field_theory.intermediate_field ⟷ Mathlib.FieldTheory.IntermediateField

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

@@ -298,10 +298,10 @@ protected theorem zsmul_mem {x : L} (hx : x ∈ S) (n : ℤ) : n • x ∈ S :=
 #align intermediate_field.zsmul_mem IntermediateField.zsmul_mem
 -/
 
-#print IntermediateField.coe_int_mem /-
-protected theorem coe_int_mem (n : ℤ) : (n : L) ∈ S :=
-  coe_int_mem S n
-#align intermediate_field.coe_int_mem IntermediateField.coe_int_mem
+#print IntermediateField.intCast_mem /-
+protected theorem intCast_mem (n : ℤ) : (n : L) ∈ S :=
+  intCast_mem S n
+#align intermediate_field.coe_int_mem IntermediateField.intCast_mem
 -/
 
 #print IntermediateField.coe_add /-
@@ -348,9 +348,9 @@ protected theorem coe_pow (x : S) (n : ℕ) : (↑(x ^ n) : L) = ↑x ^ n :=
 
 end InheritedLemmas
 
-#print IntermediateField.coe_nat_mem /-
-theorem coe_nat_mem (n : ℕ) : (n : L) ∈ S := by simpa using coe_int_mem S n
-#align intermediate_field.coe_nat_mem IntermediateField.coe_nat_mem
+#print IntermediateField.natCast_mem /-
+theorem natCast_mem (n : ℕ) : (n : L) ∈ S := by simpa using intCast_mem S n
+#align intermediate_field.coe_nat_mem IntermediateField.natCast_mem
 -/
 
 end IntermediateField

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

@@ -388,7 +388,7 @@ def Subalgebra.toIntermediateField' (S : Subalgebra K L) (hS : IsField S) : Inte
       exact S.zero_mem
     letI hS' := hS.to_field
     obtain ⟨y, hy⟩ := hS.mul_inv_cancel (show (⟨x, hx⟩ : S) ≠ 0 from Subtype.ne_of_val_ne hx0)
-    rw [Subtype.ext_iff, S.coe_mul, S.coe_one, Subtype.coe_mk, mul_eq_one_iff_inv_eq₀ hx0] at hy 
+    rw [Subtype.ext_iff, S.coe_mul, S.coe_one, Subtype.coe_mk, mul_eq_one_iff_inv_eq₀ hx0] at hy
     exact hy.symm ▸ y.2
 #align subalgebra.to_intermediate_field' Subalgebra.toIntermediateField'
 -/

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

@@ -474,12 +474,10 @@ theorem coe_smul {R} [Semiring R] [SMul R K] [Module R L] [IsScalarTower R K L]
 #align intermediate_field.coe_smul IntermediateField.coe_smul
 -/
 
-#print IntermediateField.algebra' /-
 instance algebra' {K'} [CommSemiring K'] [SMul K' K] [Algebra K' L] [IsScalarTower K' K L] :
     Algebra K' S :=
   S.toSubalgebra.algebra'
 #align intermediate_field.algebra' IntermediateField.algebra'
--/
 
 #print IntermediateField.algebra /-
 instance algebra : Algebra K S :=
@@ -487,11 +485,9 @@ instance algebra : Algebra K S :=
 #align intermediate_field.algebra IntermediateField.algebra
 -/
 
-#print IntermediateField.toAlgebra /-
 instance toAlgebra {R : Type _} [Semiring R] [Algebra L R] : Algebra S R :=
   S.toSubalgebra.toAlgebra
 #align intermediate_field.to_algebra IntermediateField.toAlgebra
--/
 
 #print IntermediateField.isScalarTower_bot /-
 instance isScalarTower_bot {R : Type _} [Semiring R] [Algebra L R] : IsScalarTower S L R :=

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

@@ -428,6 +428,9 @@ instance toField : Field S :=
 @[simp, norm_cast]
 theorem coe_sum {ι : Type _} [Fintype ι] (f : ι → S) : (↑(∑ i, f i) : L) = ∑ i, (f i : L) := by
   classical
+  induction' Finset.univ using Finset.induction_on with i s hi H
+  · simp
+  · rw [Finset.sum_insert hi, AddMemClass.coe_add, H, Finset.sum_insert hi]
 #align intermediate_field.coe_sum IntermediateField.coe_sum
 -/
 
@@ -435,6 +438,9 @@ theorem coe_sum {ι : Type _} [Fintype ι] (f : ι → S) : (↑(∑ i, f i) : L
 @[simp, norm_cast]
 theorem coe_prod {ι : Type _} [Fintype ι] (f : ι → S) : (↑(∏ i, f i) : L) = ∏ i, (f i : L) := by
   classical
+  induction' Finset.univ using Finset.induction_on with i s hi H
+  · simp
+  · rw [Finset.prod_insert hi, MulMemClass.coe_mul, H, Finset.prod_insert hi]
 #align intermediate_field.coe_prod IntermediateField.coe_prod
 -/
 

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

@@ -428,9 +428,6 @@ instance toField : Field S :=
 @[simp, norm_cast]
 theorem coe_sum {ι : Type _} [Fintype ι] (f : ι → S) : (↑(∑ i, f i) : L) = ∑ i, (f i : L) := by
   classical
-  induction' Finset.univ using Finset.induction_on with i s hi H
-  · simp
-  · rw [Finset.sum_insert hi, AddMemClass.coe_add, H, Finset.sum_insert hi]
 #align intermediate_field.coe_sum IntermediateField.coe_sum
 -/
 
@@ -438,9 +435,6 @@ theorem coe_sum {ι : Type _} [Fintype ι] (f : ι → S) : (↑(∑ i, f i) : L
 @[simp, norm_cast]
 theorem coe_prod {ι : Type _} [Fintype ι] (f : ι → S) : (↑(∏ i, f i) : L) = ∏ i, (f i : L) := by
   classical
-  induction' Finset.univ using Finset.induction_on with i s hi H
-  · simp
-  · rw [Finset.prod_insert hi, MulMemClass.coe_mul, H, Finset.prod_insert hi]
 #align intermediate_field.coe_prod IntermediateField.coe_prod
 -/
 

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

@@ -3,9 +3,9 @@ Copyright (c) 2020 Anne Baanen. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Anne Baanen
 -/
-import Mathbin.FieldTheory.Minpoly.Field
-import Mathbin.FieldTheory.Subfield
-import Mathbin.FieldTheory.Tower
+import FieldTheory.Minpoly.Field
+import FieldTheory.Subfield
+import FieldTheory.Tower
 
 #align_import field_theory.intermediate_field from "leanprover-community/mathlib"@"61db041ab8e4aaf8cb5c7dc10a7d4ff261997536"
 

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

@@ -78,7 +78,7 @@ instance : SubfieldClass (IntermediateField K L) L
   add_mem s _ _ := s.add_mem'
   zero_mem s := s.zero_mem'
   neg_mem := neg_mem'
-  mul_mem s _ _ := s.mul_mem'
+  hMul_mem s _ _ := s.hMul_mem'
   one_mem s := s.one_mem'
   inv_mem := inv_mem'
 
@@ -201,7 +201,7 @@ protected theorem zero_mem : (0 : L) ∈ S :=
 #print IntermediateField.mul_mem /-
 /-- An intermediate field is closed under multiplication. -/
 protected theorem mul_mem {x y : L} : x ∈ S → y ∈ S → x * y ∈ S :=
-  mul_mem
+  hMul_mem
 #align intermediate_field.mul_mