_subtypeₓ'. -/
 @[simp]
 theorem toSubring_subtype {R A : Type _} [CommRing R] [Ring A] [Algebra R A] (S : Subalgebra R A) :
     S.toSubring.Subtype = (S.val : S →+* A) :=
   rfl
 #align subalgebra.to_subring_subtype Subalgebra.toSubring_subtype
 
+/- warning: subalgebra.to_submodule_equiv -> Subalgebra.toSubmoduleEquiv is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A 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+Case conversion may be inaccurate. Consider using '#align subalgebra.to_submodule_equiv Subalgebra.toSubmoduleEquivₓ'. -/
 /-- Linear equivalence between `S : submodule R A` and `S`. Though these types are equal,
 we define it as a `linear_equiv` to avoid type equalities. -/
 def toSubmoduleEquiv (S : Subalgebra R A) : S.toSubmodule ≃ₗ[R] S :=
   LinearEquiv.ofEq _ _ rfl
 #align subalgebra.to_submodule_equiv Subalgebra.toSubmoduleEquiv
 
+#print Subalgebra.map /-
 /-- Transport a subalgebra via an algebra homomorphism. -/
 def map (f : A →ₐ[R] B) (S : Subalgebra R A) : Subalgebra R B :=
   { S.toSubsemiring.map (f : A →+* B) with
     algebraMap_mem' := fun r => f.commutes r ▸ Set.mem_image_of_mem _ (S.algebraMap_mem r) }
 #align subalgebra.map Subalgebra.map
+-/
 
+/- warning: subalgebra.map_mono -> Subalgebra.map_mono is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align subalgebra.map_mono Subalgebra.map_monoₓ'. -/
 theorem map_mono {S₁ S₂ : Subalgebra R A} {f : A →ₐ[R] B} : S₁ ≤ S₂ → S₁.map f ≤ S₂.map f :=
   Set.image_subset f
 #align subalgebra.map_mono Subalgebra.map_mono
 
+#print Subalgebra.map_injective /-
 theorem map_injective {f : A →ₐ[R] B} (hf : Function.Injective f) : Function.Injective (map f) :=
   fun S₁ S₂ ih =>
   ext <| Set.ext_iff.1 <| Set.image_injective.2 hf <| Set.ext <| SetLike.ext_iff.mp ih
 #align subalgebra.map_injective Subalgebra.map_injective
+-/
 
+#print Subalgebra.map_id /-
 @[simp]
 theorem map_id (S : Subalgebra R A) : S.map (AlgHom.id R A) = S :=
   SetLike.coe_injective <| Set.image_id _
 #align subalgebra.map_id Subalgebra.map_id
+-/
 
+#print Subalgebra.map_map /-
 theorem map_map (S : Subalgebra R A) (g : B →ₐ[R] C) (f : A →ₐ[R] B) :
     (S.map f).map g = S.map (g.comp f) :=
   SetLike.coe_injective <| Set.image_image _ _ _
 #align subalgebra.map_map Subalgebra.map_map
+-/
 
+/- warning: subalgebra.mem_map -> Subalgebra.mem_map is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align subalgebra.mem_map Subalgebra.mem_mapₓ'. -/
 theorem mem_map {S : Subalgebra R A} {f : A →ₐ[R] B} {y : B} : y ∈ map f S ↔ ∃ x ∈ S, f x = y :=
   Subsemiring.mem_map
 #align subalgebra.mem_map Subalgebra.mem_map
 
+/- warning: subalgebra.map_to_submodule -> Subalgebra.map_toSubmodule is a dubious translation:
+lean 3 declaration is
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(Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 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(CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) S))
+but is expected to have type
+  forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] {S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3} {f : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5}, Eq.{succ u3} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) => Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (Subalgebra.map.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 f S)) (FunLike.coe.{succ u3, succ u3, succ u3} (Function.Embedding.{succ u3, succ u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Submodule.{u1, u3} R B 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_inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) => LE.le.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (Preorder.toLE.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (PartialOrder.toPreorder.{u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instPartialOrder.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) 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+Case conversion may be inaccurate. Consider using '#align subalgebra.map_to_submodule Subalgebra.map_toSubmoduleₓ'. -/
 theorem map_toSubmodule {S : Subalgebra R A} {f : A →ₐ[R] B} :
     (S.map f).toSubmodule = S.toSubmodule.map f.toLinearMap :=
   SetLike.coe_injective rfl
 #align subalgebra.map_to_submodule Subalgebra.map_toSubmodule
 
+#print Subalgebra.map_toSubsemiring /-
 theorem map_toSubsemiring {S : Subalgebra R A} {f : A →ₐ[R] B} :
     (S.map f).toSubsemiring = S.toSubsemiring.map f.toRingHom :=
   SetLike.coe_injective rfl
 #align subalgebra.map_to_subsemiring Subalgebra.map_toSubsemiring
+-/
 
+/- warning: subalgebra.coe_map -> Subalgebra.coe_map is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align subalgebra.coe_map Subalgebra.coe_mapₓ'. -/
 @[simp]
 theorem coe_map (S : Subalgebra R A) (f : A →ₐ[R] B) : (S.map f : Set B) = f '' S :=
   rfl
 #align subalgebra.coe_map Subalgebra.coe_map
 
+#print Subalgebra.comap /-
 /-- Preimage of a subalgebra under an algebra homomorphism. -/
 def comap (f : A →ₐ[R] B) (S : Subalgebra R B) : Subalgebra R A :=
   { S.toSubsemiring.comap (f : A →+* B) with
     algebraMap_mem' := fun r =>
       show f (algebraMap R A r) ∈ S from (f.commutes r).symm ▸ S.algebraMap_mem r }
 #align subalgebra.comap Subalgebra.comap
+-/
 
+/- warning: subalgebra.map_le -> Subalgebra.map_le is a dubious translation:
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 theorem map_le {S : Subalgebra R A} {f : A →ₐ[R] B} {U : Subalgebra R B} :
     map f S ≤ U ↔ S ≤ comap f U :=
   Set.image_subset_iff
 #align subalgebra.map_le Subalgebra.map_le
 
+/- warning: subalgebra.gc_map_comap -> Subalgebra.gc_map_comap is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align subalgebra.gc_map_comap Subalgebra.gc_map_comapₓ'. -/
 theorem gc_map_comap (f : A →ₐ[R] B) : GaloisConnection (map f) (comap f) := fun S U => map_le
 #align subalgebra.gc_map_comap Subalgebra.gc_map_comap
 
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+Case conversion may be inaccurate. Consider using '#align subalgebra.mem_comap Subalgebra.mem_comapₓ'. -/
 @[simp]
 theorem mem_comap (S : Subalgebra R B) (f : A →ₐ[R] B) (x : A) : x ∈ S.comap f ↔ f x ∈ S :=
   Iff.rfl
 #align subalgebra.mem_comap Subalgebra.mem_comap
 
+/- warning: subalgebra.coe_comap -> Subalgebra.coe_comap is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align subalgebra.coe_comap Subalgebra.coe_comapₓ'. -/
 @[simp, norm_cast]
 theorem coe_comap (S : Subalgebra R B) (f : A →ₐ[R] B) : (S.comap f : Set A) = f ⁻¹' (S : Set B) :=
   rfl
 #align subalgebra.coe_comap Subalgebra.coe_comap
 
+/- warning: subalgebra.no_zero_divisors -> Subalgebra.noZeroDivisors is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align subalgebra.no_zero_divisors Subalgebra.noZeroDivisorsₓ'. -/
 instance noZeroDivisors {R A : Type _} [CommSemiring R] [Semiring A] [NoZeroDivisors A]
     [Algebra R A] (S : Subalgebra R A) : NoZeroDivisors S :=
   S.toSubsemiring.NoZeroDivisors
 #align subalgebra.no_zero_divisors Subalgebra.noZeroDivisors
 
+/- warning: subalgebra.is_domain -> Subalgebra.isDomain is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_8 : CommRing.{u1} R] [_inst_9 : Ring.{u2} A] [_inst_10 : IsDomain.{u2} A (Ring.toSemiring.{u2} A _inst_9)] [_inst_11 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9)] (S : Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_11), IsDomain.{u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_11) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_11) A (Subalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_11)) S) (Subalgebra.toSemiring.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_11 S)
+but is expected to have type
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_8 : CommRing.{u1} R] [_inst_9 : Ring.{u2} A] [_inst_10 : IsDomain.{u2} A (Ring.toSemiring.{u2} A _inst_9)] [_inst_11 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9)] (S : Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_11), IsDomain.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_11) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_11) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_11)) x S)) (Subalgebra.toSemiring.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_8) (Ring.toSemiring.{u2} A _inst_9) _inst_11 S)
+Case conversion may be inaccurate. Consider using '#align subalgebra.is_domain Subalgebra.isDomainₓ'. -/
 instance isDomain {R A : Type _} [CommRing R] [Ring A] [IsDomain A] [Algebra R A]
     (S : Subalgebra R A) : IsDomain S :=
   Subring.isDomain S.toSubring
@@ -562,6 +1052,12 @@ variable {R A : Type _} [CommSemiring R] [Semiring A] [Algebra R A]
 
 variable (p : Submodule R A)
 
+/- warning: submodule.to_subalgebra -> Submodule.toSubalgebra is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align submodule.to_subalgebra Submodule.toSubalgebraₓ'. -/
 /-- A submodule containing `1` and closed under multiplication is a subalgebra. -/
 def toSubalgebra (p : Submodule R A) (h_one : (1 : A) ∈ p)
     (h_mul : ∀ x y, x ∈ p → y ∈ p → x * y ∈ p) : Subalgebra R A :=
@@ -572,18 +1068,36 @@ def toSubalgebra (p : Submodule R A) (h_one : (1 : A) ∈ p)
       exact p.smul_mem _ h_one }
 #align submodule.to_subalgebra Submodule.toSubalgebra
 
+/- warning: submodule.mem_to_subalgebra -> Submodule.mem_toSubalgebra is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u1} A] [_inst_3 : Algebra.{u2, u1} R A _inst_1 _inst_2] {p : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)} {h_one : Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) 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(Submodule.instSetLikeSubmodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) y p) -> (Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u1, u1, u1} A A A (instHMul.{u1} A (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) x y) p)} {x : A}, Iff (Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3)) x (Submodule.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 p h_one h_mul)) (Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) x p)
+Case conversion may be inaccurate. Consider using '#align submodule.mem_to_subalgebra Submodule.mem_toSubalgebraₓ'. -/
 @[simp]
 theorem mem_toSubalgebra {p : Submodule R A} {h_one h_mul} {x} :
     x ∈ p.toSubalgebra h_one h_mul ↔ x ∈ p :=
   Iff.rfl
 #align submodule.mem_to_subalgebra Submodule.mem_toSubalgebra
 
+/- warning: submodule.coe_to_subalgebra -> Submodule.coe_toSubalgebra is a dubious translation:
+lean 3 declaration is
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(Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y) p)), Eq.{succ u2} (Set.{u2} A) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 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+but is expected to have type
+  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u1} A] [_inst_3 : Algebra.{u2, u1} R A _inst_1 _inst_2] (p : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (h_one : Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) (OfNat.ofNat.{u1} A 1 (One.toOfNat1.{u1} A (Semiring.toOne.{u1} A _inst_2))) p) (h_mul : forall (x : A) (y : A), (Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) x p) -> (Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) y p) -> (Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u1, u1, u1} A A A (instHMul.{u1} A (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) x y) p)), Eq.{succ u1} (Set.{u1} A) (SetLike.coe.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 p h_one h_mul)) (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) p)
+Case conversion may be inaccurate. Consider using '#align submodule.coe_to_subalgebra Submodule.coe_toSubalgebraₓ'. -/
 @[simp]
 theorem coe_toSubalgebra (p : Submodule R A) (h_one h_mul) :
     (p.toSubalgebra h_one h_mul : Set A) = p :=
   rfl
 #align submodule.coe_to_subalgebra Submodule.coe_toSubalgebra
 
+/- warning: submodule.to_subalgebra_mk -> Submodule.toSubalgebra_mk is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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(NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (Submonoid.toSubsemigroup.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemiring.toSubmonoid.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Subsemiring.mk.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Submonoid.mk.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemigroup.mk.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) s) hadd) h0) (fun {a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6404 : A} {b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6405 : A} => Submodule.add_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6404 b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6405) (Submodule.zero_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s)))))) (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => A) r) (Set.{u1} A) (Set.instMembershipSet.{u1} A) _a (Subsemigroup.carrier.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (Submonoid.toSubsemigroup.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemiring.toSubmonoid.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Subsemiring.mk.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Submonoid.mk.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemigroup.mk.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) s) hadd) h0) (fun {a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6404 : A} {b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6405 : A} => Submodule.add_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6404 b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6405) (Submodule.zero_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s))))))) (Eq.refl.{1} Prop (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => A) r) (Set.{u1} A) (Set.instMembershipSet.{u1} A) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => A) a) 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u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2) (RingHom.instRingHomClassRingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} A _inst_2))))) (algebraMap.{u2, u1} R A _inst_1 _inst_2 _inst_3) r) (Subsemigroup.carrier.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (Submonoid.toSubsemigroup.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemiring.toSubmonoid.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Subsemiring.mk.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2) (Submonoid.mk.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Subsemigroup.mk.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) s) hadd) h0) (fun {a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6404 : A} {b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6405 : A} => Submodule.add_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s a._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6404 b._@.Mathlib.Algebra.Algebra.Subalgebra.Basic._hyg.6405) (Submodule.zero_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s))))))) (HSMul.hSMul.{u2, u1, u1} R A A (instHSMul.{u2, u1} R A (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_2 _inst_3)) r (OfNat.ofNat.{u1} A 1 (One.toOfNat1.{u1} A (Semiring.toOne.{u1} A _inst_2)))) (Algebra.algebraMap_eq_smul_one.{u2, u1} R A _inst_1 _inst_2 _inst_3 r))) (Submodule.smul_mem.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3) s (OfNat.ofNat.{u1} A 1 (One.toOfNat1.{u1} A (Semiring.toOne.{u1} A _inst_2))) r h0)))
+Case conversion may be inaccurate. Consider using '#align submodule.to_subalgebra_mk Submodule.toSubalgebra_mkₓ'. -/
 @[simp]
 theorem toSubalgebra_mk (s : Set A) (h0 hadd hsmul h1 hmul) :
     (Submodule.mk s hadd h0 hsmul : Submodule R A).toSubalgebra h1 hmul =
@@ -594,12 +1108,24 @@ theorem toSubalgebra_mk (s : Set A) (h0 hadd hsmul h1 hmul) :
   rfl
 #align submodule.to_subalgebra_mk Submodule.toSubalgebra_mk
 
+/- warning: submodule.to_subalgebra_to_submodule -> Submodule.toSubalgebra_toSubmodule is a dubious translation:
+lean 3 declaration is
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R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (OfNat.ofNat.{u2} A 1 (OfNat.mk.{u2} A 1 (One.one.{u2} A (AddMonoidWithOne.toOne.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))))) p) (h_mul : forall (x : A) (y : A), (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x p) -> (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A 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_inst_1 _inst_2 _inst_3))))))) (fun (_x : RelEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 p h_one h_mul)) p
+but is expected to have type
+  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u1} A] [_inst_3 : Algebra.{u2, u1} R A _inst_1 _inst_2] (p : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (h_one : Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) (OfNat.ofNat.{u1} A 1 (One.toOfNat1.{u1} A (Semiring.toOne.{u1} A _inst_2))) p) (h_mul : forall (x : A) (y : A), (Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) x p) -> (Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) y p) -> (Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u1, u1, u1} A A A (instHMul.{u1} A (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) x y) p)), Eq.{succ u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Submodule.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 p h_one h_mul)) (FunLike.coe.{succ u1, succ u1, succ u1} (Function.Embedding.{succ u1, succ u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Function.instEmbeddingLikeEmbedding.{succ u1, succ u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)))) (RelEmbedding.toEmbedding.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => LE.le.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Subalgebra.toSubmodule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Submodule.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 p h_one h_mul)) p
+Case conversion may be inaccurate. Consider using '#align submodule.to_subalgebra_to_submodule Submodule.toSubalgebra_toSubmoduleₓ'. -/
 @[simp]
 theorem toSubalgebra_toSubmodule (p : Submodule R A) (h_one h_mul) :
     (p.toSubalgebra h_one h_mul).toSubmodule = p :=
   SetLike.coe_injective rfl
 #align submodule.to_subalgebra_to_submodule Submodule.toSubalgebra_toSubmodule
 
+/- warning: subalgebra.to_submodule_to_subalgebra -> Subalgebra.toSubmodule_toSubalgebra is a dubious translation:
+lean 3 declaration is
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_inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, 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_inst_1 _inst_2 _inst_3) S) (Subalgebra.one_mem.{u1, u2} R A _inst_1 _inst_2 _inst_3 S) (fun (_x : A) (_x_1 : A) => Subalgebra.mul_mem.{u1, u2} R A _inst_1 _inst_2 _inst_3 S _x _x_1)) S
+but is expected to have type
+  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u1} A] [_inst_3 : Algebra.{u2, u1} R A _inst_1 _inst_2] (S : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3), Eq.{succ u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 (FunLike.coe.{succ u1, succ u1, succ u1} (Function.Embedding.{succ u1, succ u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (fun (_x : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) _x) (EmbeddingLike.toFunLike.{succ u1, succ u1, succ u1} (Function.Embedding.{succ u1, succ u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Function.instEmbeddingLikeEmbedding.{succ u1, succ u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)))) (RelEmbedding.toEmbedding.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => LE.le.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Subalgebra.toSubmodule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) S) (Subalgebra.one_mem.{u2, u1} R A _inst_1 _inst_2 _inst_3 S) (fun (_x : A) (_x_1 : A) => Subalgebra.mul_mem.{u2, u1} R A _inst_1 _inst_2 _inst_3 S _x _x_1)) S
+Case conversion may be inaccurate. Consider using '#align subalgebra.to_submodule_to_subalgebra Subalgebra.toSubmodule_toSubalgebraₓ'. -/
 @[simp]
 theorem Subalgebra.toSubmodule_toSubalgebra (S : Subalgebra R A) :
     (S.toSubmodule.toSubalgebra S.one_mem fun _ _ => S.mul_mem) = S :=
@@ -618,20 +1144,40 @@ variable [Semiring A] [Algebra R A] [Semiring B] [Algebra R B] [Semiring C] [Alg
 
 variable (φ : A →ₐ[R] B)
 
+#print AlgHom.range /-
 /-- Range of an `alg_hom` as a subalgebra. -/
 protected def range (φ : A →ₐ[R] B) : Subalgebra R B :=
   { φ.toRingHom.srange with algebraMap_mem' := fun r => ⟨algebraMap R A r, φ.commutes r⟩ }
 #align alg_hom.range AlgHom.range
+-/
 
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 @[simp]
 theorem mem_range (φ : A →ₐ[R] B) {y : B} : y ∈ φ.range ↔ ∃ x, φ x = y :=
   RingHom.mem_rangeS
 #align alg_hom.mem_range AlgHom.mem_range
 
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+Case conversion may be inaccurate. Consider using '#align alg_hom.mem_range_self AlgHom.mem_range_selfₓ'. -/
 theorem mem_range_self (φ : A →ₐ[R] B) (x : A) : φ x ∈ φ.range :=
   φ.mem_range.2 ⟨x, rfl⟩
 #align alg_hom.mem_range_self AlgHom.mem_range_self
 
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+Case conversion may be inaccurate. Consider using '#align alg_hom.coe_range AlgHom.coe_rangeₓ'. -/
 @[simp]
 theorem coe_range (φ : A →ₐ[R] B) : (φ.range : Set B) = Set.range φ :=
   by
@@ -640,36 +1186,74 @@ theorem coe_range (φ : A →ₐ[R] B) : (φ.range : Set B) = Set.range φ :=
   rfl
 #align alg_hom.coe_range AlgHom.coe_range
 
+#print AlgHom.range_comp /-
 theorem range_comp (f : A →ₐ[R] B) (g : B →ₐ[R] C) : (g.comp f).range = f.range.map g :=
   SetLike.coe_injective (Set.range_comp g f)
 #align alg_hom.range_comp AlgHom.range_comp
+-/
 
+/- warning: alg_hom.range_comp_le_range -> AlgHom.range_comp_le_range is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align alg_hom.range_comp_le_range AlgHom.range_comp_le_rangeₓ'. -/
 theorem range_comp_le_range (f : A →ₐ[R] B) (g : B →ₐ[R] C) : (g.comp f).range ≤ g.range :=
   SetLike.coe_mono (Set.range_comp_subset_range f g)
 #align alg_hom.range_comp_le_range AlgHom.range_comp_le_range
 
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x) S) -> (AlgHom.{u1, u2, u3} R A (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) _inst_1 _inst_2 (Subalgebra.toSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S) _inst_3 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S))
+Case conversion may be inaccurate. Consider using '#align alg_hom.cod_restrict AlgHom.codRestrictₓ'. -/
 /-- Restrict the codomain of an algebra homomorphism. -/
 def codRestrict (f : A →ₐ[R] B) (S : Subalgebra R B) (hf : ∀ x, f x ∈ S) : A →ₐ[R] S :=
   { RingHom.codRestrict (f : A →+* B) S hf with commutes' := fun r => Subtype.eq <| f.commutes r }
 #align alg_hom.cod_restrict AlgHom.codRestrict
 
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+Case conversion may be inaccurate. Consider using '#align alg_hom.val_comp_cod_restrict AlgHom.val_comp_codRestrictₓ'. -/
 @[simp]
 theorem val_comp_codRestrict (f : A →ₐ[R] B) (S : Subalgebra R B) (hf : ∀ x, f x ∈ S) :
     S.val.comp (f.codRestrict S hf) = f :=
   AlgHom.ext fun _ => rfl
 #align alg_hom.val_comp_cod_restrict AlgHom.val_comp_codRestrict
 
+/- warning: alg_hom.coe_cod_restrict -> AlgHom.coe_codRestrict is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] (f : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (S : Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (hf : forall (x : A), Membership.mem.{u3, u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) x) (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) _x) (SMulHomClass.toFunLike.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 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+Case conversion may be inaccurate. Consider using '#align alg_hom.coe_cod_restrict AlgHom.coe_codRestrictₓ'. -/
 @[simp]
 theorem coe_codRestrict (f : A →ₐ[R] B) (S : Subalgebra R B) (hf : ∀ x, f x ∈ S) (x : A) :
     ↑(f.codRestrict S hf x) = f x :=
   rfl
 #align alg_hom.coe_cod_restrict AlgHom.coe_codRestrict
 
+/- warning: alg_hom.injective_cod_restrict -> AlgHom.injective_codRestrict is a dubious translation:
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+but is expected to have type
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u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) (Semiring.toNonAssocSemiring.{u3} (Subtype.{succ u3} B (fun (x : B) => 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(AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u2, u3, max u2 u3} R A (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.instSetLikeSubalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5)) x S)) _inst_1 _inst_2 (Subalgebra.toSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S) _inst_3 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 S) (AlgHom.{u1, u2, u3} R A (Subtype.{succ u3} B (fun (x : B) => Membership.mem.{u3, u3} B (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) (SetLike.instMembership.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toSMul.{u1, u3} R B (AddMonoid.toZero.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))))) (DistribSMul.toSMulZeroClass.{u1, u3} R B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))))) (DistribMulAction.toDistribSMul.{u1, u3} R B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)))) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) R A B (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4)) (Module.toDistribMulAction.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_4))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u2, u3, max u2 u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 (AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (AlgHom.algHomClass.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5))))) f))
+Case conversion may be inaccurate. Consider using '#align alg_hom.injective_cod_restrict AlgHom.injective_codRestrictₓ'. -/
 theorem injective_codRestrict (f : A →ₐ[R] B) (S : Subalgebra R B) (hf : ∀ x, f x ∈ S) :
     Function.Injective (f.codRestrict S hf) ↔ Function.Injective f :=
   ⟨fun H x y hxy => H <| Subtype.eq hxy, fun H x y hxy => H (congr_arg Subtype.val hxy : _)⟩
 #align alg_hom.injective_cod_restrict AlgHom.injective_codRestrict
 
+/- warning: alg_hom.range_restrict -> AlgHom.rangeRestrict is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] (f : AlgHom.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5), AlgHom.{u1, u2, u3} R A (coeSort.{succ u3, succ (succ u3)} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5) B (Subalgebra.setLike.{u1, u3} R B _inst_1 _inst_4 _inst_5)) (AlgHom.range.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 f)) _inst_1 _inst_2 (Subalgebra.toSemiring.{u1, u3} R B _inst_1 _inst_4 _inst_5 (AlgHom.range.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 f)) _inst_3 (Subalgebra.algebra.{u1, u3} R B _inst_1 _inst_4 _inst_5 (AlgHom.range.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 f))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align alg_hom.range_restrict AlgHom.rangeRestrictₓ'. -/
 /-- Restrict the codomain of a alg_hom `f` to `f.range`.
 
 This is the bundled version of `set.range_factorization`. -/
@@ -678,6 +1262,7 @@ def rangeRestrict (f : A →ₐ[R] B) : A →ₐ[R] f.range :=
   f.codRestrict f.range f.mem_range_self
 #align alg_hom.range_restrict AlgHom.rangeRestrict
 
+#print AlgHom.equalizer /-
 /-- The equalizer of two R-algebra homomorphisms -/
 def equalizer (ϕ ψ : A →ₐ[R] B) : Subalgebra R A
     where
@@ -688,12 +1273,25 @@ def equalizer (ϕ ψ : A →ₐ[R] B) : Subalgebra R A
     rw [Set.mem_setOf_eq, ϕ.map_mul, ψ.map_mul, hx, hy]
   algebraMap_mem' x := by rw [Set.mem_setOf_eq, AlgHom.commutes, AlgHom.commutes]
 #align alg_hom.equalizer AlgHom.equalizer
+-/
 
+/- warning: alg_hom.mem_equalizer -> AlgHom.mem_equalizer is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align alg_hom.mem_equalizer AlgHom.mem_equalizerₓ'. -/
 @[simp]
 theorem mem_equalizer (ϕ ψ : A →ₐ[R] B) (x : A) : x ∈ ϕ.equalizer ψ ↔ ϕ x = ψ x :=
   Iff.rfl
 #align alg_hom.mem_equalizer AlgHom.mem_equalizer
 
+/- warning: alg_hom.fintype_range -> AlgHom.fintypeRange is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align alg_hom.fintype_range AlgHom.fintypeRangeₓ'. -/
 /-- The range of a morphism of algebras is a fintype, if the domain is a fintype.
 
 Note that this instance can cause a diamond with `subtype.fintype` if `B` is also a fintype. -/
@@ -709,6 +1307,7 @@ variable {R : Type u} {A : Type v} {B : Type w}
 
 variable [CommSemiring R] [Semiring A] [Semiring B] [Algebra R A] [Algebra R B]
 
+#print AlgEquiv.ofLeftInverse /-
 /-- Restrict an algebra homomorphism with a left inverse to an algebra isomorphism to its range.
 
 This is a computable alternative to `alg_equiv.of_injective`. -/
@@ -722,36 +1321,57 @@ def ofLeftInverse {g : B → A} {f : A →ₐ[R] B} (h : Function.LeftInverse g
         let ⟨x', hx'⟩ := f.mem_range.mp x.Prop
         show f (g x) = x by rw [← hx', h x'] }
 #align alg_equiv.of_left_inverse AlgEquiv.ofLeftInverse
+-/
 
+#print AlgEquiv.ofLeftInverse_apply /-
 @[simp]
 theorem ofLeftInverse_apply {g : B → A} {f : A →ₐ[R] B} (h : Function.LeftInverse g f) (x : A) :
     ↑(ofLeftInverse h x) = f x :=
   rfl
 #align alg_equiv.of_left_inverse_apply AlgEquiv.ofLeftInverse_apply
+-/
 
+#print AlgEquiv.ofLeftInverse_symm_apply /-
 @[simp]
 theorem ofLeftInverse_symm_apply {g : B → A} {f : A →ₐ[R] B} (h : Function.LeftInverse g f)
     (x : f.range) : (ofLeftInverse h).symm x = g x :=
   rfl
 #align alg_equiv.of_left_inverse_symm_apply AlgEquiv.ofLeftInverse_symm_apply
+-/
 
+#print AlgEquiv.ofInjective /-
 /-- Restrict an injective algebra homomorphism to an algebra isomorphism -/
 noncomputable def ofInjective (f : A →ₐ[R] B) (hf : Function.Injective f) : A ≃ₐ[R] f.range :=
   ofLeftInverse (Classical.choose_spec hf.HasLeftInverse)
 #align alg_equiv.of_injective AlgEquiv.ofInjective
+-/
 
+#print AlgEquiv.ofInjective_apply /-
 @[simp]
 theorem ofInjective_apply (f : A →ₐ[R] B) (hf : Function.Injective f) (x : A) :
     ↑(ofInjective f hf x) = f x :=
   rfl
 #align alg_equiv.of_injective_apply AlgEquiv.ofInjective_apply
+-/
 
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 /-- Restrict an algebra homomorphism between fields to an algebra isomorphism -/
 noncomputable def ofInjectiveField {E F : Type _} [DivisionRing E] [Semiring F] [Nontrivial F]
     [Algebra R E] [Algebra R F] (f : E →ₐ[R] F) : E ≃ₐ[R] f.range :=
   ofInjective f f.toRingHom.Injective
 #align alg_equiv.of_injective_field AlgEquiv.ofInjectiveField
 
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+Case conversion may be inaccurate. Consider using '#align alg_equiv.subalgebra_map AlgEquiv.subalgebraMapₓ'. -/
 /-- Given an equivalence `e : A ≃ₐ[R] B` of `R`-algebras and a subalgebra `S` of `A`,
 `subalgebra_map` is the induced equivalence between `S` and `S.map e` -/
 @[simps]
@@ -770,20 +1390,34 @@ variable (R : Type u) {A : Type v} {B : Type w}
 
 variable [CommSemiring R] [Semiring A] [Algebra R A] [Semiring B] [Algebra R B]
 
+#print Algebra.adjoin /-
 /-- The minimal subalgebra that includes `s`. -/
 def adjoin (s : Set A) : Subalgebra R A :=
   { Subsemiring.closure (Set.range (algebraMap R A) ∪ s) with
     algebraMap_mem' := fun r => Subsemiring.subset_closure <| Or.inl ⟨r, rfl⟩ }
 #align algebra.adjoin Algebra.adjoin
+-/
 
 variable {R}
 
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+Case conversion may be inaccurate. Consider using '#align algebra.gc Algebra.gcₓ'. -/
 protected theorem gc : GaloisConnection (adjoin R : Set A → Subalgebra R A) coe := fun s S =>
   ⟨fun H => le_trans (le_trans (Set.subset_union_right _ _) Subsemiring.subset_closure) H, fun H =>
     show Subsemiring.closure (Set.range (algebraMap R A) ∪ s) ≤ S.toSubsemiring from
       Subsemiring.closure_le.2 <| Set.union_subset S.range_subset H⟩
 #align algebra.gc Algebra.gc
 
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+Case conversion may be inaccurate. Consider using '#align algebra.gi Algebra.giₓ'. -/
 /-- Galois insertion between `adjoin` and `coe`. -/
 protected def gi : GaloisInsertion (adjoin R : Set A → Subalgebra R A) coe
     where
@@ -796,116 +1430,254 @@ protected def gi : GaloisInsertion (adjoin R : Set A → Subalgebra R A) coe
 instance : CompleteLattice (Subalgebra R A) :=
   GaloisInsertion.liftCompleteLattice Algebra.gi
 
+/- warning: algebra.coe_top -> Algebra.coe_top is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align algebra.coe_top Algebra.coe_topₓ'. -/
 @[simp]
 theorem coe_top : (↑(⊤ : Subalgebra R A) : Set A) = Set.univ :=
   rfl
 #align algebra.coe_top Algebra.coe_top
 
+/- warning: algebra.mem_top -> Algebra.mem_top is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align algebra.mem_top Algebra.mem_topₓ'. -/
 @[simp]
 theorem mem_top {x : A} : x ∈ (⊤ : Subalgebra R A) :=
   Set.mem_univ x
 #align algebra.mem_top Algebra.mem_top
 
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 @[simp]
 theorem top_toSubmodule : (⊤ : Subalgebra R A).toSubmodule = ⊤ :=
   rfl
 #align algebra.top_to_submodule Algebra.top_toSubmodule
 
+/- warning: algebra.top_to_subsemiring -> Algebra.top_toSubsemiring is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align algebra.top_to_subsemiring Algebra.top_toSubsemiringₓ'. -/
 @[simp]
 theorem top_toSubsemiring : (⊤ : Subalgebra R A).toSubsemiring = ⊤ :=
   rfl
 #align algebra.top_to_subsemiring Algebra.top_toSubsemiring
 
+/- warning: algebra.top_to_subring -> Algebra.top_toSubring is a dubious translation:
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 @[simp]
 theorem top_toSubring {R A : Type _} [CommRing R] [Ring A] [Algebra R A] :
     (⊤ : Subalgebra R A).toSubring = ⊤ :=
   rfl
 #align algebra.top_to_subring Algebra.top_toSubring
 
+/- warning: algebra.to_submodule_eq_top -> Algebra.toSubmodule_eq_top is a dubious translation:
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 @[simp]
 theorem toSubmodule_eq_top {S : Subalgebra R A} : S.toSubmodule = ⊤ ↔ S = ⊤ :=
   Subalgebra.toSubmodule.Injective.eq_iff' top_toSubmodule
 #align algebra.to_submodule_eq_top Algebra.toSubmodule_eq_top
 
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 @[simp]
 theorem toSubsemiring_eq_top {S : Subalgebra R A} : S.toSubsemiring = ⊤ ↔ S = ⊤ :=
   Subalgebra.toSubsemiring_injective.eq_iff' top_toSubsemiring
 #align algebra.to_subsemiring_eq_top Algebra.toSubsemiring_eq_top
 
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 @[simp]
 theorem toSubring_eq_top {R A : Type _} [CommRing R] [Ring A] [Algebra R A] {S : Subalgebra R A} :
     S.toSubring = ⊤ ↔ S = ⊤ :=
   Subalgebra.toSubring_injective.eq_iff' top_toSubring
 #align algebra.to_subring_eq_top Algebra.toSubring_eq_top
 
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 theorem mem_sup_left {S T : Subalgebra R A} : ∀ {x : A}, x ∈ S → x ∈ S ⊔ T :=
   show S ≤ S ⊔ T from le_sup_left
 #align algebra.mem_sup_left Algebra.mem_sup_left
 
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+Case conversion may be inaccurate. Consider using '#align algebra.mem_sup_right Algebra.mem_sup_rightₓ'. -/
 theorem mem_sup_right {S T : Subalgebra R A} : ∀ {x : A}, x ∈ T → x ∈ S ⊔ T :=
   show T ≤ S ⊔ T from le_sup_right
 #align algebra.mem_sup_right Algebra.mem_sup_right
 
+/- warning: algebra.mul_mem_sup -> Algebra.mul_mem_sup is a dubious translation:
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 theorem mul_mem_sup {S T : Subalgebra R A} {x y : A} (hx : x ∈ S) (hy : y ∈ T) : x * y ∈ S ⊔ T :=
   (S ⊔ T).mul_mem (mem_sup_left hx) (mem_sup_right hy)
 #align algebra.mul_mem_sup Algebra.mul_mem_sup
 
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 theorem map_sup (f : A →ₐ[R] B) (S T : Subalgebra R A) : (S ⊔ T).map f = S.map f ⊔ T.map f :=
   (Subalgebra.gc_map_comap f).l_sup
 #align algebra.map_sup Algebra.map_sup
 
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 @[simp, norm_cast]
 theorem coe_inf (S T : Subalgebra R A) : (↑(S ⊓ T) : Set A) = S ∩ T :=
   rfl
 #align algebra.coe_inf Algebra.coe_inf
 
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+but is expected to have type
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3} {T : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3} {x : A}, Iff (Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x (Inf.inf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Lattice.toInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) S T)) (And (Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x S) (Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x T))
+Case conversion may be inaccurate. Consider using '#align algebra.mem_inf Algebra.mem_infₓ'. -/
 @[simp]
 theorem mem_inf {S T : Subalgebra R A} {x : A} : x ∈ S ⊓ T ↔ x ∈ S ∧ x ∈ T :=
   Iff.rfl
 #align algebra.mem_inf Algebra.mem_inf
 
+/- warning: algebra.inf_to_submodule -> Algebra.inf_toSubmodule is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align algebra.inf_to_submodule Algebra.inf_toSubmoduleₓ'. -/
 @[simp]
 theorem inf_toSubmodule (S T : Subalgebra R A) :
     (S ⊓ T).toSubmodule = S.toSubmodule ⊓ T.toSubmodule :=
   rfl
 #align algebra.inf_to_submodule Algebra.inf_toSubmodule
 
+/- warning: algebra.inf_to_subsemiring -> Algebra.inf_toSubsemiring is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align algebra.inf_to_subsemiring Algebra.inf_toSubsemiringₓ'. -/
 @[simp]
 theorem inf_toSubsemiring (S T : Subalgebra R A) :
     (S ⊓ T).toSubsemiring = S.toSubsemiring ⊓ T.toSubsemiring :=
   rfl
 #align algebra.inf_to_subsemiring Algebra.inf_toSubsemiring
 
+/- warning: algebra.coe_Inf -> Algebra.coe_infₛ is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align algebra.coe_Inf Algebra.coe_infₛₓ'. -/
 @[simp, norm_cast]
 theorem coe_infₛ (S : Set (Subalgebra R A)) : (↑(infₛ S) : Set A) = ⋂ s ∈ S, ↑s :=
   infₛ_image
 #align algebra.coe_Inf Algebra.coe_infₛ
 
+/- warning: algebra.mem_Inf -> Algebra.mem_infₛ is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align algebra.mem_Inf Algebra.mem_infₛₓ'. -/
 theorem mem_infₛ {S : Set (Subalgebra R A)} {x : A} : x ∈ infₛ S ↔ ∀ p ∈ S, x ∈ p := by
   simp only [← SetLike.mem_coe, coe_Inf, Set.mem_interᵢ₂]
 #align algebra.mem_Inf Algebra.mem_infₛ
 
+/- warning: algebra.Inf_to_submodule -> Algebra.infₛ_toSubmodule is a dubious translation:
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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) S))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align algebra.Inf_to_submodule Algebra.infₛ_toSubmoduleₓ'. -/
 @[simp]
 theorem infₛ_toSubmodule (S : Set (Subalgebra R A)) :
     (infₛ S).toSubmodule = infₛ (Subalgebra.toSubmodule '' S) :=
   SetLike.coe_injective <| by simp
 #align algebra.Inf_to_submodule Algebra.infₛ_toSubmodule
 
+/- warning: algebra.Inf_to_subsemiring -> Algebra.infₛ_toSubsemiring is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align algebra.Inf_to_subsemiring Algebra.infₛ_toSubsemiringₓ'. -/
 @[simp]
 theorem infₛ_toSubsemiring (S : Set (Subalgebra R A)) :
     (infₛ S).toSubsemiring = infₛ (Subalgebra.toSubsemiring '' S) :=
   SetLike.coe_injective <| by simp
 #align algebra.Inf_to_subsemiring Algebra.infₛ_toSubsemiring
 
+/- warning: algebra.coe_infi -> Algebra.coe_infᵢ is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align algebra.coe_infi Algebra.coe_infᵢₓ'. -/
 @[simp, norm_cast]
 theorem coe_infᵢ {ι : Sort _} {S : ι → Subalgebra R A} : (↑(⨅ i, S i) : Set A) = ⋂ i, S i := by
   simp [infᵢ]
 #align algebra.coe_infi Algebra.coe_infᵢ
 
+/- warning: algebra.mem_infi -> Algebra.mem_infᵢ is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {ι : Sort.{u3}} {S : ι -> (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {x : A}, Iff (Membership.Mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x (infᵢ.{u2, u3} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => S i))) (forall (i : ι), Membership.Mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) x (S i))
+but is expected to have type
+  forall {R : Type.{u2}} {A : Type.{u3}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u3} A] [_inst_3 : Algebra.{u2, u3} R A _inst_1 _inst_2] {ι : Sort.{u1}} {S : ι -> (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)} {x : A}, Iff (Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (infᵢ.{u3, u1} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toInfSet.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => S i))) (forall (i : ι), Membership.mem.{u3, u3} A (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u3, u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)) x (S i))
+Case conversion may be inaccurate. Consider using '#align algebra.mem_infi Algebra.mem_infᵢₓ'. -/
 theorem mem_infᵢ {ι : Sort _} {S : ι → Subalgebra R A} {x : A} : (x ∈ ⨅ i, S i) ↔ ∀ i, x ∈ S i := by
   simp only [infᵢ, mem_Inf, Set.forall_range_iff]
 #align algebra.mem_infi Algebra.mem_infᵢ
 
+/- warning: algebra.infi_to_submodule -> Algebra.infᵢ_toSubmodule is a dubious translation:
+lean 3 declaration is
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u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (RelEmbedding.hasCoeToFun.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (S i)))
+but is expected to have type
+  forall {R : Type.{u2}} {A : Type.{u3}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u3} A] [_inst_3 : Algebra.{u2, u3} R A _inst_1 _inst_2] {ι : Sort.{u1}} (S : ι -> (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3)), Eq.{succ u3} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (infᵢ.{u3, u1} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toInfSet.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Subalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => S i))) 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x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u3} (Submodule.{u2, u3} R A 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+Case conversion may be inaccurate. Consider using '#align algebra.infi_to_submodule Algebra.infᵢ_toSubmoduleₓ'. -/
 @[simp]
 theorem infᵢ_toSubmodule {ι : Sort _} (S : ι → Subalgebra R A) :
     (⨅ i, S i).toSubmodule = ⨅ i, (S i).toSubmodule :=
@@ -915,6 +1687,12 @@ theorem infᵢ_toSubmodule {ι : Sort _} (S : ι → Subalgebra R A) :
 instance : Inhabited (Subalgebra R A) :=
   ⟨⊥⟩
 
+/- warning: algebra.mem_bot -> Algebra.mem_bot is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align algebra.mem_bot Algebra.mem_botₓ'. -/
 theorem mem_bot {x : A} : x ∈ (⊥ : Subalgebra R A) ↔ x ∈ Set.range (algebraMap R A) :=
   suffices (ofId R A).range = (⊥ : Subalgebra R A)
     by
@@ -923,53 +1701,113 @@ theorem mem_bot {x : A} : x ∈ (⊥ : Subalgebra R A) ↔ x ∈ Set.range (alge
   le_bot_iff.mp fun x hx => Subalgebra.range_le _ ((ofId R A).coe_range ▸ hx)
 #align algebra.mem_bot Algebra.mem_bot
 
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 theorem toSubmodule_bot : (⊥ : Subalgebra R A).toSubmodule = R ∙ 1 :=
   by
   ext x
   simp [mem_bot, -Set.singleton_one, Submodule.mem_span_singleton, Algebra.smul_def]
 #align algebra.to_submodule_bot Algebra.toSubmodule_bot
 
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 @[simp]
 theorem coe_bot : ((⊥ : Subalgebra R A) : Set A) = Set.range (algebraMap R A) := by
   simp [Set.ext_iff, Algebra.mem_bot]
 #align algebra.coe_bot Algebra.coe_bot
 
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 theorem eq_top_iff {S : Subalgebra R A} : S = ⊤ ↔ ∀ x : A, x ∈ S :=
   ⟨fun h x => by rw [h] <;> exact mem_top, fun h => by
     ext x <;> exact ⟨fun _ => mem_top, fun _ => h x⟩⟩
 #align algebra.eq_top_iff Algebra.eq_top_iff
 
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(AlgHom.algHomClass.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_4 _inst_3 _inst_5))))) f))
+Case conversion may be inaccurate. Consider using '#align algebra.range_top_iff_surjective Algebra.range_top_iff_surjectiveₓ'. -/
 theorem range_top_iff_surjective (f : A →ₐ[R] B) :
     f.range = (⊤ : Subalgebra R B) ↔ Function.Surjective f :=
   Algebra.eq_top_iff
 #align algebra.range_top_iff_surjective Algebra.range_top_iff_surjective
 
+/- warning: algebra.range_id -> Algebra.range_id is a dubious translation:
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 @[simp]
 theorem range_id : (AlgHom.id R A).range = ⊤ :=
   SetLike.coe_injective Set.range_id
 #align algebra.range_id Algebra.range_id
 
+/- warning: algebra.map_top -> Algebra.map_top is a dubious translation:
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 @[simp]
 theorem map_top (f : A →ₐ[R] B) : (⊤ : Subalgebra R A).map f = f.range :=
   SetLike.coe_injective Set.image_univ
 #align algebra.map_top Algebra.map_top
 
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 @[simp]
 theorem map_bot (f : A →ₐ[R] B) : (⊥ : Subalgebra R A).map f = ⊥ :=
   SetLike.coe_injective <| by
     simp only [← Set.range_comp, (· ∘ ·), Algebra.coe_bot, Subalgebra.coe_map, f.commutes]
 #align algebra.map_bot Algebra.map_bot
 
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+Case conversion may be inaccurate. Consider using '#align algebra.comap_top Algebra.comap_topₓ'. -/
 @[simp]
 theorem comap_top (f : A →ₐ[R] B) : (⊤ : Subalgebra R B).comap f = ⊤ :=
   eq_top_iff.2 fun x => mem_top
 #align algebra.comap_top Algebra.comap_top
 
+/- warning: algebra.to_top -> Algebra.toTop is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align algebra.to_top Algebra.toTopₓ'. -/
 /-- `alg_hom` to `⊤ : subalgebra R A`. -/
 def toTop : A →ₐ[R] (⊤ : Subalgebra R A) :=
   (AlgHom.id R A).codRestrict ⊤ fun _ => mem_top
 #align algebra.to_top Algebra.toTop
 
+/- warning: algebra.surjective_algebra_map_iff -> Algebra.surjective_algebraMap_iff is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align algebra.surjective_algebra_map_iff Algebra.surjective_algebraMap_iffₓ'. -/
 theorem surjective_algebraMap_iff :
     Function.Surjective (algebraMap R A) ↔ (⊤ : Subalgebra R A) = ⊥ :=
   ⟨fun h =>
@@ -979,12 +1817,24 @@ theorem surjective_algebraMap_iff :
     fun h y => Algebra.mem_bot.1 <| eq_bot_iff.1 h (Algebra.mem_top : y ∈ _)⟩
 #align algebra.surjective_algebra_map_iff Algebra.surjective_algebraMap_iff
 
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+Case conversion may be inaccurate. Consider using '#align algebra.bijective_algebra_map_iff Algebra.bijective_algebraMap_iffₓ'. -/
 theorem bijective_algebraMap_iff {R A : Type _} [Field R] [Semiring A] [Nontrivial A]
     [Algebra R A] : Function.Bijective (algebraMap R A) ↔ (⊤ : Subalgebra R A) = ⊥ :=
   ⟨fun h => surjective_algebraMap_iff.1 h.2, fun h =>
     ⟨(algebraMap R A).Injective, surjective_algebraMap_iff.2 h⟩⟩
 #align algebra.bijective_algebra_map_iff Algebra.bijective_algebraMap_iff
 
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+Case conversion may be inaccurate. Consider using '#align algebra.bot_equiv_of_injective Algebra.botEquivOfInjectiveₓ'. -/
 /-- The bottom subalgebra is isomorphic to the base ring. -/
 noncomputable def botEquivOfInjective (h : Function.Injective (algebraMap R A)) :
     (⊥ : Subalgebra R A) ≃ₐ[R] R :=
@@ -995,6 +1845,12 @@ noncomputable def botEquivOfInjective (h : Function.Injective (algebraMap R A))
         ⟨x, Subtype.eq hx⟩⟩
 #align algebra.bot_equiv_of_injective Algebra.botEquivOfInjective
 
+/- warning: algebra.bot_equiv -> Algebra.botEquiv is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align algebra.bot_equiv Algebra.botEquivₓ'. -/
 /-- The bottom subalgebra is isomorphic to the field. -/
 @[simps symm_apply]
 noncomputable def botEquiv (F R : Type _) [Field F] [Semiring R] [Nontrivial R] [Algebra F R] :
@@ -1014,6 +1870,12 @@ variable [CommSemiring R] [Semiring A] [Algebra R A] [Semiring B] [Algebra R B]
 
 variable (S : Subalgebra R A)
 
+/- warning: subalgebra.top_equiv -> Subalgebra.topEquiv is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align subalgebra.top_equiv Subalgebra.topEquivₓ'. -/
 /-- The top subalgebra is isomorphic to the algebra.
 
 This is the algebra version of `submodule.top_equiv`. -/
@@ -1022,10 +1884,13 @@ def topEquiv : (⊤ : Subalgebra R A) ≃ₐ[R] A :=
   AlgEquiv.ofAlgHom (Subalgebra.val ⊤) toTop rfl <| AlgHom.ext fun _ => Subtype.ext rfl
 #align subalgebra.top_equiv Subalgebra.topEquiv
 
+#print Subalgebra.subsingleton_of_subsingleton /-
 instance subsingleton_of_subsingleton [Subsingleton A] : Subsingleton (Subalgebra R A) :=
   ⟨fun B C => ext fun x => by simp only [Subsingleton.elim x 0, zero_mem B, zero_mem C]⟩
 #align subalgebra.subsingleton_of_subsingleton Subalgebra.subsingleton_of_subsingleton
+-/
 
+#print AlgHom.subsingleton /-
 instance AlgHom.subsingleton [Subsingleton (Subalgebra R A)] : Subsingleton (A →ₐ[R] B) :=
   ⟨fun f g =>
     AlgHom.ext fun a =>
@@ -1033,18 +1898,25 @@ instance AlgHom.subsingleton [Subsingleton (Subalgebra R A)] : Subsingleton (A 
       let ⟨x, hx⟩ := Set.mem_range.mp (mem_bot.mp this)
       hx ▸ (f.commutes _).trans (g.commutes _).symm⟩
 #align alg_hom.subsingleton AlgHom.subsingleton
+-/
 
+#print AlgEquiv.subsingleton_left /-
 instance AlgEquiv.subsingleton_left [Subsingleton (Subalgebra R A)] : Subsingleton (A ≃ₐ[R] B) :=
   ⟨fun f g => AlgEquiv.ext fun x => AlgHom.ext_iff.mp (Subsingleton.elim f.toAlgHom g.toAlgHom) x⟩
 #align alg_equiv.subsingleton_left AlgEquiv.subsingleton_left
+-/
 
+#print AlgEquiv.subsingleton_right /-
 instance AlgEquiv.subsingleton_right [Subsingleton (Subalgebra R B)] : Subsingleton (A ≃ₐ[R] B) :=
   ⟨fun f g => by rw [← f.symm_symm, Subsingleton.elim f.symm g.symm, g.symm_symm]⟩
 #align alg_equiv.subsingleton_right AlgEquiv.subsingleton_right
+-/
 
+#print Subalgebra.range_val /-
 theorem range_val : S.val.range = S :=
   ext <| Set.ext_iff.1 <| S.val.coe_range.trans Subtype.range_val
 #align subalgebra.range_val Subalgebra.range_val
+-/
 
 instance : Unique (Subalgebra R R) :=
   { Algebra.Subalgebra.inhabited with
@@ -1053,6 +1925,12 @@ instance : Unique (Subalgebra R R) :=
       refine' le_antisymm (fun r hr => _) bot_le
       simp only [Set.mem_range, mem_bot, id.map_eq_self, exists_apply_eq_apply, default] }
 
+/- warning: subalgebra.inclusion -> Subalgebra.inclusion is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align subalgebra.inclusion Subalgebra.inclusionₓ'. -/
 /-- The map `S → T` when `S` is a subalgebra contained in the subalgebra `T`.
 
 This is the subalgebra version of `submodule.of_le`, or `subring.inclusion`  -/
@@ -1066,37 +1944,79 @@ def inclusion {S T : Subalgebra R A} (h : S ≤ T) : S →ₐ[R] T
   commutes' _ := rfl
 #align subalgebra.inclusion Subalgebra.inclusion
 
+/- warning: subalgebra.inclusion_injective -> Subalgebra.inclusion_injective is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align subalgebra.inclusion_injective Subalgebra.inclusion_injectiveₓ'. -/
 theorem inclusion_injective {S T : Subalgebra R A} (h : S ≤ T) : Function.Injective (inclusion h) :=
   fun _ _ => Subtype.ext ∘ Subtype.mk.inj
 #align subalgebra.inclusion_injective Subalgebra.inclusion_injective
 
+/- warning: subalgebra.inclusion_self -> Subalgebra.inclusion_self is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align subalgebra.inclusion_self Subalgebra.inclusion_selfₓ'. -/
 @[simp]
 theorem inclusion_self {S : Subalgebra R A} : inclusion (le_refl S) = AlgHom.id R S :=
   AlgHom.ext fun x => Subtype.ext rfl
 #align subalgebra.inclusion_self Subalgebra.inclusion_self
 
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+Case conversion may be inaccurate. Consider using '#align subalgebra.inclusion_mk Subalgebra.inclusion_mkₓ'. -/
 @[simp]
 theorem inclusion_mk {S T : Subalgebra R A} (h : S ≤ T) (x : A) (hx : x ∈ S) :
     inclusion h ⟨x, hx⟩ = ⟨x, h hx⟩ :=
   rfl
 #align subalgebra.inclusion_mk Subalgebra.inclusion_mk
 
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+Case conversion may be inaccurate. Consider using '#align subalgebra.inclusion_right Subalgebra.inclusion_rightₓ'. -/
 theorem inclusion_right {S T : Subalgebra R A} (h : S ≤ T) (x : T) (m : (x : A) ∈ S) :
     inclusion h ⟨x, m⟩ = x :=
   Subtype.ext rfl
 #align subalgebra.inclusion_right Subalgebra.inclusion_right
 
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+Case conversion may be inaccurate. Consider using '#align subalgebra.inclusion_inclusion Subalgebra.inclusion_inclusionₓ'. -/
 @[simp]
 theorem inclusion_inclusion {S T U : Subalgebra R A} (hst : S ≤ T) (htu : T ≤ U) (x : S) :
     inclusion htu (inclusion hst x) = inclusion (le_trans hst htu) x :=
   Subtype.ext rfl
 #align subalgebra.inclusion_inclusion Subalgebra.inclusion_inclusion
 
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 @[simp]
 theorem coe_inclusion {S T : Subalgebra R A} (h : S ≤ T) (s : S) : (inclusion h s : A) = s :=
   rfl
 #align subalgebra.coe_inclusion Subalgebra.coe_inclusion
 
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 /-- Two subalgebras that are equal are also equivalent as algebras.
 
 This is the `subalgebra` version of `linear_equiv.of_eq` and `equiv.set.of_eq`. -/
@@ -1111,12 +2031,24 @@ def equivOfEq (S T : Subalgebra R A) (h : S = T) : S ≃ₐ[R] T :=
     commutes' := fun _ => rfl }
 #align subalgebra.equiv_of_eq Subalgebra.equivOfEq
 
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 @[simp]
 theorem equivOfEq_symm (S T : Subalgebra R A) (h : S = T) :
     (equivOfEq S T h).symm = equivOfEq T S h.symm :=
   rfl
 #align subalgebra.equiv_of_eq_symm Subalgebra.equivOfEq_symm
 
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 @[simp]
 theorem equivOfEq_rfl (S : Subalgebra R A) : equivOfEq S S rfl = AlgEquiv.refl :=
   by
@@ -1124,6 +2056,12 @@ theorem equivOfEq_rfl (S : Subalgebra R A) : equivOfEq S S rfl = AlgEquiv.refl :
   rfl
 #align subalgebra.equiv_of_eq_rfl Subalgebra.equivOfEq_rfl
 
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 @[simp]
 theorem equivOfEq_trans (S T U : Subalgebra R A) (hST : S = T) (hTU : T = U) :
     (equivOfEq S T hST).trans (equivOfEq T U hTU) = equivOfEq S U (trans hST hTU) :=
@@ -1134,6 +2072,12 @@ section Prod
 
 variable (S₁ : Subalgebra R B)
 
+/- warning: subalgebra.prod -> Subalgebra.prod is a dubious translation:
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 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /-- The product of two subalgebras is a subalgebra. -/
 def prod : Subalgebra R (A × B) :=
@@ -1143,31 +2087,67 @@ def prod : Subalgebra R (A × B) :=
     algebraMap_mem' := fun r => ⟨algebraMap_mem _ _, algebraMap_mem _ _⟩ }
 #align subalgebra.prod Subalgebra.prod
 
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 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 @[simp]
 theorem coe_prod : (prod S S₁ : Set (A × B)) = S ×ˢ S₁ :=
   rfl
 #align subalgebra.coe_prod Subalgebra.coe_prod
 
+/- warning: subalgebra.prod_to_submodule -> Subalgebra.prod_toSubmodule is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_4 : Semiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 _inst_4] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (S₁ : Subalgebra.{u1, u3} R B _inst_1 _inst_4 _inst_5), Eq.{succ (max u2 u3)} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.semiring.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (coeFn.{succ (max u2 u3), succ (max u2 u3)} (OrderEmbedding.{max u2 u3, max u2 u3} 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.semiring.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)))))))) (fun (_x : RelEmbedding.{max u2 u3, max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.semiring.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (LE.le.{max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (Preorder.toLE.{max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (PartialOrder.toPreorder.{max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (SetLike.partialOrder.{max u2 u3, max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (Prod.{u2, u3} A B) (Subalgebra.setLike.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)))))) (LE.le.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.semiring.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (Preorder.toLE.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.semiring.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (PartialOrder.toPreorder.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.semiring.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (CompleteSemilatticeInf.toPartialOrder.{max 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A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (Submodule.completeLattice.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u3} (Prod.{u2, u3} A B) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Semiring.toNonAssocSemiring.{max u2 u3} (Prod.{u2, u3} A B) (Prod.semiring.{u2, u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))))))))) => (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) -> (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} A B) (CommSemiring.toSemiring.{u1} R _inst_1) 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u3} A B _inst_2 _inst_4)))) (Algebra.toModule.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) (LE.le.{max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (Preorder.toLE.{max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (PartialOrder.toPreorder.{max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) (SetLike.partialOrder.{max u2 u3, max u2 u3} (Subalgebra.{u1, max u2 u3} R (Prod.{u2, u3} A B) _inst_1 (Prod.semiring.{u2, u3} A B _inst_2 _inst_4) (Prod.algebra.{u1, u2, 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+but is expected to have type
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u3} R B _inst_1 _inst_4 _inst_5)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Subalgebra.toSubmodule.{u1, u3} R B _inst_1 _inst_4 _inst_5)) S₁))
+Case conversion may be inaccurate. Consider using '#align subalgebra.prod_to_submodule Subalgebra.prod_toSubmoduleₓ'. -/
 theorem prod_toSubmodule : (S.Prod S₁).toSubmodule = S.toSubmodule.Prod S₁.toSubmodule :=
   rfl
 #align subalgebra.prod_to_submodule Subalgebra.prod_toSubmodule
 
+/- warning: subalgebra.mem_prod -> Subalgebra.mem_prod is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align subalgebra.mem_prod Subalgebra.mem_prodₓ'. -/
 @[simp]
 theorem mem_prod {S : Subalgebra R A} {S₁ : Subalgebra R B} {x : A × B} :
     x ∈ prod S S₁ ↔ x.1 ∈ S ∧ x.2 ∈ S₁ :=
   Set.mem_prod
 #align subalgebra.mem_prod Subalgebra.mem_prod
 
+/- warning: subalgebra.prod_top -> Subalgebra.prod_top is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align subalgebra.prod_top Subalgebra.prod_topₓ'. -/
 @[simp]
 theorem prod_top : (prod ⊤ ⊤ : Subalgebra R (A × B)) = ⊤ := by ext <;> simp
 #align subalgebra.prod_top Subalgebra.prod_top
 
+/- warning: subalgebra.prod_mono -> Subalgebra.prod_mono is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align subalgebra.prod_mono Subalgebra.prod_monoₓ'. -/
 theorem prod_mono {S T : Subalgebra R A} {S₁ T₁ : Subalgebra R B} :
     S ≤ T → S₁ ≤ T₁ → prod S S₁ ≤ prod T T₁ :=
   Set.prod_mono
 #align subalgebra.prod_mono Subalgebra.prod_mono
 
+/- warning: subalgebra.prod_inf_prod -> Subalgebra.prod_inf_prod is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align subalgebra.prod_inf_prod Subalgebra.prod_inf_prodₓ'. -/
 @[simp]
 theorem prod_inf_prod {S T : Subalgebra R A} {S₁ T₁ : Subalgebra R B} :
     S.Prod S₁ ⊓ T.Prod T₁ = (S ⊓ T).Prod (S₁ ⊓ T₁) :=
@@ -1180,6 +2160,12 @@ section SuprLift
 
 variable {ι : Type _}
 
+/- warning: subalgebra.coe_supr_of_directed -> Subalgebra.coe_supᵢ_of_directed is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align subalgebra.coe_supr_of_directed Subalgebra.coe_supᵢ_of_directedₓ'. -/
 theorem coe_supᵢ_of_directed [Nonempty ι] {S : ι → Subalgebra R A} (dir : Directed (· ≤ ·) S) :
     ↑(supᵢ S) = ⋃ i, (S i : Set A) :=
   let K : Subalgebra R A :=
@@ -1203,9 +2189,15 @@ theorem coe_supᵢ_of_directed [Nonempty ι] {S : ι → Subalgebra R A} (dir :
   this.symm ▸ rfl
 #align subalgebra.coe_supr_of_directed Subalgebra.coe_supᵢ_of_directed
 
+/- warning: subalgebra.supr_lift -> Subalgebra.supᵢLift is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align subalgebra.supr_lift Subalgebra.supᵢLiftₓ'. -/
 /-- Define an algebra homomorphism on a directed supremum of subalgebras by defining
 it on each subalgebra, and proving that it agrees on the intersection of subalgebras. -/
-noncomputable def suprLift [Nonempty ι] (K : ι → Subalgebra R A) (dir : Directed (· ≤ ·) K)
+noncomputable def supᵢLift [Nonempty ι] (K : ι → Subalgebra R A) (dir : Directed (· ≤ ·) K)
     (f : ∀ i, K i →ₐ[R] B) (hf : ∀ (i j : ι) (h : K i ≤ K j), f i = (f j).comp (inclusion h))
     (T : Subalgebra R A) (hT : T = supᵢ K) : ↥T →ₐ[R] B := by
   subst hT <;>
@@ -1228,31 +2220,55 @@ noncomputable def suprLift [Nonempty ι] (K : ι → Subalgebra R A) (dir : Dire
         commutes' := fun r =>
           Set.unionᵢLift_const _ (fun _ => algebraMap _ _ r) (fun _ => rfl) _ fun i => by
             erw [AlgHom.commutes (f i)] }
-#align subalgebra.supr_lift Subalgebra.suprLift
+#align subalgebra.supr_lift Subalgebra.supᵢLift
 
 variable [Nonempty ι] {K : ι → Subalgebra R A} {dir : Directed (· ≤ ·) K} {f : ∀ i, K i →ₐ[R] B}
   {hf : ∀ (i j : ι) (h : K i ≤ K j), f i = (f j).comp (inclusion h)} {T : Subalgebra R A}
   {hT : T = supᵢ K}
 
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+Case conversion may be inaccurate. Consider using '#align subalgebra.supr_lift_inclusion Subalgebra.supᵢLift_inclusionₓ'. -/
 @[simp]
-theorem suprLift_inclusion {i : ι} (x : K i) (h : K i ≤ T) :
-    suprLift K dir f hf T hT (inclusion h x) = f i x := by
+theorem supᵢLift_inclusion {i : ι} (x : K i) (h : K i ≤ T) :
+    supᵢLift K dir f hf T hT (inclusion h x) = f i x := by
   subst T <;> exact Set.unionᵢLift_inclusion _ _
-#align subalgebra.supr_lift_inclusion Subalgebra.suprLift_inclusion
-
-@[simp]
-theorem suprLift_comp_inclusion {i : ι} (h : K i ≤ T) :
-    (suprLift K dir f hf T hT).comp (inclusion h) = f i := by ext <;> simp
-#align subalgebra.supr_lift_comp_inclusion Subalgebra.suprLift_comp_inclusion
-
-@[simp]
-theorem suprLift_mk {i : ι} (x : K i) (hx : (x : A) ∈ T) :
-    suprLift K dir f hf T hT ⟨x, hx⟩ = f i x := by subst hT <;> exact Set.unionᵢLift_mk x hx
-#align subalgebra.supr_lift_mk Subalgebra.suprLift_mk
-
-theorem suprLift_of_mem {i : ι} (x : T) (hx : (x : A) ∈ K i) :
-    suprLift K dir f hf T hT x = f i ⟨x, hx⟩ := by subst hT <;> exact Set.unionᵢLift_of_mem x hx
-#align subalgebra.supr_lift_of_mem Subalgebra.suprLift_of_mem
+#align subalgebra.supr_lift_inclusion Subalgebra.supᵢLift_inclusion
+
+/- warning: subalgebra.supr_lift_comp_inclusion -> Subalgebra.supᵢLift_comp_inclusion is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align subalgebra.supr_lift_comp_inclusion Subalgebra.supᵢLift_comp_inclusionₓ'. -/
+@[simp]
+theorem supᵢLift_comp_inclusion {i : ι} (h : K i ≤ T) :
+    (supᵢLift K dir f hf T hT).comp (inclusion h) = f i := by ext <;> simp
+#align subalgebra.supr_lift_comp_inclusion Subalgebra.supᵢLift_comp_inclusion
+
+/- warning: subalgebra.supr_lift_mk -> Subalgebra.supᵢLift_mk is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align subalgebra.supr_lift_mk Subalgebra.supᵢLift_mkₓ'. -/
+@[simp]
+theorem supᵢLift_mk {i : ι} (x : K i) (hx : (x : A) ∈ T) :
+    supᵢLift K dir f hf T hT ⟨x, hx⟩ = f i x := by subst hT <;> exact Set.unionᵢLift_mk x hx
+#align subalgebra.supr_lift_mk Subalgebra.supᵢLift_mk
+
+/- warning: subalgebra.supr_lift_of_mem -> Subalgebra.supᵢLift_of_mem is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align subalgebra.supr_lift_of_mem Subalgebra.supᵢLift_of_memₓ'. -/
+theorem supᵢLift_of_mem {i : ι} (x : T) (hx : (x : A) ∈ K i) :
+    supᵢLift K dir f hf T hT x = f i ⟨x, hx⟩ := by subst hT <;> exact Set.unionᵢLift_of_mem x hx
+#align subalgebra.supr_lift_of_mem Subalgebra.supᵢLift_of_mem
 
 end SuprLift
 
@@ -1271,26 +2287,56 @@ variable {α β : Type _}
 instance [SMul A α] (S : Subalgebra R A) : SMul S α :=
   S.toSubsemiring.SMul
 
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 theorem smul_def [SMul A α] {S : Subalgebra R A} (g : S) (m : α) : g • m = (g : A) • m :=
   rfl
 #align subalgebra.smul_def Subalgebra.smul_def
 
+/- warning: subalgebra.smul_comm_class_left -> Subalgebra.sMulCommClass_left is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align subalgebra.smul_comm_class_left Subalgebra.sMulCommClass_leftₓ'. -/
 instance sMulCommClass_left [SMul A β] [SMul α β] [SMulCommClass A α β] (S : Subalgebra R A) :
     SMulCommClass S α β :=
   S.toSubsemiring.smulCommClass_left
 #align subalgebra.smul_comm_class_left Subalgebra.sMulCommClass_left
 
+/- warning: subalgebra.smul_comm_class_right -> Subalgebra.sMulCommClass_right is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align subalgebra.smul_comm_class_right Subalgebra.sMulCommClass_rightₓ'. -/
 instance sMulCommClass_right [SMul α β] [SMul A β] [SMulCommClass α A β] (S : Subalgebra R A) :
     SMulCommClass α S β :=
   S.toSubsemiring.smulCommClass_right
 #align subalgebra.smul_comm_class_right Subalgebra.sMulCommClass_right
 
+/- warning: subalgebra.is_scalar_tower_left -> Subalgebra.isScalarTower_left is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align subalgebra.is_scalar_tower_left Subalgebra.isScalarTower_leftₓ'. -/
 /-- Note that this provides `is_scalar_tower S R R` which is needed by `smul_mul_assoc`. -/
 instance isScalarTower_left [SMul α β] [SMul A α] [SMul A β] [IsScalarTower A α β]
     (S : Subalgebra R A) : IsScalarTower S α β :=
   S.toSubsemiring.IsScalarTower
 #align subalgebra.is_scalar_tower_left Subalgebra.isScalarTower_left
 
+/- warning: subalgebra.is_scalar_tower_mid -> Subalgebra.isScalarTower_mid is a dubious translation:
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_inst_9)) S') (Semiring.toNonAssocSemiring.{u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9) S (Subalgebra.setLike.{u1, u2} R S _inst_6 _inst_7 _inst_9)) S') (Subalgebra.toSemiring.{u1, u2} R S _inst_6 _inst_7 _inst_9 S')))) (Subalgebra.module.{u1, u2} R S _inst_6 _inst_7 _inst_9 S'))))) (Subalgebra.hasSmul.{u1, u2, u3} R S _inst_6 _inst_7 _inst_9 T (SMulZeroClass.toHasSmul.{u2, u3} S T (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8))) (SMulWithZero.toSmulZeroClass.{u2, u3} S T (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_7)))) (AddZeroClass.toHasZero.{u3} T (AddMonoid.toAddZeroClass.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8))) (MulActionWithZero.toSMulWithZero.{u2, u3} S T 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(CommSemiring.toSemiring.{u1} R _inst_6) _inst_8 _inst_10))))
+but is expected to have type
+  forall {R : Type.{u1}} {S : Type.{u2}} {T : Type.{u3}} [_inst_6 : CommSemiring.{u1} R] [_inst_7 : Semiring.{u2} S] [_inst_8 : AddCommMonoid.{u3} T] [_inst_9 : Algebra.{u1, u2} R S _inst_6 _inst_7] [_inst_10 : Module.{u1, u3} R T (CommSemiring.toSemiring.{u1} R _inst_6) _inst_8] [_inst_11 : Module.{u2, u3} S T _inst_7 _inst_8] [_inst_12 : IsScalarTower.{u1, u2, u3} R S T (Algebra.toSMul.{u1, u2} R S _inst_6 _inst_7 _inst_9) (SMulZeroClass.toSMul.{u2, u3} S T (AddMonoid.toZero.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8)) (SMulWithZero.toSMulZeroClass.{u2, u3} S T (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_7)) (AddMonoid.toZero.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8)) (MulActionWithZero.toSMulWithZero.{u2, u3} S T (Semiring.toMonoidWithZero.{u2} S _inst_7) (AddMonoid.toZero.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8)) (Module.toMulActionWithZero.{u2, u3} S T _inst_7 _inst_8 _inst_11)))) (SMulZeroClass.toSMul.{u1, u3} R T (AddMonoid.toZero.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8)) (SMulWithZero.toSMulZeroClass.{u1, u3} R T (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_6)) (AddMonoid.toZero.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8)) (MulActionWithZero.toSMulWithZero.{u1, u3} R T (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_6)) (AddMonoid.toZero.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8)) (Module.toMulActionWithZero.{u1, u3} R T (CommSemiring.toSemiring.{u1} R _inst_6) _inst_8 _inst_10))))] (S' : Subalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9), IsScalarTower.{u1, u2, u3} R (Subtype.{succ u2} S (fun (x : S) => Membership.mem.{u2, u2} S (Subalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9) S (Subalgebra.instSetLikeSubalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9)) x S')) T (Algebra.toSMul.{u1, u2} R (Subtype.{succ u2} S (fun (x : S) => Membership.mem.{u2, u2} S (Subalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9) S (Subalgebra.instSetLikeSubalgebra.{u1, u2} R S _inst_6 _inst_7 _inst_9)) x S')) _inst_6 (Subalgebra.toSemiring.{u1, u2} R S _inst_6 _inst_7 _inst_9 S') (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R S _inst_6 _inst_7 _inst_9 S')) (Subalgebra.instSMulSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebra.{u1, u2, u3} R S _inst_6 _inst_7 _inst_9 T (SMulZeroClass.toSMul.{u2, u3} S T (AddMonoid.toZero.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8)) (SMulWithZero.toSMulZeroClass.{u2, u3} S T (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_7)) (AddMonoid.toZero.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8)) (MulActionWithZero.toSMulWithZero.{u2, u3} S T (Semiring.toMonoidWithZero.{u2} S _inst_7) (AddMonoid.toZero.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8)) (Module.toMulActionWithZero.{u2, u3} S T _inst_7 _inst_8 _inst_11)))) S') (SMulZeroClass.toSMul.{u1, u3} R T (AddMonoid.toZero.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8)) (SMulWithZero.toSMulZeroClass.{u1, u3} R T (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_6)) (AddMonoid.toZero.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8)) (MulActionWithZero.toSMulWithZero.{u1, u3} R T (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_6)) (AddMonoid.toZero.{u3} T (AddCommMonoid.toAddMonoid.{u3} T _inst_8)) (Module.toMulActionWithZero.{u1, u3} R T (CommSemiring.toSemiring.{u1} R _inst_6) _inst_8 _inst_10))))
+Case conversion may be inaccurate. Consider using '#align subalgebra.is_scalar_tower_mid Subalgebra.isScalarTower_midₓ'. -/
 instance isScalarTower_mid {R S T : Type _} [CommSemiring R] [Semiring S] [AddCommMonoid T]
     [Algebra R S] [Module R T] [Module S T] [IsScalarTower R S T] (S' : Subalgebra R S) :
     IsScalarTower R S' T :=
@@ -1316,22 +2362,46 @@ instance [Zero α] [SMulWithZero A α] (S : Subalgebra R A) : SMulWithZero S α
 instance [Zero α] [MulActionWithZero A α] (S : Subalgebra R A) : MulActionWithZero S α :=
   S.toSubsemiring.MulActionWithZero
 
+/- warning: subalgebra.module_left -> Subalgebra.moduleLeft is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align subalgebra.module_left Subalgebra.moduleLeftₓ'. -/
 /-- The action by a subalgebra is the action by the underlying algebra. -/
 instance moduleLeft [AddCommMonoid α] [Module A α] (S : Subalgebra R A) : Module S α :=
   S.toSubsemiring.Module
 #align subalgebra.module_left Subalgebra.moduleLeft
 
+/- warning: subalgebra.to_algebra -> Subalgebra.toAlgebra is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align subalgebra.to_algebra Subalgebra.toAlgebraₓ'. -/
 /-- The action by a subalgebra is the action by the underlying algebra. -/
 instance toAlgebra {R A : Type _} [CommSemiring R] [CommSemiring A] [Semiring α] [Algebra R A]
     [Algebra A α] (S : Subalgebra R A) : Algebra S α :=
   Algebra.ofSubsemiring S.toSubsemiring
 #align subalgebra.to_algebra Subalgebra.toAlgebra
 
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align subalgebra.algebra_map_eq Subalgebra.algebraMap_eqₓ'. -/
 theorem algebraMap_eq {R A : Type _} [CommSemiring R] [CommSemiring A] [Semiring α] [Algebra R A]
     [Algebra A α] (S : Subalgebra R A) : algebraMap S α = (algebraMap A α).comp S.val :=
   rfl
 #align subalgebra.algebra_map_eq Subalgebra.algebraMap_eq
 
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+Case conversion may be inaccurate. Consider using '#align subalgebra.srange_algebra_map Subalgebra.rangeS_algebraMapₓ'. -/
 @[simp]
 theorem rangeS_algebraMap {R A : Type _} [CommSemiring R] [CommSemiring A] [Algebra R A]
     (S : Subalgebra R A) : (algebraMap S A).srange = S.toSubsemiring := by
@@ -1339,6 +2409,12 @@ theorem rangeS_algebraMap {R A : Type _} [CommSemiring R] [CommSemiring A] [Alge
     Subsemiring.rangeS_subtype]
 #align subalgebra.srange_algebra_map Subalgebra.rangeS_algebraMap
 
+/- warning: subalgebra.range_algebra_map -> Subalgebra.range_algebraMap is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align subalgebra.range_algebra_map Subalgebra.range_algebraMapₓ'. -/
 @[simp]
 theorem range_algebraMap {R A : Type _} [CommRing R] [CommRing A] [Algebra R A]
     (S : Subalgebra R A) : (algebraMap S A).range = S.toSubring := by
@@ -1346,6 +2422,12 @@ theorem range_algebraMap {R A : Type _} [CommRing R] [CommRing A] [Algebra R A]
     Subring.range_subtype]
 #align subalgebra.range_algebra_map Subalgebra.range_algebraMap
 
+/- warning: subalgebra.no_zero_smul_divisors_top -> Subalgebra.noZeroSMulDivisors_top is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align subalgebra.no_zero_smul_divisors_top Subalgebra.noZeroSMulDivisors_topₓ'. -/
 instance noZeroSMulDivisors_top [NoZeroDivisors A] (S : Subalgebra R A) : NoZeroSMulDivisors S A :=
   ⟨fun c x h =>
     have : (c : A) = 0 ∨ x = 0 := eq_zero_or_eq_zero_of_mul_eq_zero h
@@ -1356,33 +2438,61 @@ end Actions
 
 section Center
 
+/- warning: set.algebra_map_mem_center -> Set.algebraMap_mem_center is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align set.algebra_map_mem_center Set.algebraMap_mem_centerₓ'. -/
 theorem Set.algebraMap_mem_center (r : R) : algebraMap R A r ∈ Set.center A := by
   simp [Algebra.commutes, Set.mem_center_iff]
 #align set.algebra_map_mem_center Set.algebraMap_mem_center
 
 variable (R A)
 
+#print Subalgebra.center /-
 /-- The center of an algebra is the set of elements which commute with every element. They form a
 subalgebra. -/
 def center : Subalgebra R A :=
   { Subsemiring.center A with algebraMap_mem' := Set.algebraMap_mem_center }
 #align subalgebra.center Subalgebra.center
+-/
 
+/- warning: subalgebra.coe_center -> Subalgebra.coe_center is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align subalgebra.coe_center Subalgebra.coe_centerₓ'. -/
 theorem coe_center : (center R A : Set A) = Set.center A :=
   rfl
 #align subalgebra.coe_center Subalgebra.coe_center
 
+#print Subalgebra.center_toSubsemiring /-
 @[simp]
 theorem center_toSubsemiring : (center R A).toSubsemiring = Subsemiring.center A :=
   rfl
 #align subalgebra.center_to_subsemiring Subalgebra.center_toSubsemiring
+-/
 
+/- warning: subalgebra.center_to_subring -> Subalgebra.center_toSubring is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall (R : Type.{u2}) (A : Type.{u1}) [_inst_6 : CommRing.{u2} R] [_inst_7 : Ring.{u1} A] [_inst_8 : Algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_6) (Ring.toSemiring.{u1} A _inst_7)], Eq.{succ u1} (Subring.{u1} A _inst_7) (Subalgebra.toSubring.{u2, u1} R A _inst_6 _inst_7 _inst_8 (Subalgebra.center.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_6) (Ring.toSemiring.{u1} A _inst_7) _inst_8)) (Subring.center.{u1} A _inst_7)
+Case conversion may be inaccurate. Consider using '#align subalgebra.center_to_subring Subalgebra.center_toSubringₓ'. -/
 @[simp]
 theorem center_toSubring (R A : Type _) [CommRing R] [Ring A] [Algebra R A] :
     (center R A).toSubring = Subring.center A :=
   rfl
 #align subalgebra.center_to_subring Subalgebra.center_toSubring
 
+/- warning: subalgebra.center_eq_top -> Subalgebra.center_eq_top is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) [_inst_1 : CommSemiring.{u1} R] (A : Type.{u2}) [_inst_6 : CommSemiring.{u2} A] [_inst_7 : Algebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_6)], Eq.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_6) _inst_7) (Subalgebra.center.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_6) _inst_7) (Top.top.{u2} (Subalgebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_6) _inst_7) (CompleteLattice.toHasTop.{u2} (Subalgebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_6) _inst_7) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_6) _inst_7)))
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+Case conversion may be inaccurate. Consider using '#align subalgebra.center_eq_top Subalgebra.center_eq_topₓ'. -/
 @[simp]
 theorem center_eq_top (A : Type _) [CommSemiring A] [Algebra R A] : center R A = ⊤ :=
   SetLike.coe_injective (Set.center_eq_univ A)
@@ -1396,6 +2506,12 @@ instance : CommSemiring (center R A) :=
 instance {A : Type _} [Ring A] [Algebra R A] : CommRing (center R A) :=
   Subring.center.commRing
 
+/- warning: subalgebra.mem_center_iff -> Subalgebra.mem_center_iff is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align subalgebra.mem_center_iff Subalgebra.mem_center_iffₓ'. -/
 theorem mem_center_iff {a : A} : a ∈ center R A ↔ ∀ b : A, b * a = a * b :=
   Iff.rfl
 #align subalgebra.mem_center_iff Subalgebra.mem_center_iff
@@ -1404,6 +2520,12 @@ end Center
 
 section Centralizer
 
+/- warning: set.algebra_map_mem_centralizer -> Set.algebraMap_mem_centralizer is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align set.algebra_map_mem_centralizer Set.algebraMap_mem_centralizerₓ'. -/
 @[simp]
 theorem Set.algebraMap_mem_centralizer {s : Set A} (r : R) : algebraMap R A r ∈ s.centralizer :=
   fun a h => (Algebra.commutes _ _).symm
@@ -1411,31 +2533,59 @@ theorem Set.algebraMap_mem_centralizer {s : Set A} (r : R) : algebraMap R A r 
 
 variable (R)
 
+#print Subalgebra.centralizer /-
 /-- The centralizer of a set as a subalgebra. -/
 def centralizer (s : Set A) : Subalgebra R A :=
   { Subsemiring.centralizer s with algebraMap_mem' := Set.algebraMap_mem_centralizer }
 #align subalgebra.centralizer Subalgebra.centralizer
+-/
 
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 @[simp, norm_cast]
 theorem coe_centralizer (s : Set A) : (centralizer R s : Set A) = s.centralizer :=
   rfl
 #align subalgebra.coe_centralizer Subalgebra.coe_centralizer
 
+/- warning: subalgebra.mem_centralizer_iff -> Subalgebra.mem_centralizer_iff is a dubious translation:
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 theorem mem_centralizer_iff {s : Set A} {z : A} : z ∈ centralizer R s ↔ ∀ g ∈ s, g * z = z * g :=
   Iff.rfl
 #align subalgebra.mem_centralizer_iff Subalgebra.mem_centralizer_iff
 
+/- warning: subalgebra.centralizer_le -> Subalgebra.centralizer_le is a dubious translation:
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 theorem centralizer_le (s t : Set A) (h : s ⊆ t) : centralizer R t ≤ centralizer R s :=
   Set.centralizer_subset h
 #align subalgebra.centralizer_le Subalgebra.centralizer_le
 
+#print Subalgebra.centralizer_univ /-
 @[simp]
 theorem centralizer_univ : centralizer R Set.univ = center R A :=
   SetLike.ext' (Set.centralizer_univ A)
 #align subalgebra.centralizer_univ Subalgebra.centralizer_univ
+-/
 
 end Centralizer
 
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+Case conversion may be inaccurate. Consider using '#align subalgebra.mem_of_finset_sum_eq_one_of_pow_smul_mem Subalgebra.mem_of_finset_sum_eq_one_of_pow_smul_memₓ'. -/
 /-- Suppose we are given `∑ i, lᵢ * sᵢ = 1` in `S`, and `S'` a subalgebra of `S` that contains
 `lᵢ` and `sᵢ`. To check that an `x : S` falls in `S'`, we only need to show that
 `r ^ n • x ∈ M'` for some `n` for each `r : s`. -/
@@ -1471,6 +2621,12 @@ theorem mem_of_finset_sum_eq_one_of_pow_smul_mem {S : Type _} [CommRing S] [Alge
     exact ⟨⟨_, hn i⟩, rfl⟩
 #align subalgebra.mem_of_finset_sum_eq_one_of_pow_smul_mem Subalgebra.mem_of_finset_sum_eq_one_of_pow_smul_mem
 
+/- warning: subalgebra.mem_of_span_eq_top_of_smul_pow_mem -> Subalgebra.mem_of_span_eq_top_of_smul_pow_mem is a dubious translation:
+lean 3 declaration is
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(Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)))) (_private.Mathlib.RingTheory.Ideal.Operations.0.Ideal.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRing.{u1, u1} S S (CommRing.toCommSemiring.{u1} S _inst_6) _inst_6 (Algebra.id.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)))) (Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6))))) (fun (_x : Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6))))) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6))))) => S) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} S S (Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6))))) S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) (Finsupp.addCommMonoid.{u1, u1} (Set.Elem.{u1} S s) S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_6))))) (Finsupp.module.{u1, u1, u1} (Set.Elem.{u1} S s) S S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6))))) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)))) (_private.Mathlib.RingTheory.Ideal.Operations.0.Ideal.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRing.{u1, u1} S S (CommRing.toCommSemiring.{u1} S _inst_6) _inst_6 (Algebra.id.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6))) (RingHom.id.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6))))) (Finsupp.total.{u1, u1, u1} (Set.Elem.{u1} S s) S S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_6))))) (_private.Mathlib.RingTheory.Ideal.Operations.0.Ideal.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRing.{u1, u1} S S (CommRing.toCommSemiring.{u1} S _inst_6) _inst_6 (Algebra.id.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6))) (Subtype.val.{succ u1} S (fun (x : S) => Membership.mem.{u1, u1} S (Set.{u1} S) (Set.instMembershipSet.{u1} S) x s))) l) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6))))) => S) l) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6))))) => S) l) (NonAssocRing.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6))))) => S) l) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6))))) => S) l) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (MonoidWithZero.toZero.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6))))) => S) l) _inst_6)))))) -> (HasSubset.Subset.{u1} (Set.{u1} S) (Set.instHasSubsetSet.{u1} S) s (SetLike.coe.{u1, u1} (Subalgebra.{u2, u1} R S _inst_1 (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) _inst_7) S (Subalgebra.instSetLikeSubalgebra.{u2, u1} R S _inst_1 (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) _inst_7) S')) -> (forall (i : Set.Elem.{u1} S s), Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : Set.Elem.{u1} S s) => S) i) (Subalgebra.{u2, u1} R S _inst_1 (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) _inst_7) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R S _inst_1 (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) _inst_7) S (Subalgebra.instSetLikeSubalgebra.{u2, u1} R S _inst_1 (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) _inst_7)) (FunLike.coe.{succ u1, succ u1, succ u1} (Finsupp.{u1, u1} (Set.Elem.{u1} S s) S (CommMonoidWithZero.toZero.{u1} S (CommSemiring.toCommMonoidWithZero.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)))) (Set.Elem.{u1} S s) (fun (_x : Set.Elem.{u1} S s) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : Set.Elem.{u1} S s) => S) _x) (Finsupp.funLike.{u1, u1} (Set.Elem.{u1} S s) S (CommMonoidWithZero.toZero.{u1} S (CommSemiring.toCommMonoidWithZero.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)))) l i) S') -> (forall (x : S), (forall (r : Set.Elem.{u1} S s), Exists.{1} Nat (fun (n : Nat) => Membership.mem.{u1, u1} S (Subalgebra.{u2, u1} R S _inst_1 (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) _inst_7) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R S _inst_1 (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) _inst_7) S (Subalgebra.instSetLikeSubalgebra.{u2, u1} R S _inst_1 (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) _inst_7)) (HSMul.hSMul.{u1, u1, u1} S S S (instHSMul.{u1, u1} S S (Algebra.toSMul.{u1, u1} S S (CommRing.toCommSemiring.{u1} S _inst_6) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) (Algebra.id.{u1} S (CommRing.toCommSemiring.{u1} S _inst_6)))) (HPow.hPow.{u1, 0, u1} S Nat S (instHPow.{u1, 0} S Nat (Monoid.Pow.{u1} S (MonoidWithZero.toMonoid.{u1} S (Semiring.toMonoidWithZero.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)))))) (Subtype.val.{succ u1} S (fun (x : S) => Membership.mem.{u1, u1} S (Set.{u1} S) (Set.instMembershipSet.{u1} S) x s) r) n) x) S')) -> (Membership.mem.{u1, u1} S (Subalgebra.{u2, u1} R S _inst_1 (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) _inst_7) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R S _inst_1 (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) _inst_7) S (Subalgebra.instSetLikeSubalgebra.{u2, u1} R S _inst_1 (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_6)) _inst_7)) x S'))
+Case conversion may be inaccurate. Consider using '#align subalgebra.mem_of_span_eq_top_of_smul_pow_mem Subalgebra.mem_of_span_eq_top_of_smul_pow_memₓ'. -/
 theorem mem_of_span_eq_top_of_smul_pow_mem {S : Type _} [CommRing S] [Algebra R S]
     (S' : Subalgebra R S) (s : Set S) (l : s →₀ S) (hs : Finsupp.total s S S coe l = 1)
     (hs' : s ⊆ S') (hl : ∀ i, l i ∈ S') (x : S) (H : ∀ r : s, ∃ n : ℕ, (r ^ n : S) • x ∈ S') :
@@ -1484,11 +2640,19 @@ section Nat
 
 variable {R : Type _} [Semiring R]
 
+#print subalgebraOfSubsemiring /-
 /-- A subsemiring is a `ℕ`-subalgebra. -/
 def subalgebraOfSubsemiring (S : Subsemiring R) : Subalgebra ℕ R :=
   { S with algebraMap_mem' := fun i => coe_nat_mem S i }
 #align subalgebra_of_subsemiring subalgebraOfSubsemiring
+-/
 
+/- warning: mem_subalgebra_of_subsemiring -> mem_subalgebraOfSubsemiring is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {x : R} {S : Subsemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)}, Iff (Membership.Mem.{u1, u1} R (Subalgebra.{0, u1} Nat R Nat.commSemiring _inst_1 (algebraNat.{u1} R _inst_1)) (SetLike.hasMem.{u1, u1} (Subalgebra.{0, u1} Nat R Nat.commSemiring _inst_1 (algebraNat.{u1} R _inst_1)) R (Subalgebra.setLike.{0, u1} Nat R Nat.commSemiring _inst_1 (algebraNat.{u1} R _inst_1))) x (subalgebraOfSubsemiring.{u1} R _inst_1 S)) (Membership.Mem.{u1, u1} R (Subsemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (SetLike.hasMem.{u1, u1} (Subsemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Subsemiring.setLike.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) x S)
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {x : R} {S : Subsemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)}, Iff (Membership.mem.{u1, u1} R (Subalgebra.{0, u1} Nat R Nat.commSemiring _inst_1 (algebraNat.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Subalgebra.{0, u1} Nat R Nat.commSemiring _inst_1 (algebraNat.{u1} R _inst_1)) R (Subalgebra.instSetLikeSubalgebra.{0, u1} Nat R Nat.commSemiring _inst_1 (algebraNat.{u1} R _inst_1))) x (subalgebraOfSubsemiring.{u1} R _inst_1 S)) (Membership.mem.{u1, u1} R (Subsemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Subsemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Subsemiring.instSetLikeSubsemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) x S)
+Case conversion may be inaccurate. Consider using '#align mem_subalgebra_of_subsemiring mem_subalgebraOfSubsemiringₓ'. -/
 @[simp]
 theorem mem_subalgebraOfSubsemiring {x : R} {S : Subsemiring R} :
     x ∈ subalgebraOfSubsemiring S ↔ x ∈ S :=
@@ -1501,6 +2665,12 @@ section Int
 
 variable {R : Type _} [Ring R]
 
+/- warning: subalgebra_of_subring -> subalgebraOfSubring is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R], (Subring.{u1} R _inst_1) -> (Subalgebra.{0, u1} Int R Int.commSemiring (Ring.toSemiring.{u1} R _inst_1) (algebraInt.{u1} R _inst_1))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R], (Subring.{u1} R _inst_1) -> (Subalgebra.{0, u1} Int R Int.instCommSemiringInt (Ring.toSemiring.{u1} R _inst_1) (algebraInt.{u1} R _inst_1))
+Case conversion may be inaccurate. Consider using '#align subalgebra_of_subring subalgebraOfSubringₓ'. -/
 /-- A subring is a `ℤ`-subalgebra. -/
 def subalgebraOfSubring (S : Subring R) : Subalgebra ℤ R :=
   { S with
@@ -1514,6 +2684,12 @@ def subalgebraOfSubring (S : Subring R) : Subalgebra ℤ R :=
 
 variable {S : Type _} [Semiring S]
 
+/- warning: mem_subalgebra_of_subring -> mem_subalgebraOfSubring is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {x : R} {S : Subring.{u1} R _inst_1}, Iff (Membership.Mem.{u1, u1} R (Subalgebra.{0, u1} Int R Int.commSemiring (Ring.toSemiring.{u1} R _inst_1) (algebraInt.{u1} R _inst_1)) (SetLike.hasMem.{u1, u1} (Subalgebra.{0, u1} Int R Int.commSemiring (Ring.toSemiring.{u1} R _inst_1) (algebraInt.{u1} R _inst_1)) R (Subalgebra.setLike.{0, u1} Int R Int.commSemiring (Ring.toSemiring.{u1} R _inst_1) (algebraInt.{u1} R _inst_1))) x (subalgebraOfSubring.{u1} R _inst_1 S)) (Membership.Mem.{u1, u1} R (Subring.{u1} R _inst_1) (SetLike.hasMem.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)) x S)
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {x : R} {S : Subring.{u1} R _inst_1}, Iff (Membership.mem.{u1, u1} R (Subalgebra.{0, u1} Int R Int.instCommSemiringInt (Ring.toSemiring.{u1} R _inst_1) (algebraInt.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Subalgebra.{0, u1} Int R Int.instCommSemiringInt (Ring.toSemiring.{u1} R _inst_1) (algebraInt.{u1} R _inst_1)) R (Subalgebra.instSetLikeSubalgebra.{0, u1} Int R Int.instCommSemiringInt (Ring.toSemiring.{u1} R _inst_1) (algebraInt.{u1} R _inst_1))) x (subalgebraOfSubring.{u1} R _inst_1 S)) (Membership.mem.{u1, u1} R (Subring.{u1} R _inst_1) (SetLike.instMembership.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1)) x S)
+Case conversion may be inaccurate. Consider using '#align mem_subalgebra_of_subring mem_subalgebraOfSubringₓ'. -/
 @[simp]
 theorem mem_subalgebraOfSubring {x : R} {S : Subring R} : x ∈ subalgebraOfSubring S ↔ x ∈ S :=
   Iff.rfl

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

chore(Algebra/Algebra): split Subalgebra.Basic (#12267)

This PR was supposed to be simultaneous with #12090 but I got ill last week.

This is based on seeing the import Algebra.Algebra.Subalgebra.Basic → RingTheory.Ideal.Operations on the longest pole. It feels like Ideal.Operations should not be needed to define the notion of subalgebra, only to construct some interesting examples. So I removed the import and split off anything that wouldn't fit.

The following results and their corollaries were split off:

Subalgebra.prod
Subalgebra.iSupLift
AlgHom.ker_rangeRestrict
Subalgebra.mem_of_finset_sum_eq_one_of_pow_smul_mem

Co-authored-by: Anne Baanen <Vierkantor@users.noreply.github.com>

chore(Algebra/Algebra): split Subalgebra.Basic (#12267)

This PR was supposed to be simultaneous with #12090 but I got ill last week.

The following results and their corollaries were split off:

Subalgebra.prod
Subalgebra.iSupLift
AlgHom.ker_rangeRestrict
Subalgebra.mem_of_finset_sum_eq_one_of_pow_smul_mem

Co-authored-by: Anne Baanen <Vierkantor@users.noreply.github.com>

chore(Algebra/Algebra): split Subalgebra.Basic (#12267)

This PR was supposed to be simultaneous with #12090 but I got ill last week.

The following results and their corollaries were split off:

Subalgebra.prod
Subalgebra.iSupLift
AlgHom.ker_rangeRestrict
Subalgebra.mem_of_finset_sum_eq_one_of_pow_smul_mem

Co-authored-by: Anne Baanen <Vierkantor@users.noreply.github.com>

chore(Algebra/Algebra): split Subalgebra.Basic (#12267)

This PR was supposed to be simultaneous with #12090 but I got ill last week.

The following results and their corollaries were split off:

Subalgebra.prod
Subalgebra.iSupLift
AlgHom.ker_rangeRestrict
Subalgebra.mem_of_finset_sum_eq_one_of_pow_smul_mem

Co-authored-by: Anne Baanen <Vierkantor@users.noreply.github.com>

Diff

@@ -3,11 +3,7 @@ Copyright (c) 2018 Kenny Lau. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau, Yury Kudryashov
 -/
-import Mathlib.Algebra.Algebra.Basic
-import Mathlib.Algebra.Algebra.Prod
-import Mathlib.Data.Set.UnionLift
-import Mathlib.LinearAlgebra.Finsupp
-import Mathlib.RingTheory.Ideal.Operations
+import Mathlib.Algebra.Algebra.Operations
 
 #align_import algebra.algebra.subalgebra.basic from "leanprover-community/mathlib"@"b915e9392ecb2a861e1e766f0e1df6ac481188ca"
 
@@ -630,9 +626,6 @@ theorem rangeRestrict_surjective (f : A →ₐ[R] B) : Function.Surjective (f.ra
     let ⟨x, hx⟩ := hy
     ⟨x, SetCoe.ext hx⟩
 
-theorem ker_rangeRestrict (f : A →ₐ[R] B) : RingHom.ker f.rangeRestrict = RingHom.ker f :=
-  Ideal.ext fun _ ↦ Subtype.ext_iff
-
 /-- The equalizer of two R-algebra homomorphisms -/
 def equalizer (ϕ ψ : A →ₐ[R] B) : Subalgebra R A where
   carrier := { a | ϕ a = ψ a }
@@ -1079,125 +1072,6 @@ theorem coe_equivMapOfInjective_apply (x : S) : ↑(equivMapOfInjective S f hf x
 
 end equivMapOfInjective
 
-section Prod
-
-variable (S₁ : Subalgebra R B)
-
-/-- The product of two subalgebras is a subalgebra. -/
-def prod : Subalgebra R (A × B) :=
-  { S.toSubsemiring.prod S₁.toSubsemiring with
-    carrier := S ×ˢ S₁
-    algebraMap_mem' := fun _ => ⟨algebraMap_mem _ _, algebraMap_mem _ _⟩ }
-#align subalgebra.prod Subalgebra.prod
-
-@[simp]
-theorem coe_prod : (prod S S₁ : Set (A × B)) = (S : Set A) ×ˢ (S₁ : Set B) :=
-  rfl
-#align subalgebra.coe_prod Subalgebra.coe_prod
-
-open Subalgebra in
-theorem prod_toSubmodule : toSubmodule (S.prod S₁) = (toSubmodule S).prod (toSubmodule S₁) := rfl
-#align subalgebra.prod_to_submodule Subalgebra.prod_toSubmodule
-
-@[simp]
-theorem mem_prod {S : Subalgebra R A} {S₁ : Subalgebra R B} {x : A × B} :
-    x ∈ prod S S₁ ↔ x.1 ∈ S ∧ x.2 ∈ S₁ := Set.mem_prod
-#align subalgebra.mem_prod Subalgebra.mem_prod
-
-@[simp]
-theorem prod_top : (prod ⊤ ⊤ : Subalgebra R (A × B)) = ⊤ := by ext; simp
-#align subalgebra.prod_top Subalgebra.prod_top
-
-theorem prod_mono {S T : Subalgebra R A} {S₁ T₁ : Subalgebra R B} :
-    S ≤ T → S₁ ≤ T₁ → prod S S₁ ≤ prod T T₁ :=
-  Set.prod_mono
-#align subalgebra.prod_mono Subalgebra.prod_mono
-
-@[simp]
-theorem prod_inf_prod {S T : Subalgebra R A} {S₁ T₁ : Subalgebra R B} :
-    S.prod S₁ ⊓ T.prod T₁ = (S ⊓ T).prod (S₁ ⊓ T₁) :=
-  SetLike.coe_injective Set.prod_inter_prod
-#align subalgebra.prod_inf_prod Subalgebra.prod_inf_prod
-
-end Prod
-
-section iSupLift
-
-variable {ι : Type*} [Nonempty ι] {K : ι → Subalgebra R A} (dir : Directed (· ≤ ·) K)
-
-theorem coe_iSup_of_directed : ↑(iSup K) = ⋃ i, (K i : Set A) :=
-  let s : Subalgebra R A :=
-    { __ := Subsemiring.copy _ _ (Subsemiring.coe_iSup_of_directed dir).symm
-      algebraMap_mem' := fun _ ↦ Set.mem_iUnion.2
-        ⟨Classical.arbitrary ι, Subalgebra.algebraMap_mem _ _⟩ }
-  have : iSup K = s := le_antisymm
-    (iSup_le fun i ↦ le_iSup (fun i ↦ (K i : Set A)) i) (Set.iUnion_subset fun _ ↦ le_iSup K _)
-  this.symm ▸ rfl
-#align subalgebra.coe_supr_of_directed Subalgebra.coe_iSup_of_directed
-
-variable (K)
-variable (f : ∀ i, K i →ₐ[R] B) (hf : ∀ (i j : ι) (h : K i ≤ K j), f i = (f j).comp (inclusion h))
-  (T : Subalgebra R A) (hT : T = iSup K)
-
--- Porting note (#11215): TODO: turn `hT` into an assumption `T ≤ iSup K`.
--- That's what `Set.iUnionLift` needs
--- Porting note: the proofs of `map_{zero,one,add,mul}` got a bit uglier, probably unification trbls
-/-- Define an algebra homomorphism on a directed supremum of subalgebras by defining
-it on each subalgebra, and proving that it agrees on the intersection of subalgebras. -/
-noncomputable def iSupLift : ↥T →ₐ[R] B :=
-  { toFun := Set.iUnionLift (fun i => ↑(K i)) (fun i x => f i x)
-        (fun i j x hxi hxj => by
-          let ⟨k, hik, hjk⟩ := dir i j
-          dsimp
-          rw [hf i k hik, hf j k hjk]
-          rfl)
-        T (by rw [hT, coe_iSup_of_directed dir])
-    map_one' := by apply Set.iUnionLift_const _ (fun _ => 1) <;> simp
-    map_zero' := by dsimp; apply Set.iUnionLift_const _ (fun _ => 0) <;> simp
-    map_mul' := by
-      subst hT; dsimp
-      apply Set.iUnionLift_binary (coe_iSup_of_directed dir) dir _ (fun _ => (· * ·))
-      on_goal 3 => rw [coe_iSup_of_directed dir]
-      all_goals simp
-    map_add' := by
-      subst hT; dsimp
-      apply Set.iUnionLift_binary (coe_iSup_of_directed dir) dir _ (fun _ => (· + ·))
-      on_goal 3 => rw [coe_iSup_of_directed dir]
-      all_goals simp
-    commutes' := fun r => by
-      dsimp
-      apply Set.iUnionLift_const _ (fun _ => algebraMap R _ r) <;> simp }
-#align subalgebra.supr_lift Subalgebra.iSupLift
-
-variable {K dir f hf T hT}
-
-@[simp]
-theorem iSupLift_inclusion {i : ι} (x : K i) (h : K i ≤ T) :
-    iSupLift K dir f hf T hT (inclusion h x) = f i x := by
-  dsimp [iSupLift, inclusion]
-  rw [Set.iUnionLift_inclusion]
-#align subalgebra.supr_lift_inclusion Subalgebra.iSupLift_inclusion
-
-@[simp]
-theorem iSupLift_comp_inclusion {i : ι} (h : K i ≤ T) :
-    (iSupLift K dir f hf T hT).comp (inclusion h) = f i := by ext; simp
-#align subalgebra.supr_lift_comp_inclusion Subalgebra.iSupLift_comp_inclusion
-
-@[simp]
-theorem iSupLift_mk {i : ι} (x : K i) (hx : (x : A) ∈ T) :
-    iSupLift K dir f hf T hT ⟨x, hx⟩ = f i x := by
-  dsimp [iSupLift, inclusion]
-  rw [Set.iUnionLift_mk]
-#align subalgebra.supr_lift_mk Subalgebra.iSupLift_mk
-
-theorem iSupLift_of_mem {i : ι} (x : T) (hx : (x : A) ∈ K i) :
-    iSupLift K dir f hf T hT x = f i ⟨x, hx⟩ := by
-  dsimp [iSupLift, inclusion]
-  rw [Set.iUnionLift_of_mem]
-#align subalgebra.supr_lift_of_mem Subalgebra.iSupLift_of_mem
-
-end iSupLift
-
 /-! ## Actions by `Subalgebra`s
 
 These are just copies of the definitions about `Subsemiring` starting from
@@ -1387,47 +1261,6 @@ theorem centralizer_univ : centralizer R Set.univ = center R A :=
 
 end Centralizer
 
-/-- Suppose we are given `∑ i, lᵢ * sᵢ = 1` in `S`, and `S'` a subalgebra of `S` that contains
-`lᵢ` and `sᵢ`. To check that an `x : S` falls in `S'`, we only need to show that
-`sᵢ ^ n • x ∈ S'` for some `n` for each `sᵢ`. -/
-theorem mem_of_finset_sum_eq_one_of_pow_smul_mem {S : Type*} [CommRing S] [Algebra R S]
-    (S' : Subalgebra R S) {ι : Type*} (ι' : Finset ι) (s : ι → S) (l : ι → S)
-    (e : ∑ i in ι', l i * s i = 1) (hs : ∀ i, s i ∈ S') (hl : ∀ i, l i ∈ S') (x : S)
-    (H : ∀ i, ∃ n : ℕ, (s i ^ n : S) • x ∈ S') : x ∈ S' := by
-  -- Porting note: needed to add this instance
-  let _i : Algebra { x // x ∈ S' } { x // x ∈ S' } := Algebra.id _
-  suffices x ∈ Subalgebra.toSubmodule (Algebra.ofId S' S).range by
-    obtain ⟨x, rfl⟩ := this
-    exact x.2
-  choose n hn using H
-  let s' : ι → S' := fun x => ⟨s x, hs x⟩
-  let l' : ι → S' := fun x => ⟨l x, hl x⟩
-  have e' : ∑ i in ι', l' i * s' i = 1 := by
-    ext
-    show S'.subtype (∑ i in ι', l' i * s' i) = 1
-    simpa only [map_sum, map_mul] using e
-  have : Ideal.span (s' '' ι') = ⊤ := by
-    rw [Ideal.eq_top_iff_one, ← e']
-    apply sum_mem
-    intros i hi
-    exact Ideal.mul_mem_left _ _ <| Ideal.subset_span <| Set.mem_image_of_mem s' hi
-  let N := ι'.sup n
-  have hN := Ideal.span_pow_eq_top _ this N
-  apply (Algebra.ofId S' S).range.toSubmodule.mem_of_span_top_of_smul_mem _ hN
-  rintro ⟨_, _, ⟨i, hi, rfl⟩, rfl⟩
-  change s' i ^ N • x ∈ _
-  rw [← tsub_add_cancel_of_le (show n i ≤ N from Finset.le_sup hi), pow_add, mul_smul]
-  refine' Submodule.smul_mem _ (⟨_, pow_mem (hs i) _⟩ : S') _
-  exact ⟨⟨_, hn i⟩, rfl⟩
-#align subalgebra.mem_of_finset_sum_eq_one_of_pow_smul_mem Subalgebra.mem_of_finset_sum_eq_one_of_pow_smul_mem
-
-theorem mem_of_span_eq_top_of_smul_pow_mem {S : Type*} [CommRing S] [Algebra R S]
-    (S' : Subalgebra R S) (s : Set S) (l : s →₀ S) (hs : Finsupp.total s S S (↑) l = 1)
-    (hs' : s ⊆ S') (hl : ∀ i, l i ∈ S') (x : S) (H : ∀ r : s, ∃ n : ℕ, (r : S) ^ n • x ∈ S') :
-    x ∈ S' :=
-  mem_of_finset_sum_eq_one_of_pow_smul_mem S' l.support (↑) l hs (fun x => hs' x.2) hl x H
-#align subalgebra.mem_of_span_eq_top_of_smul_pow_mem Subalgebra.mem_of_span_eq_top_of_smul_pow_mem
-
 end Subalgebra
 
 section Nat

chore: replace refine' that already have a ?_ (#12261)

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

94b44d32

Diff

@@ -986,7 +986,7 @@ instance : Unique (Subalgebra R R) :=
   { inferInstanceAs (Inhabited (Subalgebra R R)) with
     uniq := by
       intro S
-      refine' le_antisymm ?_ bot_le
+      refine le_antisymm ?_ bot_le
       intro _ _
       simp only [Set.mem_range, mem_bot, id.map_eq_self, exists_apply_eq_apply, default] }

chore: small splits of RingTheory.Ideal.Operations; clean imports (#12090)

This is based on seeing the import RingTheory.Ideal.Operations → LinearAlgebra.Basis on the longest pole. It feels like Ideal.Operations is a bit of a chokepoint for compiling Mathlib since it imports many files and is imported by many files. So splitting out a few obvious parts should help with compile times. Moreover, there are a bunch of imports that I could remove and have the file still compile: presumably these are (were) transitive dependencies that shake does not remove.

The following results and their corollaries were split off:

Ideal.basisSpanSingleton
Basis.mem_ideal_iff
Ideal.colon

In particular, now Ideal.Operations should no longer need to know about Basis or submodule quotients.

46c2efe1

Diff

@@ -4,6 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau, Yury Kudryashov
 -/
 import Mathlib.Algebra.Algebra.Basic
+import Mathlib.Algebra.Algebra.Prod
 import Mathlib.Data.Set.UnionLift
 import Mathlib.LinearAlgebra.Finsupp
 import Mathlib.RingTheory.Ideal.Operations

chore: Rename coe_nat/coe_int/coe_rat to natCast/intCast/ratCast (#11499)

This is less exhaustive than its sibling #11486 because edge cases are harder to classify. No fundamental difficulty, just me being a bit fast and lazy.

Reduce the diff of #11203

b2af0d13

Diff

@@ -151,9 +151,9 @@ protected theorem nsmul_mem {x : A} (hx : x ∈ S) (n : ℕ) : n • x ∈ S :=
   nsmul_mem hx n
 #align subalgebra.nsmul_mem Subalgebra.nsmul_mem
 
-protected theorem coe_nat_mem (n : ℕ) : (n : A) ∈ S :=
-  coe_nat_mem S n
-#align subalgebra.coe_nat_mem Subalgebra.coe_nat_mem
+protected theorem natCast_mem (n : ℕ) : (n : A) ∈ S :=
+  natCast_mem S n
+#align subalgebra.coe_nat_mem Subalgebra.natCast_mem
 
 protected theorem list_prod_mem {L : List A} (h : ∀ x ∈ L, x ∈ S) : L.prod ∈ S :=
   list_prod_mem h
@@ -202,10 +202,14 @@ protected theorem zsmul_mem {R : Type u} {A : Type v} [CommRing R] [Ring A] [Alg
   zsmul_mem hx n
 #align subalgebra.zsmul_mem Subalgebra.zsmul_mem
 
-protected theorem coe_int_mem {R : Type u} {A : Type v} [CommRing R] [Ring A] [Algebra R A]
+protected theorem intCast_mem {R : Type u} {A : Type v} [CommRing R] [Ring A] [Algebra R A]
     (S : Subalgebra R A) (n : ℤ) : (n : A) ∈ S :=
-  coe_int_mem S n
-#align subalgebra.coe_int_mem Subalgebra.coe_int_mem
+  intCast_mem S n
+#align subalgebra.coe_int_mem Subalgebra.intCast_mem
+
+-- 2024-04-05
+@[deprecated natCast_mem] alias coe_nat_mem := Subalgebra.natCast_mem
+@[deprecated intCast_mem] alias coe_int_mem := Subalgebra.intCast_mem
 
 /-- The projection from a subalgebra of `A` to an additive submonoid of `A`. -/
 def toAddSubmonoid {R : Type u} {A : Type v} [CommSemiring R] [Semiring A] [Algebra R A]
@@ -1431,7 +1435,7 @@ variable {R : Type*} [Semiring R]
 
 /-- A subsemiring is an `ℕ`-subalgebra. -/
 def subalgebraOfSubsemiring (S : Subsemiring R) : Subalgebra ℕ R :=
-  { S with algebraMap_mem' := fun i => coe_nat_mem S i }
+  { S with algebraMap_mem' := fun i => natCast_mem S i }
 #align subalgebra_of_subsemiring subalgebraOfSubsemiring
 
 @[simp]

chore: tidy various files (#11490)

b3a2821f

Diff

@@ -620,14 +620,12 @@ def rangeRestrict (f : A →ₐ[R] B) : A →ₐ[R] f.range :=
   f.codRestrict f.range f.mem_range_self
 #align alg_hom.range_restrict AlgHom.rangeRestrict
 
-theorem rangeRestrict_surjective (f : A →ₐ[R] B):
-    Function.Surjective (f.rangeRestrict) :=
+theorem rangeRestrict_surjective (f : A →ₐ[R] B) : Function.Surjective (f.rangeRestrict) :=
   fun ⟨_y, hy⟩ =>
-  let ⟨x, hx⟩ := hy
-  ⟨x, SetCoe.ext hx⟩
+    let ⟨x, hx⟩ := hy
+    ⟨x, SetCoe.ext hx⟩
 
-theorem ker_rangeRestrict (f : A →ₐ[R] B) :
-    RingHom.ker f.rangeRestrict = RingHom.ker f :=
+theorem ker_rangeRestrict (f : A →ₐ[R] B) : RingHom.ker f.rangeRestrict = RingHom.ker f :=
   Ideal.ext fun _ ↦ Subtype.ext_iff
 
 /-- The equalizer of two R-algebra homomorphisms -/

chore(*): remove empty lines between variable statements (#11418)

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)

75c86f04

Diff

@@ -38,9 +38,7 @@ add_decl_doc Subalgebra.toSubsemiring
 namespace Subalgebra
 
 variable {R' : Type u'} {R : Type u} {A : Type v} {B : Type w} {C : Type w'}
-
 variable [CommSemiring R]
-
 variable [Semiring A] [Algebra R A] [Semiring B] [Algebra R B] [Semiring C] [Algebra R C]
 
 instance : SetLike (Subalgebra R A) A where
@@ -510,7 +508,6 @@ end Subalgebra
 namespace Submodule
 
 variable {R A : Type*} [CommSemiring R] [Semiring A] [Algebra R A]
-
 variable (p : Submodule R A)
 
 /-- A submodule containing `1` and closed under multiplication is a subalgebra. -/
@@ -560,11 +557,8 @@ end Submodule
 namespace AlgHom
 
 variable {R' : Type u'} {R : Type u} {A : Type v} {B : Type w} {C : Type w'}
-
 variable [CommSemiring R]
-
 variable [Semiring A] [Algebra R A] [Semiring B] [Algebra R B] [Semiring C] [Algebra R C]
-
 variable (φ : A →ₐ[R] B)
 
 /-- Range of an `AlgHom` as a subalgebra. -/
@@ -665,7 +659,6 @@ end AlgHom
 namespace AlgEquiv
 
 variable {R : Type u} {A : Type v} {B : Type w}
-
 variable [CommSemiring R] [Semiring A] [Semiring B] [Algebra R A] [Algebra R B]
 
 /-- Restrict an algebra homomorphism with a left inverse to an algebra isomorphism to its range.
@@ -726,7 +719,6 @@ end AlgEquiv
 namespace Algebra
 
 variable (R : Type u) {A : Type v} {B : Type w}
-
 variable [CommSemiring R] [Semiring A] [Algebra R A] [Semiring B] [Algebra R B]
 
 /-- The minimal subalgebra that includes `s`. -/
@@ -950,9 +942,7 @@ namespace Subalgebra
 open Algebra
 
 variable {R : Type u} {A : Type v} {B : Type w}
-
 variable [CommSemiring R] [Semiring A] [Algebra R A] [Semiring B] [Algebra R B]
-
 variable (S : Subalgebra R A)
 
 /-- The top subalgebra is isomorphic to the algebra.

chore: classify todo porting notes (#11216)

Classifies by adding issue number #11215 to porting notes claiming "TODO".

86f95a40

Diff

@@ -1146,7 +1146,8 @@ variable (K)
 variable (f : ∀ i, K i →ₐ[R] B) (hf : ∀ (i j : ι) (h : K i ≤ K j), f i = (f j).comp (inclusion h))
   (T : Subalgebra R A) (hT : T = iSup K)
 
--- Porting note: TODO: turn `hT` into an assumption `T ≤ iSup K`. That's what `Set.iUnionLift` needs
+-- Porting note (#11215): TODO: turn `hT` into an assumption `T ≤ iSup K`.
+-- That's what `Set.iUnionLift` needs
 -- Porting note: the proofs of `map_{zero,one,add,mul}` got a bit uglier, probably unification trbls
 /-- Define an algebra homomorphism on a directed supremum of subalgebras by defining
 it on each subalgebra, and proving that it agrees on the intersection of subalgebras. -/

chore: Remove ball and bex from lemma names (#10816)

ball for "bounded forall" and bex for "bounded exists" are from experience very confusing abbreviations. This PR renames them to forall_mem and exists_mem in the few Set lemma names that mention them.

Also deprecate ball_image_of_ball, mem_image_elim, mem_image_elim_on since those lemmas are duplicates of the renamed lemmas (apart from argument order and implicitness, which I am also fixing by making the binder in the RHS of forall_mem_image semi-implicit), have obscure names and are completely unused.

c697e040

Diff

@@ -856,7 +856,7 @@ theorem coe_iInf {ι : Sort*} {S : ι → Subalgebra R A} : (↑(⨅ i, S i) : S
 #align algebra.coe_infi Algebra.coe_iInf
 
 theorem mem_iInf {ι : Sort*} {S : ι → Subalgebra R A} {x : A} : (x ∈ ⨅ i, S i) ↔ ∀ i, x ∈ S i := by
-  simp only [iInf, mem_sInf, Set.forall_range_iff]
+  simp only [iInf, mem_sInf, Set.forall_mem_range]
 #align algebra.mem_infi Algebra.mem_iInf
 
 open Subalgebra in

feat(Mathlib/RingTheory/Ideal/QuotientOperations): First Isomorphism Theorem for algebras (#11027)

We add the First Isomorphism Theorem for algebras. (only the surjective version was present in mathlib). We also adjust the docstring on top of the file.

Co-authored-by: Antoine Chambert-Loir <antoine.chambert-loir@math.univ-paris-diderot.fr>

d6136815

Diff

@@ -626,6 +626,16 @@ def rangeRestrict (f : A →ₐ[R] B) : A →ₐ[R] f.range :=
   f.codRestrict f.range f.mem_range_self
 #align alg_hom.range_restrict AlgHom.rangeRestrict
 
+theorem rangeRestrict_surjective (f : A →ₐ[R] B):
+    Function.Surjective (f.rangeRestrict) :=
+  fun ⟨_y, hy⟩ =>
+  let ⟨x, hx⟩ := hy
+  ⟨x, SetCoe.ext hx⟩
+
+theorem ker_rangeRestrict (f : A →ₐ[R] B) :
+    RingHom.ker f.rangeRestrict = RingHom.ker f :=
+  Ideal.ext fun _ ↦ Subtype.ext_iff
+
 /-- The equalizer of two R-algebra homomorphisms -/
 def equalizer (ϕ ψ : A →ₐ[R] B) : Subalgebra R A where
   carrier := { a | ϕ a = ψ a }

chore: bump aesop; update syntax (#10955)

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

46974e92

Diff

@@ -104,7 +104,7 @@ variable (S : Subalgebra R A)
 instance instSMulMemClass : SMulMemClass (Subalgebra R A) R A where
   smul_mem {S} r x hx := (Algebra.smul_def r x).symm ▸ mul_mem (S.algebraMap_mem' r) hx
 
-@[aesop safe apply (rule_sets [SetLike])]
+@[aesop safe apply (rule_sets := [SetLike])]
 theorem _root_.algebraMap_mem {S R A : Type*} [CommSemiring R] [Semiring A] [Algebra R A]
     [SetLike S A] [OneMemClass S A] [SMulMemClass S R A] (s : S) (r : R) :
     algebraMap R A r ∈ s :=

chore: split Ordered instances for subobjects into separate files (#10900)

Moving these to separate files should make typeclass synthesis less expensive. Additionally two of them are quite long and this shrinks them slightly.

This handles:

Submonoid
Subgroup
Subsemiring
Subring
Subfield
Submodule
Subalgebra

This also moves Units.posSubgroup into its own file.

The copyright headers are from:

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

46be2770

Diff

@@ -278,56 +278,6 @@ instance toCommRing {R A} [CommRing R] [CommRing A] [Algebra R A] (S : Subalgebr
   S.toSubring.toCommRing
 #align subalgebra.to_comm_ring Subalgebra.toCommRing
 
-instance toOrderedSemiring {R A} [CommSemiring R] [OrderedSemiring A] [Algebra R A]
-    (S : Subalgebra R A) : OrderedSemiring S :=
-  S.toSubsemiring.toOrderedSemiring
-#align subalgebra.to_ordered_semiring Subalgebra.toOrderedSemiring
-
-instance toStrictOrderedSemiring {R A} [CommSemiring R] [StrictOrderedSemiring A] [Algebra R A]
-    (S : Subalgebra R A) : StrictOrderedSemiring S :=
-  S.toSubsemiring.toStrictOrderedSemiring
-#align subalgebra.to_strict_ordered_semiring Subalgebra.toStrictOrderedSemiring
-
-instance toOrderedCommSemiring {R A} [CommSemiring R] [OrderedCommSemiring A] [Algebra R A]
-    (S : Subalgebra R A) : OrderedCommSemiring S :=
-  S.toSubsemiring.toOrderedCommSemiring
-#align subalgebra.to_ordered_comm_semiring Subalgebra.toOrderedCommSemiring
-
-instance toStrictOrderedCommSemiring {R A} [CommSemiring R] [StrictOrderedCommSemiring A]
-    [Algebra R A] (S : Subalgebra R A) : StrictOrderedCommSemiring S :=
-  S.toSubsemiring.toStrictOrderedCommSemiring
-#align subalgebra.to_strict_ordered_comm_semiring Subalgebra.toStrictOrderedCommSemiring
-
-instance toOrderedRing {R A} [CommRing R] [OrderedRing A] [Algebra R A] (S : Subalgebra R A) :
-    OrderedRing S :=
-  S.toSubring.toOrderedRing
-#align subalgebra.to_ordered_ring Subalgebra.toOrderedRing
-
-instance toOrderedCommRing {R A} [CommRing R] [OrderedCommRing A] [Algebra R A]
-    (S : Subalgebra R A) : OrderedCommRing S :=
-  S.toSubring.toOrderedCommRing
-#align subalgebra.to_ordered_comm_ring Subalgebra.toOrderedCommRing
-
-instance toLinearOrderedSemiring {R A} [CommSemiring R] [LinearOrderedSemiring A] [Algebra R A]
-    (S : Subalgebra R A) : LinearOrderedSemiring S :=
-  S.toSubsemiring.toLinearOrderedSemiring
-#align subalgebra.to_linear_ordered_semiring Subalgebra.toLinearOrderedSemiring
-
-instance toLinearOrderedCommSemiring {R A} [CommSemiring R] [LinearOrderedCommSemiring A]
-    [Algebra R A] (S : Subalgebra R A) : LinearOrderedCommSemiring S :=
-  S.toSubsemiring.toLinearOrderedCommSemiring
-#align subalgebra.to_linear_ordered_comm_semiring Subalgebra.toLinearOrderedCommSemiring
-
-instance toLinearOrderedRing {R A} [CommRing R] [LinearOrderedRing A] [Algebra R A]
-    (S : Subalgebra R A) : LinearOrderedRing S :=
-  S.toSubring.toLinearOrderedRing
-#align subalgebra.to_linear_ordered_ring Subalgebra.toLinearOrderedRing
-
-instance toLinearOrderedCommRing {R A} [CommRing R] [LinearOrderedCommRing A] [Algebra R A]
-    (S : Subalgebra R A) : LinearOrderedCommRing S :=
-  S.toSubring.toLinearOrderedCommRing
-#align subalgebra.to_linear_ordered_comm_ring Subalgebra.toLinearOrderedCommRing
-
 end
 
 /-- The forgetful map from `Subalgebra` to `Submodule` as an `OrderEmbedding` -/

chore: classify simp can do this porting notes (#10619)

Classify by adding issue number (#10618) to porting notes claiming anything semantically equivalent to simp can prove this or simp can simplify this.

de765f60

Diff

@@ -58,7 +58,7 @@ theorem mem_toSubsemiring {S : Subalgebra R A} {x} : x ∈ S.toSubsemiring ↔ x
   Iff.rfl
 #align subalgebra.mem_to_subsemiring Subalgebra.mem_toSubsemiring
 
--- @[simp] -- Porting note: simp can prove this
+-- @[simp] -- Porting note (#10618): simp can prove this
 theorem mem_carrier {s : Subalgebra R A} {x : A} : x ∈ s.carrier ↔ x ∈ s :=
   Iff.rfl
 #align subalgebra.mem_carrier Subalgebra.mem_carrier

Zulip discussions: https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/Algebra.2Eid.20for.20IntermediateField https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/Timeout.20in.20Submodule.20.28.F0.9D.93.9E.20K.29.20.28.F0.9D.93.9E.20K.29

perf: de-prioritize Subalgebra.algebra' and IntermediateField.algebra' (#9936)

Like in #9655, these instances tend to be slow to fail, so we should assign them a low priority.

Co-authored-by: Anne Baanen <Vierkantor@users.noreply.github.com>

725f123f

Diff

@@ -371,7 +371,14 @@ instance : Module R S :=
 instance [Semiring R'] [SMul R' R] [Module R' A] [IsScalarTower R' R A] : IsScalarTower R' R S :=
   inferInstanceAs (IsScalarTower R' R (toSubmodule S))
 
-instance algebra' [CommSemiring R'] [SMul R' R] [Algebra R' A] [IsScalarTower R' R A] :
+/- More general form of `Subalgebra.algebra`.
+
+This instance should have low priority since it is slow to fail:
+before failing, it will cause a search through all `SMul R' R` instances,
+which can quickly get expensive.
+-/
+instance (priority := 500) algebra' [CommSemiring R'] [SMul R' R] [Algebra R' A]
+    [IsScalarTower R' R A] :
     Algebra R' S :=
   { (algebraMap R' A).codRestrict S fun x => by
       rw [Algebra.algebraMap_eq_smul_one, ← smul_one_smul R x (1 : A), ←

feat: add equivMap[OfInjective] for subalgebra and intermediate field (#9709)

... parallel to Subring.equivMapOfInjective, Subsemiring.equivMapOfInjective, etc. etc.

6e66ddcd

Diff

@@ -745,7 +745,7 @@ noncomputable def ofInjectiveField {E F : Type*} [DivisionRing E] [Semiring F] [
 #align alg_equiv.of_injective_field AlgEquiv.ofInjectiveField
 
 /-- Given an equivalence `e : A ≃ₐ[R] B` of `R`-algebras and a subalgebra `S` of `A`,
-`subalgebra_map` is the induced equivalence between `S` and `S.map e` -/
+`subalgebraMap` is the induced equivalence between `S` and `S.map e` -/
 @[simps!]
 def subalgebraMap (e : A ≃ₐ[R] B) (S : Subalgebra R A) : S ≃ₐ[R] S.map (e : A →ₐ[R] B) :=
   { e.toRingEquiv.subsemiringMap S.toSubsemiring with
@@ -1100,6 +1100,25 @@ theorem equivOfEq_trans (S T U : Subalgebra R A) (hST : S = T) (hTU : T = U) :
     (equivOfEq S T hST).trans (equivOfEq T U hTU) = equivOfEq S U (hST.trans hTU) := rfl
 #align subalgebra.equiv_of_eq_trans Subalgebra.equivOfEq_trans
 
+section equivMapOfInjective
+
+variable (f : A →ₐ[R] B)
+
+theorem range_comp_val : (f.comp S.val).range = S.map f := by
+  rw [AlgHom.range_comp, range_val]
+
+variable (hf : Function.Injective f)
+
+/-- A subalgebra is isomorphic to its image under an injective `AlgHom` -/
+noncomputable def equivMapOfInjective : S ≃ₐ[R] S.map f :=
+  (AlgEquiv.ofInjective (f.comp S.val) (hf.comp Subtype.val_injective)).trans
+    (equivOfEq _ _ (range_comp_val S f))
+
+@[simp]
+theorem coe_equivMapOfInjective_apply (x : S) : ↑(equivMapOfInjective S f hf x) = f x := rfl
+
+end equivMapOfInjective
+
 section Prod
 
 variable (S₁ : Subalgebra R B)

perf (Subalgebra.Basic): de-prioritize Subalgebra.module' (#9655)

This can send TC search off on a wild goose chase. Discussion on Zulip

bb3b00ad

Diff

@@ -360,7 +360,8 @@ section
 /-! `Subalgebra`s inherit structure from their `Submodule` coercions. -/
 
 
-instance module' [Semiring R'] [SMul R' R] [Module R' A] [IsScalarTower R' R A] : Module R' S :=
+instance (priority := low) module' [Semiring R'] [SMul R' R] [Module R' A] [IsScalarTower R' R A] :
+    Module R' S :=
   S.toSubmodule.module'
 #align subalgebra.module' Subalgebra.module'

chore(*): replace $ with <| (#9319)

See Zulip thread for the discussion.

9f6d3388

Diff

@@ -499,7 +499,7 @@ theorem mem_map {S : Subalgebra R A} {f : A →ₐ[R] B} {y : B} : y ∈ map f S
 #align subalgebra.mem_map Subalgebra.mem_map
 
 theorem map_toSubmodule {S : Subalgebra R A} {f : A →ₐ[R] B} :
-    (toSubmodule $ S.map f) = S.toSubmodule.map f.toLinearMap :=
+    (toSubmodule <| S.map f) = S.toSubmodule.map f.toLinearMap :=
   SetLike.coe_injective rfl
 #align subalgebra.map_to_submodule Subalgebra.map_toSubmodule

chore(*): drop $/<| before fun (#9361)

Subset of #9319

3694e27d

Diff

@@ -338,7 +338,7 @@ def toSubmodule : Subalgebra R A ↪o Submodule R A where
           carrier := S
           smul_mem' := fun c {x} hx ↦
             (Algebra.smul_def c x).symm ▸ mul_mem (S.range_le ⟨c, rfl⟩) hx }
-      inj' := fun _ _ h ↦ ext <| fun x ↦ SetLike.ext_iff.mp h x }
+      inj' := fun _ _ h ↦ ext fun x ↦ SetLike.ext_iff.mp h x }
   map_rel_iff' := SetLike.coe_subset_coe.symm.trans SetLike.coe_subset_coe
 #align subalgebra.to_submodule Subalgebra.toSubmodule

refactor: rename Submodule.ofLe to Submodule.inclusion (#8470)

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

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

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

As requested by @alreadydone.

b1febe50

Diff

@@ -1031,7 +1031,7 @@ instance : Unique (Subalgebra R R) :=
 
 /-- The map `S → T` when `S` is a subalgebra contained in the subalgebra `T`.
 
-This is the subalgebra version of `Submodule.ofLe`, or `Subring.inclusion`  -/
+This is the subalgebra version of `Submodule.inclusion`, or `Subring.inclusion`  -/
 def inclusion {S T : Subalgebra R A} (h : S ≤ T) : S →ₐ[R] T
     where
   toFun := Set.inclusion h

refactor(Algebra): Define the center appropriately for non-associative algebras (#6996)

For a sensible theory, we require that the centre of an algebra is closed under multiplication. The definition currently in Mathlib works for associative algebras, but not non-associative algebras. This PR uses the definition from Cabrera García and Rodríguez Palacios, which works for any multiplication (addition) and which coincides with the current definition in the associative case.

I did consider whether the centralizer should also be re-defined in terms of operator commutation, but this still results in a centralizer which is not closed under multiplication in the non-associative case. I have therefore retained the current definition, but changed centralizer_eq_top_iff_subset and centralizer_univ to only work in the associative case.

Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Christopher Hoskin <mans0954@users.noreply.github.com> Co-authored-by: Christopher Hoskin <christopher.hoskin@overleaf.com>

2fed2bb8

Diff

@@ -1317,7 +1317,7 @@ end Actions
 section Center
 
 theorem _root_.Set.algebraMap_mem_center (r : R) : algebraMap R A r ∈ Set.center A := by
-  simp [Algebra.commutes, Set.mem_center_iff]
+  simp only [Semigroup.mem_center_iff, commutes, forall_const]
 #align set.algebra_map_mem_center Set.algebraMap_mem_center
 
 variable (R A)
@@ -1357,7 +1357,7 @@ instance {A : Type*} [Ring A] [Algebra R A] : CommRing (center R A) :=
   inferInstanceAs (CommRing (Subring.center A))
 
 theorem mem_center_iff {a : A} : a ∈ center R A ↔ ∀ b : A, b * a = a * b :=
-  Iff.rfl
+  Subsemigroup.mem_center_iff
 #align subalgebra.mem_center_iff Subalgebra.mem_center_iff
 
 end Center

chore: golf all coe_iSup_of_directed (#8232)

b7825966

Diff

@@ -1077,12 +1077,12 @@ theorem coe_inclusion {S T : Subalgebra R A} (h : S ≤ T) (s : S) : (inclusion
 
 This is the `Subalgebra` version of `LinearEquiv.ofEq` and `Equiv.Set.ofEq`. -/
 @[simps apply]
-def equivOfEq (S T : Subalgebra R A) (h : S = T) : S ≃ₐ[R] T :=
-  { LinearEquiv.ofEq _ _ (congr_arg toSubmodule h) with
-    toFun := fun x => ⟨x, h ▸ x.2⟩
-    invFun := fun x => ⟨x, h.symm ▸ x.2⟩
-    map_mul' := fun _ _ => rfl
-    commutes' := fun _ => rfl }
+def equivOfEq (S T : Subalgebra R A) (h : S = T) : S ≃ₐ[R] T where
+  __ := LinearEquiv.ofEq _ _ (congr_arg toSubmodule h)
+  toFun x := ⟨x, h ▸ x.2⟩
+  invFun x := ⟨x, h.symm ▸ x.2⟩
+  map_mul' _ _ := rfl
+  commutes' _ := rfl
 #align subalgebra.equiv_of_eq Subalgebra.equivOfEq
 
 @[simp]
@@ -1141,44 +1141,29 @@ theorem prod_inf_prod {S T : Subalgebra R A} {S₁ T₁ : Subalgebra R B} :
 
 end Prod
 
-section SuprLift
-
-variable {ι : Type*}
-
-theorem coe_iSup_of_directed [Nonempty ι] {S : ι → Subalgebra R A} (dir : Directed (· ≤ ·) S) :
-    ↑(iSup S) = ⋃ i, (S i : Set A) :=
-  -- Porting note: moved up the `let i` to use it in `zero_mem'` and `one_mem'`
-  let i := @Nonempty.some ι inferInstance
-  let K : Subalgebra R A :=
-    { carrier := ⋃ i, S i
-      -- Porting note: auto_params failing, need to provide these explicitly
-      zero_mem' := by simp only [Set.mem_iUnion, SetLike.mem_coe]; exact ⟨i, zero_mem _⟩
-      one_mem' := by simp only [Set.mem_iUnion, SetLike.mem_coe]; exact ⟨i, one_mem _⟩
-      mul_mem' := fun hx hy =>
-        let ⟨i, hi⟩ := Set.mem_iUnion.1 hx
-        let ⟨j, hj⟩ := Set.mem_iUnion.1 hy
-        let ⟨k, hik, hjk⟩ := dir i j
-        Set.mem_iUnion.2 ⟨k, Subalgebra.mul_mem (S k) (hik hi) (hjk hj)⟩
-      add_mem' := fun hx hy =>
-        let ⟨i, hi⟩ := Set.mem_iUnion.1 hx
-        let ⟨j, hj⟩ := Set.mem_iUnion.1 hy
-        let ⟨k, hik, hjk⟩ := dir i j
-        Set.mem_iUnion.2 ⟨k, Subalgebra.add_mem (S k) (hik hi) (hjk hj)⟩
-      algebraMap_mem' := fun _ ↦
-        Set.mem_iUnion.2 ⟨i, Subalgebra.algebraMap_mem _ _⟩ }
-  have : iSup S = K :=
-    le_antisymm (iSup_le fun i => Set.subset_iUnion (fun i => (↑(S i) : Set A)) i)
-      (SetLike.coe_subset_coe.1 (Set.iUnion_subset fun i => SetLike.coe_subset_coe.2 (le_iSup _ _)))
+section iSupLift
+
+variable {ι : Type*} [Nonempty ι] {K : ι → Subalgebra R A} (dir : Directed (· ≤ ·) K)
+
+theorem coe_iSup_of_directed : ↑(iSup K) = ⋃ i, (K i : Set A) :=
+  let s : Subalgebra R A :=
+    { __ := Subsemiring.copy _ _ (Subsemiring.coe_iSup_of_directed dir).symm
+      algebraMap_mem' := fun _ ↦ Set.mem_iUnion.2
+        ⟨Classical.arbitrary ι, Subalgebra.algebraMap_mem _ _⟩ }
+  have : iSup K = s := le_antisymm
+    (iSup_le fun i ↦ le_iSup (fun i ↦ (K i : Set A)) i) (Set.iUnion_subset fun _ ↦ le_iSup K _)
   this.symm ▸ rfl
 #align subalgebra.coe_supr_of_directed Subalgebra.coe_iSup_of_directed
 
+variable (K)
+variable (f : ∀ i, K i →ₐ[R] B) (hf : ∀ (i j : ι) (h : K i ≤ K j), f i = (f j).comp (inclusion h))
+  (T : Subalgebra R A) (hT : T = iSup K)
+
 -- Porting note: TODO: turn `hT` into an assumption `T ≤ iSup K`. That's what `Set.iUnionLift` needs
 -- Porting note: the proofs of `map_{zero,one,add,mul}` got a bit uglier, probably unification trbls
 /-- Define an algebra homomorphism on a directed supremum of subalgebras by defining
 it on each subalgebra, and proving that it agrees on the intersection of subalgebras. -/
-noncomputable def iSupLift [Nonempty ι] (K : ι → Subalgebra R A) (dir : Directed (· ≤ ·) K)
-    (f : ∀ i, K i →ₐ[R] B) (hf : ∀ (i j : ι) (h : K i ≤ K j), f i = (f j).comp (inclusion h))
-    (T : Subalgebra R A) (hT : T = iSup K) : ↥T →ₐ[R] B :=
+noncomputable def iSupLift : ↥T →ₐ[R] B :=
   { toFun := Set.iUnionLift (fun i => ↑(K i)) (fun i x => f i x)
         (fun i j x hxi hxj => by
           let ⟨k, hik, hjk⟩ := dir i j
@@ -1203,9 +1188,7 @@ noncomputable def iSupLift [Nonempty ι] (K : ι → Subalgebra R A) (dir : Dire
       apply Set.iUnionLift_const _ (fun _ => algebraMap R _ r) <;> simp }
 #align subalgebra.supr_lift Subalgebra.iSupLift
 
-variable [Nonempty ι] {K : ι → Subalgebra R A} {dir : Directed (· ≤ ·) K} {f : ∀ i, K i →ₐ[R] B}
-  {hf : ∀ (i j : ι) (h : K i ≤ K j), f i = (f j).comp (inclusion h)} {T : Subalgebra R A}
-  {hT : T = iSup K}
+variable {K dir f hf T hT}
 
 @[simp]
 theorem iSupLift_inclusion {i : ι} (x : K i) (h : K i ≤ T) :
@@ -1232,7 +1215,7 @@ theorem iSupLift_of_mem {i : ι} (x : T) (hx : (x : A) ∈ K i) :
   rw [Set.iUnionLift_of_mem]
 #align subalgebra.supr_lift_of_mem Subalgebra.iSupLift_of_mem
 
-end SuprLift
+end iSupLift
 
 /-! ## Actions by `Subalgebra`s

refactor(Algebra/Algebra/Subalgebra/Basic): use a better defeq for ⊥ : Subalgebra R A (#8038)

And the same thing for StarSubalgebra R A. IntermediateField was already handled in #7957.

As a result, nine (obvious) lemmas are now true by definition.

This slightly adjusts the statement of Algebra.toSubmodule_bot to make it simpler and true by definition; the original statement can be recovered by rewriting by Submodule.one_eq_span, which I've had to add in some downstream proofs.

2b448f2d

Diff

@@ -352,6 +352,9 @@ theorem mem_toSubmodule {x} : x ∈ (toSubmodule S) ↔ x ∈ S := Iff.rfl
 theorem coe_toSubmodule (S : Subalgebra R A) : (toSubmodule S : Set A) = S := rfl
 #align subalgebra.coe_to_submodule Subalgebra.coe_toSubmodule
 
+theorem toSubmodule_injective : Function.Injective (toSubmodule : Subalgebra R A → Submodule R A) :=
+  fun _S₁ _S₂ h => SetLike.ext (SetLike.ext_iff.mp h :)
+
 section
 
 /-! `Subalgebra`s inherit structure from their `Submodule` coercions. -/
@@ -780,8 +783,10 @@ protected def gi : GaloisInsertion (adjoin R : Set A → Subalgebra R A) (↑) w
   choice_eq _ _ := Subalgebra.copy_eq _ _ _
 #align algebra.gi Algebra.gi
 
-instance : CompleteLattice (Subalgebra R A) :=
-  GaloisInsertion.liftCompleteLattice Algebra.gi
+instance : CompleteLattice (Subalgebra R A) where
+  __ := GaloisInsertion.liftCompleteLattice Algebra.gi
+  bot := (Algebra.ofId R A).range
+  bot_le _S := fun _a ⟨_r, hr⟩ => hr ▸ algebraMap_mem _ _
 
 @[simp]
 theorem coe_top : (↑(⊤ : Subalgebra R A) : Set A) = Set.univ := rfl
@@ -895,21 +900,14 @@ theorem iInf_toSubmodule {ι : Sort*} (S : ι → Subalgebra R A) :
 
 instance : Inhabited (Subalgebra R A) := ⟨⊥⟩
 
-theorem mem_bot {x : A} : x ∈ (⊥ : Subalgebra R A) ↔ x ∈ Set.range (algebraMap R A) :=
-  suffices (ofId R A).range = (⊥ : Subalgebra R A) by
-    rw [← this, ← SetLike.mem_coe, AlgHom.coe_range]
-    rfl
-  le_bot_iff.mp fun x hx => Subalgebra.range_le _ ((ofId R A).coe_range ▸ hx)
+theorem mem_bot {x : A} : x ∈ (⊥ : Subalgebra R A) ↔ x ∈ Set.range (algebraMap R A) := Iff.rfl
 #align algebra.mem_bot Algebra.mem_bot
 
-theorem toSubmodule_bot : Subalgebra.toSubmodule (⊥ : Subalgebra R A) = R ∙ 1 := by
-  ext x
-  simp [mem_bot, Submodule.mem_span_singleton, Algebra.smul_def]
+theorem toSubmodule_bot : Subalgebra.toSubmodule (⊥ : Subalgebra R A) = 1 := rfl
 #align algebra.to_submodule_bot Algebra.toSubmodule_bot
 
 @[simp]
-theorem coe_bot : ((⊥ : Subalgebra R A) : Set A) = Set.range (algebraMap R A) := by
-  simp [Set.ext_iff, Algebra.mem_bot]
+theorem coe_bot : ((⊥ : Subalgebra R A) : Set A) = Set.range (algebraMap R A) := rfl
 #align algebra.coe_bot Algebra.coe_bot
 
 theorem eq_top_iff {S : Subalgebra R A} : S = ⊤ ↔ ∀ x : A, x ∈ S :=
@@ -934,8 +932,7 @@ theorem map_top (f : A →ₐ[R] B) : (⊤ : Subalgebra R A).map f = f.range :=
 
 @[simp]
 theorem map_bot (f : A →ₐ[R] B) : (⊥ : Subalgebra R A).map f = ⊥ :=
-  SetLike.coe_injective <| by
-    simp only [← Set.range_comp, (· ∘ ·), Algebra.coe_bot, Subalgebra.coe_map, f.commutes]
+  Subalgebra.toSubmodule_injective <| Submodule.map_one _
 #align algebra.map_bot Algebra.map_bot
 
 @[simp]
@@ -968,9 +965,7 @@ noncomputable def botEquivOfInjective (h : Function.Injective (algebraMap R A))
     (⊥ : Subalgebra R A) ≃ₐ[R] R :=
   AlgEquiv.symm <|
     AlgEquiv.ofBijective (Algebra.ofId R _)
-      ⟨fun _x _y hxy => h (congr_arg Subtype.val hxy : _), fun ⟨_y, hy⟩ =>
-        let ⟨x, hx⟩ := Algebra.mem_bot.1 hy
-        ⟨x, Subtype.eq hx⟩⟩
+      ⟨fun _x _y hxy => h (congr_arg Subtype.val hxy : _), fun ⟨_y, x, hx⟩ => ⟨x, Subtype.eq hx⟩⟩
 #align algebra.bot_equiv_of_injective Algebra.botEquivOfInjective
 
 /-- The bottom subalgebra is isomorphic to the field. -/

fix: resolve some nolint simpNF commands (#7929)

220023c1

Diff

@@ -743,16 +743,13 @@ noncomputable def ofInjectiveField {E F : Type*} [DivisionRing E] [Semiring F] [
 /-- Given an equivalence `e : A ≃ₐ[R] B` of `R`-algebras and a subalgebra `S` of `A`,
 `subalgebra_map` is the induced equivalence between `S` and `S.map e` -/
 @[simps!]
-def subalgebraMap (e : A ≃ₐ[R] B) (S : Subalgebra R A) : S ≃ₐ[R] S.map e.toAlgHom :=
+def subalgebraMap (e : A ≃ₐ[R] B) (S : Subalgebra R A) : S ≃ₐ[R] S.map (e : A →ₐ[R] B) :=
   { e.toRingEquiv.subsemiringMap S.toSubsemiring with
     commutes' := fun r => by
       ext; dsimp only; erw [RingEquiv.subsemiringMap_apply_coe]
       exact e.commutes _ }
 #align alg_equiv.subalgebra_map AlgEquiv.subalgebraMap
 
--- These lemmas have always been bad (#7657), but lean4#2644 made `simp` start noticing
-attribute [nolint simpNF] AlgEquiv.subalgebraMap_apply_coe AlgEquiv.subalgebraMap_symm_apply_coe
-
 end AlgEquiv
 
 namespace Algebra

feat: add a SetLike default rule set for aesop (#7111)

This creates a new aesop rule set called SetLike to house lemmas about membership in subobjects.

Lemmas like pow_mem should be included in the rule set:

@[to_additive (attr := aesop safe apply (rule_sets [SetLike]))]
theorem pow_mem {M A} [Monoid M] [SetLike A M] [SubmonoidClass A M] {S : A} {x : M}
(hx : x ∈ S) : ∀ n : ℕ, x ^ n ∈ S

Lemmas about closures, like AddSubmonoid.closure should be included in the rule set, but they should be assigned a penalty (here we choose 20 throughout) so that they are not attempted before the general purpose ones like pow_mem.

@[to_additive (attr := simp, aesop safe 20 apply (rule_sets [SetLike]))
  "The `AddSubmonoid` generated by a set includes the set."]
theorem subset_closure : s ⊆ closure s := fun _ hx => mem_closure.2 fun _ hS => hS hx

In order for aesop to make effective use of AddSubmonoid.closure it needs the following new lemma.

@[aesop 5% apply (rule_sets [SetLike])]
lemma mem_of_subset {s : Set B} (hp : s ⊆ p) {x : B} (hx : x ∈ s) : x ∈ p := hp hx

Note: this lemma is marked as very unsafe (5%) because it will apply whenever the goal is of the form x ∈ p where p is any term of a SetLike instance; and moreover, it will create s as a metavariable, which is in general a terrible idea, but necessary for the reason mentioned above.

214e72fd

Diff

@@ -104,6 +104,7 @@ variable (S : Subalgebra R A)
 instance instSMulMemClass : SMulMemClass (Subalgebra R A) R A where
   smul_mem {S} r x hx := (Algebra.smul_def r x).symm ▸ mul_mem (S.algebraMap_mem' r) hx
 
+@[aesop safe apply (rule_sets [SetLike])]
 theorem _root_.algebraMap_mem {S R A : Type*} [CommSemiring R] [Semiring A] [Algebra R A]
     [SetLike S A] [OneMemClass S A] [SMulMemClass S R A] (s : S) (r : R) :
     algebraMap R A r ∈ s :=

Revert "chore: revert #7703 (#7710)"

This reverts commit f3695eb2.

ab56fa28

Diff

@@ -749,6 +749,9 @@ def subalgebraMap (e : A ≃ₐ[R] B) (S : Subalgebra R A) : S ≃ₐ[R] S.map e
       exact e.commutes _ }
 #align alg_equiv.subalgebra_map AlgEquiv.subalgebraMap
 
+-- These lemmas have always been bad (#7657), but lean4#2644 made `simp` start noticing
+attribute [nolint simpNF] AlgEquiv.subalgebraMap_apply_coe AlgEquiv.subalgebraMap_symm_apply_coe
+
 end AlgEquiv
 
 namespace Algebra

chore: revert #7703 (#7710)

This reverts commit 26eb2b0a.

f3695eb2

Diff

@@ -749,9 +749,6 @@ def subalgebraMap (e : A ≃ₐ[R] B) (S : Subalgebra R A) : S ≃ₐ[R] S.map e
       exact e.commutes _ }
 #align alg_equiv.subalgebra_map AlgEquiv.subalgebraMap
 
--- These lemmas have always been bad (#7657), but lean4#2644 made `simp` start noticing
-attribute [nolint simpNF] AlgEquiv.subalgebraMap_apply_coe AlgEquiv.subalgebraMap_symm_apply_coe
-
 end AlgEquiv
 
 namespace Algebra

chore: bump toolchain to v4.2.0-rc2 (#7703)

This includes all the changes from #7606.

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

26eb2b0a

Diff

@@ -749,6 +749,9 @@ def subalgebraMap (e : A ≃ₐ[R] B) (S : Subalgebra R A) : S ≃ₐ[R] S.map e
       exact e.commutes _ }
 #align alg_equiv.subalgebra_map AlgEquiv.subalgebraMap
 
+-- These lemmas have always been bad (#7657), but lean4#2644 made `simp` start noticing
+attribute [nolint simpNF] AlgEquiv.subalgebraMap_apply_coe AlgEquiv.subalgebraMap_symm_apply_coe
+
 end AlgEquiv
 
 namespace Algebra

chore: adjust priorities of mem_map lemmas (#6327)

The mem_map lemmas were inconsistently either not simp lemmas at all, simp lemmas, or simp lemmas with a lowered priority.

This PR makes them uniformly low priority simp lemmas, and adds a few simp attributes to "better" simp lemmas instead. (However these lemmas are themselves quite inconsistent across different algebraic structures, and I haven't attempted to add missing ones.)

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

47d15c35

Diff

@@ -489,6 +489,7 @@ theorem map_map (S : Subalgebra R A) (g : B →ₐ[R] C) (f : A →ₐ[R] B) :
   SetLike.coe_injective <| Set.image_image _ _ _
 #align subalgebra.map_map Subalgebra.map_map
 
+@[simp]
 theorem mem_map {S : Subalgebra R A} {f : A →ₐ[R] B} {y : B} : y ∈ map f S ↔ ∃ x ∈ S, f x = y :=
   Subsemiring.mem_map
 #align subalgebra.mem_map Subalgebra.mem_map

chore: banish Type _ and Sort _ (#6499)

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

This has nice performance benefits.

32de3f67

Diff

@@ -104,7 +104,7 @@ variable (S : Subalgebra R A)
 instance instSMulMemClass : SMulMemClass (Subalgebra R A) R A where
   smul_mem {S} r x hx := (Algebra.smul_def r x).symm ▸ mul_mem (S.algebraMap_mem' r) hx
 
-theorem _root_.algebraMap_mem {S R A : Type _} [CommSemiring R] [Semiring A] [Algebra R A]
+theorem _root_.algebraMap_mem {S R A : Type*} [CommSemiring R] [Semiring A] [Algebra R A]
     [SetLike S A] [OneMemClass S A] [SMulMemClass S R A] (s : S) (r : R) :
     algebraMap R A r ∈ s :=
   Algebra.algebraMap_eq_smul_one (A := A) r ▸ SMulMemClass.smul_mem r (one_mem s)
@@ -184,7 +184,7 @@ protected theorem prod_mem {R : Type u} {A : Type v} [CommSemiring R] [CommSemir
   prod_mem h
 #align subalgebra.prod_mem Subalgebra.prod_mem
 
-instance {R A : Type _} [CommRing R] [Ring A] [Algebra R A] : SubringClass (Subalgebra R A) A :=
+instance {R A : Type*} [CommRing R] [Ring A] [Algebra R A] : SubringClass (Subalgebra R A) A :=
   { Subalgebra.SubsemiringClass with
     neg_mem := fun {S x} hx => neg_one_smul R x ▸ S.smul_mem hx _ }
 
@@ -454,7 +454,7 @@ theorem toSubsemiring_subtype : S.toSubsemiring.subtype = (S.val : S →+* A) :=
 #align subalgebra.to_subsemiring_subtype Subalgebra.toSubsemiring_subtype
 
 @[simp]
-theorem toSubring_subtype {R A : Type _} [CommRing R] [Ring A] [Algebra R A] (S : Subalgebra R A) :
+theorem toSubring_subtype {R A : Type*} [CommRing R] [Ring A] [Algebra R A] (S : Subalgebra R A) :
     S.toSubring.subtype = (S.val : S →+* A) := rfl
 #align subalgebra.to_subring_subtype Subalgebra.toSubring_subtype
 
@@ -532,12 +532,12 @@ theorem coe_comap (S : Subalgebra R B) (f : A →ₐ[R] B) : (S.comap f : Set A)
   rfl
 #align subalgebra.coe_comap Subalgebra.coe_comap
 
-instance noZeroDivisors {R A : Type _} [CommSemiring R] [Semiring A] [NoZeroDivisors A]
+instance noZeroDivisors {R A : Type*} [CommSemiring R] [Semiring A] [NoZeroDivisors A]
     [Algebra R A] (S : Subalgebra R A) : NoZeroDivisors S :=
   inferInstanceAs (NoZeroDivisors S.toSubsemiring)
 #align subalgebra.no_zero_divisors Subalgebra.noZeroDivisors
 
-instance isDomain {R A : Type _} [CommRing R] [Ring A] [IsDomain A] [Algebra R A]
+instance isDomain {R A : Type*} [CommRing R] [Ring A] [IsDomain A] [Algebra R A]
     (S : Subalgebra R A) : IsDomain S :=
   inferInstanceAs (IsDomain S.toSubring)
 #align subalgebra.is_domain Subalgebra.isDomain
@@ -546,7 +546,7 @@ end Subalgebra
 
 namespace Submodule
 
-variable {R A : Type _} [CommSemiring R] [Semiring A] [Algebra R A]
+variable {R A : Type*} [CommSemiring R] [Semiring A] [Algebra R A]
 
 variable (p : Submodule R A)
 
@@ -733,7 +733,7 @@ theorem ofInjective_apply (f : A →ₐ[R] B) (hf : Function.Injective f) (x : A
 #align alg_equiv.of_injective_apply AlgEquiv.ofInjective_apply
 
 /-- Restrict an algebra homomorphism between fields to an algebra isomorphism -/
-noncomputable def ofInjectiveField {E F : Type _} [DivisionRing E] [Semiring F] [Nontrivial F]
+noncomputable def ofInjectiveField {E F : Type*} [DivisionRing E] [Semiring F] [Nontrivial F]
     [Algebra R E] [Algebra R F] (f : E →ₐ[R] F) : E ≃ₐ[R] f.range :=
   ofInjective f f.toRingHom.injective
 #align alg_equiv.of_injective_field AlgEquiv.ofInjectiveField
@@ -798,7 +798,7 @@ theorem top_toSubsemiring : (⊤ : Subalgebra R A).toSubsemiring = ⊤ := rfl
 #align algebra.top_to_subsemiring Algebra.top_toSubsemiring
 
 @[simp]
-theorem top_toSubring {R A : Type _} [CommRing R] [Ring A] [Algebra R A] :
+theorem top_toSubring {R A : Type*} [CommRing R] [Ring A] [Algebra R A] :
     (⊤ : Subalgebra R A).toSubring = ⊤ := rfl
 #align algebra.top_to_subring Algebra.top_toSubring
 
@@ -813,7 +813,7 @@ theorem toSubsemiring_eq_top {S : Subalgebra R A} : S.toSubsemiring = ⊤ ↔ S
 #align algebra.to_subsemiring_eq_top Algebra.toSubsemiring_eq_top
 
 @[simp]
-theorem toSubring_eq_top {R A : Type _} [CommRing R] [Ring A] [Algebra R A] {S : Subalgebra R A} :
+theorem toSubring_eq_top {R A : Type*} [CommRing R] [Ring A] [Algebra R A] {S : Subalgebra R A} :
     S.toSubring = ⊤ ↔ S = ⊤ :=
   Subalgebra.toSubring_injective.eq_iff' top_toSubring
 #align algebra.to_subring_eq_top Algebra.toSubring_eq_top
@@ -876,17 +876,17 @@ theorem sInf_toSubsemiring (S : Set (Subalgebra R A)) :
 #align algebra.Inf_to_subsemiring Algebra.sInf_toSubsemiring
 
 @[simp, norm_cast]
-theorem coe_iInf {ι : Sort _} {S : ι → Subalgebra R A} : (↑(⨅ i, S i) : Set A) = ⋂ i, S i := by
+theorem coe_iInf {ι : Sort*} {S : ι → Subalgebra R A} : (↑(⨅ i, S i) : Set A) = ⋂ i, S i := by
   simp [iInf]
 #align algebra.coe_infi Algebra.coe_iInf
 
-theorem mem_iInf {ι : Sort _} {S : ι → Subalgebra R A} {x : A} : (x ∈ ⨅ i, S i) ↔ ∀ i, x ∈ S i := by
+theorem mem_iInf {ι : Sort*} {S : ι → Subalgebra R A} {x : A} : (x ∈ ⨅ i, S i) ↔ ∀ i, x ∈ S i := by
   simp only [iInf, mem_sInf, Set.forall_range_iff]
 #align algebra.mem_infi Algebra.mem_iInf
 
 open Subalgebra in
 @[simp]
-theorem iInf_toSubmodule {ι : Sort _} (S : ι → Subalgebra R A) :
+theorem iInf_toSubmodule {ι : Sort*} (S : ι → Subalgebra R A) :
     toSubmodule (⨅ i, S i) = ⨅ i, toSubmodule (S i) :=
   SetLike.coe_injective <| by simp
 #align algebra.infi_to_submodule Algebra.iInf_toSubmodule
@@ -955,7 +955,7 @@ theorem surjective_algebraMap_iff :
     fun h y => Algebra.mem_bot.1 <| eq_bot_iff.1 h (Algebra.mem_top : y ∈ _)⟩
 #align algebra.surjective_algebra_map_iff Algebra.surjective_algebraMap_iff
 
-theorem bijective_algebraMap_iff {R A : Type _} [Field R] [Semiring A] [Nontrivial A]
+theorem bijective_algebraMap_iff {R A : Type*} [Field R] [Semiring A] [Nontrivial A]
     [Algebra R A] : Function.Bijective (algebraMap R A) ↔ (⊤ : Subalgebra R A) = ⊥ :=
   ⟨fun h => surjective_algebraMap_iff.1 h.2, fun h =>
     ⟨(algebraMap R A).injective, surjective_algebraMap_iff.2 h⟩⟩
@@ -973,7 +973,7 @@ noncomputable def botEquivOfInjective (h : Function.Injective (algebraMap R A))
 
 /-- The bottom subalgebra is isomorphic to the field. -/
 @[simps! symm_apply]
-noncomputable def botEquiv (F R : Type _) [Field F] [Semiring R] [Nontrivial R] [Algebra F R] :
+noncomputable def botEquiv (F R : Type*) [Field F] [Semiring R] [Nontrivial R] [Algebra F R] :
     (⊥ : Subalgebra F R) ≃ₐ[F] F :=
   botEquivOfInjective (RingHom.injective _)
 #align algebra.bot_equiv Algebra.botEquiv
@@ -1146,7 +1146,7 @@ end Prod
 
 section SuprLift
 
-variable {ι : Type _}
+variable {ι : Type*}
 
 theorem coe_iSup_of_directed [Nonempty ι] {S : ι → Subalgebra R A} (dir : Directed (· ≤ ·) S) :
     ↑(iSup S) = ⋃ i, (S i : Set A) :=
@@ -1246,7 +1246,7 @@ These are just copies of the definitions about `Subsemiring` starting from
 
 section Actions
 
-variable {α β : Type _}
+variable {α β : Type*}
 
 /-- The action by a subalgebra is the action by the underlying algebra. -/
 instance [SMul A α] (S : Subalgebra R A) : SMul S α :=
@@ -1271,7 +1271,7 @@ instance isScalarTower_left [SMul α β] [SMul A α] [SMul A β] [IsScalarTower
   inferInstanceAs (IsScalarTower S.toSubsemiring α β)
 #align subalgebra.is_scalar_tower_left Subalgebra.isScalarTower_left
 
-instance isScalarTower_mid {R S T : Type _} [CommSemiring R] [Semiring S] [AddCommMonoid T]
+instance isScalarTower_mid {R S T : Type*} [CommSemiring R] [Semiring S] [AddCommMonoid T]
     [Algebra R S] [Module R T] [Module S T] [IsScalarTower R S T] (S' : Subalgebra R S) :
     IsScalarTower R S' T :=
   ⟨fun _x y _z => (smul_assoc _ (y : S) _ : _)⟩
@@ -1302,25 +1302,25 @@ instance moduleLeft [AddCommMonoid α] [Module A α] (S : Subalgebra R A) : Modu
 #align subalgebra.module_left Subalgebra.moduleLeft
 
 /-- The action by a subalgebra is the action by the underlying algebra. -/
-instance toAlgebra {R A : Type _} [CommSemiring R] [CommSemiring A] [Semiring α] [Algebra R A]
+instance toAlgebra {R A : Type*} [CommSemiring R] [CommSemiring A] [Semiring α] [Algebra R A]
     [Algebra A α] (S : Subalgebra R A) : Algebra S α :=
   Algebra.ofSubsemiring S.toSubsemiring
 #align subalgebra.to_algebra Subalgebra.toAlgebra
 
-theorem algebraMap_eq {R A : Type _} [CommSemiring R] [CommSemiring A] [Semiring α] [Algebra R A]
+theorem algebraMap_eq {R A : Type*} [CommSemiring R] [CommSemiring A] [Semiring α] [Algebra R A]
     [Algebra A α] (S : Subalgebra R A) : algebraMap S α = (algebraMap A α).comp S.val :=
   rfl
 #align subalgebra.algebra_map_eq Subalgebra.algebraMap_eq
 
 @[simp]
-theorem rangeS_algebraMap {R A : Type _} [CommSemiring R] [CommSemiring A] [Algebra R A]
+theorem rangeS_algebraMap {R A : Type*} [CommSemiring R] [CommSemiring A] [Algebra R A]
     (S : Subalgebra R A) : (algebraMap S A).rangeS = S.toSubsemiring := by
   rw [algebraMap_eq, Algebra.id.map_eq_id, RingHom.id_comp, ← toSubsemiring_subtype,
     Subsemiring.rangeS_subtype]
 #align subalgebra.srange_algebra_map Subalgebra.rangeS_algebraMap
 
 @[simp]
-theorem range_algebraMap {R A : Type _} [CommRing R] [CommRing A] [Algebra R A]
+theorem range_algebraMap {R A : Type*} [CommRing R] [CommRing A] [Algebra R A]
     (S : Subalgebra R A) : (algebraMap S A).range = S.toSubring := by
   rw [algebraMap_eq, Algebra.id.map_eq_id, RingHom.id_comp, ← toSubring_subtype,
     Subring.range_subtype]
@@ -1358,13 +1358,13 @@ theorem center_toSubsemiring : (center R A).toSubsemiring = Subsemiring.center A
 #align subalgebra.center_to_subsemiring Subalgebra.center_toSubsemiring
 
 @[simp]
-theorem center_toSubring (R A : Type _) [CommRing R] [Ring A] [Algebra R A] :
+theorem center_toSubring (R A : Type*) [CommRing R] [Ring A] [Algebra R A] :
     (center R A).toSubring = Subring.center A :=
   rfl
 #align subalgebra.center_to_subring Subalgebra.center_toSubring
 
 @[simp]
-theorem center_eq_top (A : Type _) [CommSemiring A] [Algebra R A] : center R A = ⊤ :=
+theorem center_eq_top (A : Type*) [CommSemiring A] [Algebra R A] : center R A = ⊤ :=
   SetLike.coe_injective (Set.center_eq_univ A)
 #align subalgebra.center_eq_top Subalgebra.center_eq_top
 
@@ -1373,7 +1373,7 @@ variable {R A}
 instance : CommSemiring (center R A) :=
   inferInstanceAs (CommSemiring (Subsemiring.center A))
 
-instance {A : Type _} [Ring A] [Algebra R A] : CommRing (center R A) :=
+instance {A : Type*} [Ring A] [Algebra R A] : CommRing (center R A) :=
   inferInstanceAs (CommRing (Subring.center A))
 
 theorem mem_center_iff {a : A} : a ∈ center R A ↔ ∀ b : A, b * a = a * b :=
@@ -1429,8 +1429,8 @@ end Centralizer
 /-- Suppose we are given `∑ i, lᵢ * sᵢ = 1` in `S`, and `S'` a subalgebra of `S` that contains
 `lᵢ` and `sᵢ`. To check that an `x : S` falls in `S'`, we only need to show that
 `sᵢ ^ n • x ∈ S'` for some `n` for each `sᵢ`. -/
-theorem mem_of_finset_sum_eq_one_of_pow_smul_mem {S : Type _} [CommRing S] [Algebra R S]
-    (S' : Subalgebra R S) {ι : Type _} (ι' : Finset ι) (s : ι → S) (l : ι → S)
+theorem mem_of_finset_sum_eq_one_of_pow_smul_mem {S : Type*} [CommRing S] [Algebra R S]
+    (S' : Subalgebra R S) {ι : Type*} (ι' : Finset ι) (s : ι → S) (l : ι → S)
     (e : ∑ i in ι', l i * s i = 1) (hs : ∀ i, s i ∈ S') (hl : ∀ i, l i ∈ S') (x : S)
     (H : ∀ i, ∃ n : ℕ, (s i ^ n : S) • x ∈ S') : x ∈ S' := by
   -- Porting note: needed to add this instance
@@ -1460,7 +1460,7 @@ theorem mem_of_finset_sum_eq_one_of_pow_smul_mem {S : Type _} [CommRing S] [Alge
   exact ⟨⟨_, hn i⟩, rfl⟩
 #align subalgebra.mem_of_finset_sum_eq_one_of_pow_smul_mem Subalgebra.mem_of_finset_sum_eq_one_of_pow_smul_mem
 
-theorem mem_of_span_eq_top_of_smul_pow_mem {S : Type _} [CommRing S] [Algebra R S]
+theorem mem_of_span_eq_top_of_smul_pow_mem {S : Type*} [CommRing S] [Algebra R S]
     (S' : Subalgebra R S) (s : Set S) (l : s →₀ S) (hs : Finsupp.total s S S (↑) l = 1)
     (hs' : s ⊆ S') (hl : ∀ i, l i ∈ S') (x : S) (H : ∀ r : s, ∃ n : ℕ, (r : S) ^ n • x ∈ S') :
     x ∈ S' :=
@@ -1471,7 +1471,7 @@ end Subalgebra
 
 section Nat
 
-variable {R : Type _} [Semiring R]
+variable {R : Type*} [Semiring R]
 
 /-- A subsemiring is an `ℕ`-subalgebra. -/
 def subalgebraOfSubsemiring (S : Subsemiring R) : Subalgebra ℕ R :=
@@ -1488,7 +1488,7 @@ end Nat
 
 section Int
 
-variable {R : Type _} [Ring R]
+variable {R : Type*} [Ring R]
 
 /-- A subring is a `ℤ`-subalgebra. -/
 def subalgebraOfSubring (S : Subring R) : Subalgebra ℤ R :=
@@ -1501,7 +1501,7 @@ def subalgebraOfSubring (S : Subring R) : Subalgebra ℤ R :=
           exact S.sub_mem ih S.one_mem }
 #align subalgebra_of_subring subalgebraOfSubring
 
-variable {S : Type _} [Semiring S]
+variable {S : Type*} [Semiring S]
 
 @[simp]
 theorem mem_subalgebraOfSubring {x : R} {S : Subring R} : x ∈ subalgebraOfSubring S ↔ x ∈ S :=

chore: fix grammar mistakes (#6121)

a16538af

Diff

@@ -1473,7 +1473,7 @@ section Nat
 
 variable {R : Type _} [Semiring R]
 
-/-- A subsemiring is a `ℕ`-subalgebra. -/
+/-- A subsemiring is an `ℕ`-subalgebra. -/
 def subalgebraOfSubsemiring (S : Subsemiring R) : Subalgebra ℕ R :=
   { S with algebraMap_mem' := fun i => coe_nat_mem S i }
 #align subalgebra_of_subsemiring subalgebraOfSubsemiring

chore: script to replace headers with #align_import statements (#5979)

depends on: #5966

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

89aa3a3b

Diff

@@ -2,17 +2,14 @@
 Copyright (c) 2018 Kenny Lau. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau, Yury Kudryashov
-
-! This file was ported from Lean 3 source module algebra.algebra.subalgebra.basic
-! leanprover-community/mathlib commit b915e9392ecb2a861e1e766f0e1df6ac481188ca
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Algebra.Algebra.Basic
 import Mathlib.Data.Set.UnionLift
 import Mathlib.LinearAlgebra.Finsupp
 import Mathlib.RingTheory.Ideal.Operations
 
+#align_import algebra.algebra.subalgebra.basic from "leanprover-community/mathlib"@"b915e9392ecb2a861e1e766f0e1df6ac481188ca"
+
 /-!
 # Subalgebras over Commutative Semiring

fix: ∑' precedence (#5615)

Also remove most superfluous parentheses around big operators (∑, ∏ and variants).
roughly the used regex: ([^a-zA-Zα-ωΑ-Ω'𝓝ℳ₀𝕂ₛ)]) $([∑∏][^()∑∏]*,[^()∑∏:]*)$ ([⊂⊆=<≤]) replaced by $1 $2 $3

03fc68aa

Diff

@@ -1434,7 +1434,7 @@ end Centralizer
 `sᵢ ^ n • x ∈ S'` for some `n` for each `sᵢ`. -/
 theorem mem_of_finset_sum_eq_one_of_pow_smul_mem {S : Type _} [CommRing S] [Algebra R S]
     (S' : Subalgebra R S) {ι : Type _} (ι' : Finset ι) (s : ι → S) (l : ι → S)
-    (e : (∑ i in ι', l i * s i) = 1) (hs : ∀ i, s i ∈ S') (hl : ∀ i, l i ∈ S') (x : S)
+    (e : ∑ i in ι', l i * s i = 1) (hs : ∀ i, s i ∈ S') (hl : ∀ i, l i ∈ S') (x : S)
     (H : ∀ i, ∃ n : ℕ, (s i ^ n : S) • x ∈ S') : x ∈ S' := by
   -- Porting note: needed to add this instance
   let _i : Algebra { x // x ∈ S' } { x // x ∈ S' } := Algebra.id _
@@ -1444,7 +1444,7 @@ theorem mem_of_finset_sum_eq_one_of_pow_smul_mem {S : Type _} [CommRing S] [Alge
   choose n hn using H
   let s' : ι → S' := fun x => ⟨s x, hs x⟩
   let l' : ι → S' := fun x => ⟨l x, hl x⟩
-  have e' : (∑ i in ι', l' i * s' i) = 1 := by
+  have e' : ∑ i in ι', l' i * s' i = 1 := by
     ext
     show S'.subtype (∑ i in ι', l' i * s' i) = 1
     simpa only [map_sum, map_mul] using e

feat: algebraMap_mem for SetLike instances (#5594)

This adds an algebraMap_mem in the root namespace and protects Subalgebra.algebraMap_mem. The new declaration holds for terms of S where S is a Setlike satisfying OneMemClass S A and SMulMemClass S R A and A is an R-algebra.

6f81a92b

Diff

@@ -104,8 +104,16 @@ theorem copy_eq (S : Subalgebra R A) (s : Set A) (hs : s = ↑S) : S.copy s hs =
 
 variable (S : Subalgebra R A)
 
-theorem algebraMap_mem (r : R) : algebraMap R A r ∈ S :=
-  S.algebraMap_mem' r
+instance instSMulMemClass : SMulMemClass (Subalgebra R A) R A where
+  smul_mem {S} r x hx := (Algebra.smul_def r x).symm ▸ mul_mem (S.algebraMap_mem' r) hx
+
+theorem _root_.algebraMap_mem {S R A : Type _} [CommSemiring R] [Semiring A] [Algebra R A]
+    [SetLike S A] [OneMemClass S A] [SMulMemClass S R A] (s : S) (r : R) :
+    algebraMap R A r ∈ s :=
+  Algebra.algebraMap_eq_smul_one (A := A) r ▸ SMulMemClass.smul_mem r (one_mem s)
+
+protected theorem algebraMap_mem (r : R) : algebraMap R A r ∈ S :=
+  algebraMap_mem S r
 #align subalgebra.algebra_map_mem Subalgebra.algebraMap_mem
 
 theorem rangeS_le : (algebraMap R A).rangeS ≤ S.toSubsemiring := fun _x ⟨r, hr⟩ =>
@@ -120,11 +128,9 @@ theorem range_le : Set.range (algebraMap R A) ≤ S :=
 #align subalgebra.range_le Subalgebra.range_le
 
 theorem smul_mem {x : A} (hx : x ∈ S) (r : R) : r • x ∈ S :=
-  (Algebra.smul_def r x).symm ▸ mul_mem (S.algebraMap_mem r) hx
+  SMulMemClass.smul_mem r hx
 #align subalgebra.smul_mem Subalgebra.smul_mem
 
-instance : SMulMemClass (Subalgebra R A) R A where smul_mem r _x hx := smul_mem _ hx r
-
 protected theorem one_mem : (1 : A) ∈ S :=
   one_mem S
 #align subalgebra.one_mem Subalgebra.one_mem

chore: fix grammar 1/3 (#5001)

All of these are doc fixes

d8caa37d

Diff

@@ -652,7 +652,7 @@ theorem injective_codRestrict (f : A →ₐ[R] B) (S : Subalgebra R B) (hf : ∀
   ⟨fun H _x _y hxy => H <| Subtype.eq hxy, fun H _x _y hxy => H (congr_arg Subtype.val hxy : _)⟩
 #align alg_hom.injective_cod_restrict AlgHom.injective_codRestrict
 
-/-- Restrict the codomain of a alg_hom `f` to `f.range`.
+/-- Restrict the codomain of an `AlgHom` `f` to `f.range`.
 
 This is the bundled version of `Set.rangeFactorization`. -/
 @[reducible]

chore: port leanprover-community/mathlib#18861 (#4896)

I forgot to put some required to_additives in Lean3, I am currently backporting this change in leanprover-community/mathlib#19168.

Co-authored-by: Eric Rodriguez <37984851+ericrbg@users.noreply.github.com>

b0a21674

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau, Yury Kudryashov
 
 ! This file was ported from Lean 3 source module algebra.algebra.subalgebra.basic
-! leanprover-community/mathlib commit 8130e5155d637db35907c272de9aec9dc851c03a
+! leanprover-community/mathlib commit b915e9392ecb2a861e1e766f0e1df6ac481188ca
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -1403,10 +1403,19 @@ theorem mem_centralizer_iff {s : Set A} {z : A} : z ∈ centralizer R s ↔ ∀
   Iff.rfl
 #align subalgebra.mem_centralizer_iff Subalgebra.mem_centralizer_iff
 
+theorem center_le_centralizer (s) : center R A ≤ centralizer R s :=
+  s.center_subset_centralizer
+#align subalgebra.center_le_centralizer Subalgebra.center_le_centralizer
+
 theorem centralizer_le (s t : Set A) (h : s ⊆ t) : centralizer R t ≤ centralizer R s :=
   Set.centralizer_subset h
 #align subalgebra.centralizer_le Subalgebra.centralizer_le
 
+@[simp]
+theorem centralizer_eq_top_iff_subset {s : Set A} : centralizer R s = ⊤ ↔ s ⊆ center R A :=
+  SetLike.ext'_iff.trans Set.centralizer_eq_top_iff_subset
+#align subalgebra.centralizer_eq_top_iff_subset Subalgebra.centralizer_eq_top_iff_subset
+
 @[simp]
 theorem centralizer_univ : centralizer R Set.univ = center R A :=
   SetLike.ext' (Set.centralizer_univ A)

refactor: use the typeclass SProd to implement overloaded notation · ×ˢ · (#4200)

Currently, the following notations are changed from · ×ˢ · because Lean 4 can't deal with ambiguous notations. | Definition | Notation | | :

Co-authored-by: Jeremy Tan Jie Rui <reddeloostw@gmail.com> Co-authored-by: Kyle Miller <kmill31415@gmail.com> Co-authored-by: Chris Hughes <chrishughes24@gmail.com>

6c01dc6e

Diff

@@ -1111,7 +1111,7 @@ def prod : Subalgebra R (A × B) :=
 #align subalgebra.prod Subalgebra.prod
 
 @[simp]
-theorem coe_prod : (prod S S₁ : Set (A × B)) = S ×ˢ S₁ :=
+theorem coe_prod : (prod S S₁ : Set (A × B)) = (S : Set A) ×ˢ (S₁ : Set B) :=
   rfl
 #align subalgebra.coe_prod Subalgebra.coe_prod

feat: port RingTheory.IntegralClosure (#4196)

I tried to fix what I could, but this contains a lot of sorries!

Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com>

b6c41003

Diff

@@ -374,7 +374,8 @@ instance algebra' [CommSemiring R'] [SMul R' R] [Algebra R' A] [IsScalarTower R'
     smul_def' := fun c x => Subtype.eq <| Algebra.smul_def _ _ }
 #align subalgebra.algebra' Subalgebra.algebra'
 
-instance : Algebra R S := S.algebra'
+instance algebra : Algebra R S := S.algebra'
+#align subalgebra.algebra Subalgebra.algebra
 
 end

chore: delete 2074 references (#4030)

1877b122

Diff

@@ -449,8 +449,6 @@ theorem val_apply (x : S) : S.val x = (x : A) := rfl
 theorem toSubsemiring_subtype : S.toSubsemiring.subtype = (S.val : S →+* A) := rfl
 #align subalgebra.to_subsemiring_subtype Subalgebra.toSubsemiring_subtype
 
--- Porting note: workaround for lean#2074
-attribute [-instance] Ring.toNonAssocRing
 @[simp]
 theorem toSubring_subtype {R A : Type _} [CommRing R] [Ring A] [Algebra R A] (S : Subalgebra R A) :
     S.toSubring.subtype = (S.val : S →+* A) := rfl

chore: reenable eta, bump to nightly 2023-05-16 (#3414)

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>

a6e1045f

Diff

@@ -181,8 +181,6 @@ protected theorem prod_mem {R : Type u} {A : Type v} [CommSemiring R] [CommSemir
   prod_mem h
 #align subalgebra.prod_mem Subalgebra.prod_mem
 
--- instance : Module R A := Algebra.toModule -- Porting note: doesn't help
-set_option synthInstance.etaExperiment true in
 instance {R A : Type _} [CommRing R] [Ring A] [Algebra R A] : SubringClass (Subalgebra R A) A :=
   { Subalgebra.SubsemiringClass with
     neg_mem := fun {S x} hx => neg_one_smul R x ▸ S.smul_mem hx _ }
@@ -1417,9 +1415,6 @@ theorem centralizer_univ : centralizer R Set.univ = center R A :=
 
 end Centralizer
 
--- Porting note: in the following proof, we manually add the instances `_i₁` and `_i₂`
--- Removing those lines and enabling `etaExperiment` on the next line gives a *broken* proof
--- set_option synthInstance.etaExperiment true in
 /-- Suppose we are given `∑ i, lᵢ * sᵢ = 1` in `S`, and `S'` a subalgebra of `S` that contains
 `lᵢ` and `sᵢ`. To check that an `x : S` falls in `S'`, we only need to show that
 `sᵢ ^ n • x ∈ S'` for some `n` for each `sᵢ`. -/
@@ -1428,7 +1423,7 @@ theorem mem_of_finset_sum_eq_one_of_pow_smul_mem {S : Type _} [CommRing S] [Alge
     (e : (∑ i in ι', l i * s i) = 1) (hs : ∀ i, s i ∈ S') (hl : ∀ i, l i ∈ S') (x : S)
     (H : ∀ i, ∃ n : ℕ, (s i ^ n : S) • x ∈ S') : x ∈ S' := by
   -- Porting note: needed to add this instance
-  let _i₁ : Algebra { x // x ∈ S' } { x // x ∈ S' } := Algebra.id _
+  let _i : Algebra { x // x ∈ S' } { x // x ∈ S' } := Algebra.id _
   suffices x ∈ Subalgebra.toSubmodule (Algebra.ofId S' S).range by
     obtain ⟨x, rfl⟩ := this
     exact x.2
@@ -1450,13 +1445,10 @@ theorem mem_of_finset_sum_eq_one_of_pow_smul_mem {S : Type _} [CommRing S] [Alge
   rintro ⟨_, _, ⟨i, hi, rfl⟩, rfl⟩
   change s' i ^ N • x ∈ _
   rw [← tsub_add_cancel_of_le (show n i ≤ N from Finset.le_sup hi), pow_add, mul_smul]
-  -- Porting note: needed to add this instance
-  let _i₂ : SubmonoidClass (Subalgebra R S) S := Subalgebra.SubsemiringClass.toSubmonoidClass
   refine' Submodule.smul_mem _ (⟨_, pow_mem (hs i) _⟩ : S') _
   exact ⟨⟨_, hn i⟩, rfl⟩
 #align subalgebra.mem_of_finset_sum_eq_one_of_pow_smul_mem Subalgebra.mem_of_finset_sum_eq_one_of_pow_smul_mem
 
-set_option synthInstance.etaExperiment true in
 theorem mem_of_span_eq_top_of_smul_pow_mem {S : Type _} [CommRing S] [Algebra R S]
     (S' : Subalgebra R S) (s : Set S) (l : s →₀ S) (hs : Finsupp.total s S S (↑) l = 1)
     (hs' : s ⊆ S') (hl : ∀ i, l i ∈ S') (x : S) (H : ∀ r : s, ∃ n : ℕ, (r : S) ^ n • x ∈ S') :

chore: Rename to sSup/iSup (#3938)

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>

d1eb6264

Diff

@@ -855,41 +855,41 @@ theorem inf_toSubsemiring (S T : Subalgebra R A) :
 #align algebra.inf_to_subsemiring Algebra.inf_toSubsemiring
 
 @[simp, norm_cast]
-theorem coe_infₛ (S : Set (Subalgebra R A)) : (↑(infₛ S) : Set A) = ⋂ s ∈ S, ↑s :=
-  infₛ_image
-#align algebra.coe_Inf Algebra.coe_infₛ
+theorem coe_sInf (S : Set (Subalgebra R A)) : (↑(sInf S) : Set A) = ⋂ s ∈ S, ↑s :=
+  sInf_image
+#align algebra.coe_Inf Algebra.coe_sInf
 
-theorem mem_infₛ {S : Set (Subalgebra R A)} {x : A} : x ∈ infₛ S ↔ ∀ p ∈ S, x ∈ p := by
-  simp only [← SetLike.mem_coe, coe_infₛ, Set.mem_interᵢ₂]
-#align algebra.mem_Inf Algebra.mem_infₛ
+theorem mem_sInf {S : Set (Subalgebra R A)} {x : A} : x ∈ sInf S ↔ ∀ p ∈ S, x ∈ p := by
+  simp only [← SetLike.mem_coe, coe_sInf, Set.mem_iInter₂]
+#align algebra.mem_Inf Algebra.mem_sInf
 
 @[simp]
-theorem infₛ_toSubmodule (S : Set (Subalgebra R A)) :
-    Subalgebra.toSubmodule (infₛ S) = infₛ (Subalgebra.toSubmodule '' S) :=
+theorem sInf_toSubmodule (S : Set (Subalgebra R A)) :
+    Subalgebra.toSubmodule (sInf S) = sInf (Subalgebra.toSubmodule '' S) :=
   SetLike.coe_injective <| by simp
-#align algebra.Inf_to_submodule Algebra.infₛ_toSubmodule
+#align algebra.Inf_to_submodule Algebra.sInf_toSubmodule
 
 @[simp]
-theorem infₛ_toSubsemiring (S : Set (Subalgebra R A)) :
-    (infₛ S).toSubsemiring = infₛ (Subalgebra.toSubsemiring '' S) :=
+theorem sInf_toSubsemiring (S : Set (Subalgebra R A)) :
+    (sInf S).toSubsemiring = sInf (Subalgebra.toSubsemiring '' S) :=
   SetLike.coe_injective <| by simp
-#align algebra.Inf_to_subsemiring Algebra.infₛ_toSubsemiring
+#align algebra.Inf_to_subsemiring Algebra.sInf_toSubsemiring
 
 @[simp, norm_cast]
-theorem coe_infᵢ {ι : Sort _} {S : ι → Subalgebra R A} : (↑(⨅ i, S i) : Set A) = ⋂ i, S i := by
-  simp [infᵢ]
-#align algebra.coe_infi Algebra.coe_infᵢ
+theorem coe_iInf {ι : Sort _} {S : ι → Subalgebra R A} : (↑(⨅ i, S i) : Set A) = ⋂ i, S i := by
+  simp [iInf]
+#align algebra.coe_infi Algebra.coe_iInf
 
-theorem mem_infᵢ {ι : Sort _} {S : ι → Subalgebra R A} {x : A} : (x ∈ ⨅ i, S i) ↔ ∀ i, x ∈ S i := by
-  simp only [infᵢ, mem_infₛ, Set.forall_range_iff]
-#align algebra.mem_infi Algebra.mem_infᵢ
+theorem mem_iInf {ι : Sort _} {S : ι → Subalgebra R A} {x : A} : (x ∈ ⨅ i, S i) ↔ ∀ i, x ∈ S i := by
+  simp only [iInf, mem_sInf, Set.forall_range_iff]
+#align algebra.mem_infi Algebra.mem_iInf
 
 open Subalgebra in
 @[simp]
-theorem infᵢ_toSubmodule {ι : Sort _} (S : ι → Subalgebra R A) :
+theorem iInf_toSubmodule {ι : Sort _} (S : ι → Subalgebra R A) :
     toSubmodule (⨅ i, S i) = ⨅ i, toSubmodule (S i) :=
   SetLike.coe_injective <| by simp
-#align algebra.infi_to_submodule Algebra.infᵢ_toSubmodule
+#align algebra.infi_to_submodule Algebra.iInf_toSubmodule
 
 instance : Inhabited (Subalgebra R A) := ⟨⊥⟩
 
@@ -1148,92 +1148,92 @@ section SuprLift
 
 variable {ι : Type _}
 
-theorem coe_supᵢ_of_directed [Nonempty ι] {S : ι → Subalgebra R A} (dir : Directed (· ≤ ·) S) :
-    ↑(supᵢ S) = ⋃ i, (S i : Set A) :=
+theorem coe_iSup_of_directed [Nonempty ι] {S : ι → Subalgebra R A} (dir : Directed (· ≤ ·) S) :
+    ↑(iSup S) = ⋃ i, (S i : Set A) :=
   -- Porting note: moved up the `let i` to use it in `zero_mem'` and `one_mem'`
   let i := @Nonempty.some ι inferInstance
   let K : Subalgebra R A :=
     { carrier := ⋃ i, S i
       -- Porting note: auto_params failing, need to provide these explicitly
-      zero_mem' := by simp only [Set.mem_unionᵢ, SetLike.mem_coe]; exact ⟨i, zero_mem _⟩
-      one_mem' := by simp only [Set.mem_unionᵢ, SetLike.mem_coe]; exact ⟨i, one_mem _⟩
+      zero_mem' := by simp only [Set.mem_iUnion, SetLike.mem_coe]; exact ⟨i, zero_mem _⟩
+      one_mem' := by simp only [Set.mem_iUnion, SetLike.mem_coe]; exact ⟨i, one_mem _⟩
       mul_mem' := fun hx hy =>
-        let ⟨i, hi⟩ := Set.mem_unionᵢ.1 hx
-        let ⟨j, hj⟩ := Set.mem_unionᵢ.1 hy
+        let ⟨i, hi⟩ := Set.mem_iUnion.1 hx
+        let ⟨j, hj⟩ := Set.mem_iUnion.1 hy
         let ⟨k, hik, hjk⟩ := dir i j
-        Set.mem_unionᵢ.2 ⟨k, Subalgebra.mul_mem (S k) (hik hi) (hjk hj)⟩
+        Set.mem_iUnion.2 ⟨k, Subalgebra.mul_mem (S k) (hik hi) (hjk hj)⟩
       add_mem' := fun hx hy =>
-        let ⟨i, hi⟩ := Set.mem_unionᵢ.1 hx
-        let ⟨j, hj⟩ := Set.mem_unionᵢ.1 hy
+        let ⟨i, hi⟩ := Set.mem_iUnion.1 hx
+        let ⟨j, hj⟩ := Set.mem_iUnion.1 hy
         let ⟨k, hik, hjk⟩ := dir i j
-        Set.mem_unionᵢ.2 ⟨k, Subalgebra.add_mem (S k) (hik hi) (hjk hj)⟩
+        Set.mem_iUnion.2 ⟨k, Subalgebra.add_mem (S k) (hik hi) (hjk hj)⟩
       algebraMap_mem' := fun _ ↦
-        Set.mem_unionᵢ.2 ⟨i, Subalgebra.algebraMap_mem _ _⟩ }
-  have : supᵢ S = K :=
-    le_antisymm (supᵢ_le fun i => Set.subset_unionᵢ (fun i => (↑(S i) : Set A)) i)
-      (SetLike.coe_subset_coe.1 (Set.unionᵢ_subset fun i => SetLike.coe_subset_coe.2 (le_supᵢ _ _)))
+        Set.mem_iUnion.2 ⟨i, Subalgebra.algebraMap_mem _ _⟩ }
+  have : iSup S = K :=
+    le_antisymm (iSup_le fun i => Set.subset_iUnion (fun i => (↑(S i) : Set A)) i)
+      (SetLike.coe_subset_coe.1 (Set.iUnion_subset fun i => SetLike.coe_subset_coe.2 (le_iSup _ _)))
   this.symm ▸ rfl
-#align subalgebra.coe_supr_of_directed Subalgebra.coe_supᵢ_of_directed
+#align subalgebra.coe_supr_of_directed Subalgebra.coe_iSup_of_directed
 
--- Porting note: TODO: turn `hT` into an assumption `T ≤ supᵢ K`. That's what `Set.unionᵢLift` needs
+-- Porting note: TODO: turn `hT` into an assumption `T ≤ iSup K`. That's what `Set.iUnionLift` needs
 -- Porting note: the proofs of `map_{zero,one,add,mul}` got a bit uglier, probably unification trbls
 /-- Define an algebra homomorphism on a directed supremum of subalgebras by defining
 it on each subalgebra, and proving that it agrees on the intersection of subalgebras. -/
-noncomputable def supᵢLift [Nonempty ι] (K : ι → Subalgebra R A) (dir : Directed (· ≤ ·) K)
+noncomputable def iSupLift [Nonempty ι] (K : ι → Subalgebra R A) (dir : Directed (· ≤ ·) K)
     (f : ∀ i, K i →ₐ[R] B) (hf : ∀ (i j : ι) (h : K i ≤ K j), f i = (f j).comp (inclusion h))
-    (T : Subalgebra R A) (hT : T = supᵢ K) : ↥T →ₐ[R] B :=
-  { toFun := Set.unionᵢLift (fun i => ↑(K i)) (fun i x => f i x)
+    (T : Subalgebra R A) (hT : T = iSup K) : ↥T →ₐ[R] B :=
+  { toFun := Set.iUnionLift (fun i => ↑(K i)) (fun i x => f i x)
         (fun i j x hxi hxj => by
           let ⟨k, hik, hjk⟩ := dir i j
           dsimp
           rw [hf i k hik, hf j k hjk]
           rfl)
-        T (by rw [hT, coe_supᵢ_of_directed dir])
-    map_one' := by apply Set.unionᵢLift_const _ (fun _ => 1) <;> simp
-    map_zero' := by dsimp; apply Set.unionᵢLift_const _ (fun _ => 0) <;> simp
+        T (by rw [hT, coe_iSup_of_directed dir])
+    map_one' := by apply Set.iUnionLift_const _ (fun _ => 1) <;> simp
+    map_zero' := by dsimp; apply Set.iUnionLift_const _ (fun _ => 0) <;> simp
     map_mul' := by
       subst hT; dsimp
-      apply Set.unionᵢLift_binary (coe_supᵢ_of_directed dir) dir _ (fun _ => (· * ·))
-      on_goal 3 => rw [coe_supᵢ_of_directed dir]
+      apply Set.iUnionLift_binary (coe_iSup_of_directed dir) dir _ (fun _ => (· * ·))
+      on_goal 3 => rw [coe_iSup_of_directed dir]
       all_goals simp
     map_add' := by
       subst hT; dsimp
-      apply Set.unionᵢLift_binary (coe_supᵢ_of_directed dir) dir _ (fun _ => (· + ·))
-      on_goal 3 => rw [coe_supᵢ_of_directed dir]
+      apply Set.iUnionLift_binary (coe_iSup_of_directed dir) dir _ (fun _ => (· + ·))
+      on_goal 3 => rw [coe_iSup_of_directed dir]
       all_goals simp
     commutes' := fun r => by
       dsimp
-      apply Set.unionᵢLift_const _ (fun _ => algebraMap R _ r) <;> simp }
-#align subalgebra.supr_lift Subalgebra.supᵢLift
+      apply Set.iUnionLift_const _ (fun _ => algebraMap R _ r) <;> simp }
+#align subalgebra.supr_lift Subalgebra.iSupLift
 
 variable [Nonempty ι] {K : ι → Subalgebra R A} {dir : Directed (· ≤ ·) K} {f : ∀ i, K i →ₐ[R] B}
   {hf : ∀ (i j : ι) (h : K i ≤ K j), f i = (f j).comp (inclusion h)} {T : Subalgebra R A}
-  {hT : T = supᵢ K}
+  {hT : T = iSup K}
 
 @[simp]
-theorem supᵢLift_inclusion {i : ι} (x : K i) (h : K i ≤ T) :
-    supᵢLift K dir f hf T hT (inclusion h x) = f i x := by
-  dsimp [supᵢLift, inclusion]
-  rw [Set.unionᵢLift_inclusion]
-#align subalgebra.supr_lift_inclusion Subalgebra.supᵢLift_inclusion
+theorem iSupLift_inclusion {i : ι} (x : K i) (h : K i ≤ T) :
+    iSupLift K dir f hf T hT (inclusion h x) = f i x := by
+  dsimp [iSupLift, inclusion]
+  rw [Set.iUnionLift_inclusion]
+#align subalgebra.supr_lift_inclusion Subalgebra.iSupLift_inclusion
 
 @[simp]
-theorem supᵢLift_comp_inclusion {i : ι} (h : K i ≤ T) :
-    (supᵢLift K dir f hf T hT).comp (inclusion h) = f i := by ext; simp
-#align subalgebra.supr_lift_comp_inclusion Subalgebra.supᵢLift_comp_inclusion
+theorem iSupLift_comp_inclusion {i : ι} (h : K i ≤ T) :
+    (iSupLift K dir f hf T hT).comp (inclusion h) = f i := by ext; simp
+#align subalgebra.supr_lift_comp_inclusion Subalgebra.iSupLift_comp_inclusion
 
 @[simp]
-theorem supᵢLift_mk {i : ι} (x : K i) (hx : (x : A) ∈ T) :
-    supᵢLift K dir f hf T hT ⟨x, hx⟩ = f i x := by
-  dsimp [supᵢLift, inclusion]
-  rw [Set.unionᵢLift_mk]
-#align subalgebra.supr_lift_mk Subalgebra.supᵢLift_mk
+theorem iSupLift_mk {i : ι} (x : K i) (hx : (x : A) ∈ T) :
+    iSupLift K dir f hf T hT ⟨x, hx⟩ = f i x := by
+  dsimp [iSupLift, inclusion]
+  rw [Set.iUnionLift_mk]
+#align subalgebra.supr_lift_mk Subalgebra.iSupLift_mk
 
-theorem supᵢLift_of_mem {i : ι} (x : T) (hx : (x : A) ∈ K i) :
-    supᵢLift K dir f hf T hT x = f i ⟨x, hx⟩ := by
-  dsimp [supᵢLift, inclusion]
-  rw [Set.unionᵢLift_of_mem]
-#align subalgebra.supr_lift_of_mem Subalgebra.supᵢLift_of_mem
+theorem iSupLift_of_mem {i : ι} (x : T) (hx : (x : A) ∈ K i) :
+    iSupLift K dir f hf T hT x = f i ⟨x, hx⟩ := by
+  dsimp [iSupLift, inclusion]
+  rw [Set.iUnionLift_of_mem]
+#align subalgebra.supr_lift_of_mem Subalgebra.iSupLift_of_mem
 
 end SuprLift

chore: forward-port leanprover-community/mathlib#18902 (#3770)

84ce374f

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau, Yury Kudryashov
 
 ! This file was ported from Lean 3 source module algebra.algebra.subalgebra.basic
-! leanprover-community/mathlib commit c4658a649d216f57e99621708b09dcb3dcccbd23
+! leanprover-community/mathlib commit 8130e5155d637db35907c272de9aec9dc851c03a
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -123,6 +123,8 @@ theorem smul_mem {x : A} (hx : x ∈ S) (r : R) : r • x ∈ S :=
   (Algebra.smul_def r x).symm ▸ mul_mem (S.algebraMap_mem r) hx
 #align subalgebra.smul_mem Subalgebra.smul_mem
 
+instance : SMulMemClass (Subalgebra R A) R A where smul_mem r _x hx := smul_mem _ hx r
+
 protected theorem one_mem : (1 : A) ∈ S :=
   one_mem S
 #align subalgebra.one_mem Subalgebra.one_mem

chore: bye-bye, solo bys! (#3825)

This PR puts, with one exception, every single remaining by that lies all by itself on its own line to the previous line, thus matching the current behaviour of start-port.sh. The exception is when the by begins the second or later argument to a tuple or anonymous constructor; see https://github.com/leanprover-community/mathlib4/pull/3825#discussion_r1186702599.

Essentially this is s/\n *by$/ by/g, but with manual editing to satisfy the linter's max-100-char-line requirement. The Python style linter is also modified to catch these "isolated bys".

14167e48

Diff

@@ -892,8 +892,7 @@ theorem infᵢ_toSubmodule {ι : Sort _} (S : ι → Subalgebra R A) :
 instance : Inhabited (Subalgebra R A) := ⟨⊥⟩
 
 theorem mem_bot {x : A} : x ∈ (⊥ : Subalgebra R A) ↔ x ∈ Set.range (algebraMap R A) :=
-  suffices (ofId R A).range = (⊥ : Subalgebra R A)
-    by
+  suffices (ofId R A).range = (⊥ : Subalgebra R A) by
     rw [← this, ← SetLike.mem_coe, AlgHom.coe_range]
     rfl
   le_bot_iff.mp fun x hx => Subalgebra.range_le _ ((ofId R A).coe_range ▸ hx)

chore: use etaExperiment rather than hacking with instances (#3668)

This is to fix timeouts in https://github.com/leanprover-community/mathlib4/pull/3552.

See discussion at https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/!4.233552.20.28LinearAlgebra.2EMatrix.2EToLin.29.

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

0f225a7f

Diff

@@ -1455,6 +1455,7 @@ theorem mem_of_finset_sum_eq_one_of_pow_smul_mem {S : Type _} [CommRing S] [Alge
   exact ⟨⟨_, hn i⟩, rfl⟩
 #align subalgebra.mem_of_finset_sum_eq_one_of_pow_smul_mem Subalgebra.mem_of_finset_sum_eq_one_of_pow_smul_mem
 
+set_option synthInstance.etaExperiment true in
 theorem mem_of_span_eq_top_of_smul_pow_mem {S : Type _} [CommRing S] [Algebra R S]
     (S' : Subalgebra R S) (s : Set S) (l : s →₀ S) (hs : Finsupp.total s S S (↑) l = 1)
     (hs' : s ⊆ S') (hl : ∀ i, l i ∈ S') (x : S) (H : ∀ r : s, ∃ n : ℕ, (r : S) ^ n • x ∈ S') :

chore: tidy various files (#2999)

f02ff00e

Diff

@@ -18,7 +18,7 @@ import Mathlib.RingTheory.Ideal.Operations
 
 In this file we define `Subalgebra`s and the usual operations on them (`map`, `comap`).
 
-More lemmas about `adjoin` can be found in `ring_theory.adjoin`.
+More lemmas about `adjoin` can be found in `RingTheory.Adjoin`.
 -/
 
 
@@ -1080,8 +1080,7 @@ theorem coe_inclusion {S T : Subalgebra R A} (h : S ≤ T) (s : S) : (inclusion
 This is the `Subalgebra` version of `LinearEquiv.ofEq` and `Equiv.Set.ofEq`. -/
 @[simps apply]
 def equivOfEq (S T : Subalgebra R A) (h : S = T) : S ≃ₐ[R] T :=
-  { LinearEquiv.ofEq _ _
-      (congr_arg toSubmodule h) with
+  { LinearEquiv.ofEq _ _ (congr_arg toSubmodule h) with
     toFun := fun x => ⟨x, h ▸ x.2⟩
     invFun := fun x => ⟨x, h.symm ▸ x.2⟩
     map_mul' := fun _ _ => rfl
@@ -1106,7 +1105,6 @@ section Prod
 
 variable (S₁ : Subalgebra R B)
 
-/- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /-- The product of two subalgebras is a subalgebra. -/
 def prod : Subalgebra R (A × B) :=
   { S.toSubsemiring.prod S₁.toSubsemiring with
@@ -1114,7 +1112,6 @@ def prod : Subalgebra R (A × B) :=
     algebraMap_mem' := fun _ => ⟨algebraMap_mem _ _, algebraMap_mem _ _⟩ }
 #align subalgebra.prod Subalgebra.prod
 
-/- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 @[simp]
 theorem coe_prod : (prod S S₁ : Set (A × B)) = S ×ˢ S₁ :=
   rfl
@@ -1242,7 +1239,7 @@ end SuprLift
 /-! ## Actions by `Subalgebra`s
 
 These are just copies of the definitions about `Subsemiring` starting from
-`subring.mul_action`.
+`Subring.mulAction`.
 -/
 
 
@@ -1257,15 +1254,15 @@ instance [SMul A α] (S : Subalgebra R A) : SMul S α :=
 theorem smul_def [SMul A α] {S : Subalgebra R A} (g : S) (m : α) : g • m = (g : A) • m := rfl
 #align subalgebra.smul_def Subalgebra.smul_def
 
-instance sMulCommClass_left [SMul A β] [SMul α β] [SMulCommClass A α β] (S : Subalgebra R A) :
+instance smulCommClass_left [SMul A β] [SMul α β] [SMulCommClass A α β] (S : Subalgebra R A) :
     SMulCommClass S α β :=
   S.toSubsemiring.smulCommClass_left
-#align subalgebra.smul_comm_class_left Subalgebra.sMulCommClass_left
+#align subalgebra.smul_comm_class_left Subalgebra.smulCommClass_left
 
-instance sMulCommClass_right [SMul α β] [SMul A β] [SMulCommClass α A β] (S : Subalgebra R A) :
+instance smulCommClass_right [SMul α β] [SMul A β] [SMulCommClass α A β] (S : Subalgebra R A) :
     SMulCommClass α S β :=
   S.toSubsemiring.smulCommClass_right
-#align subalgebra.smul_comm_class_right Subalgebra.sMulCommClass_right
+#align subalgebra.smul_comm_class_right Subalgebra.smulCommClass_right
 
 /-- Note that this provides `IsScalarTower S R R` which is needed by `smul_mul_assoc`. -/
 instance isScalarTower_left [SMul α β] [SMul A α] [SMul A β] [IsScalarTower A α β]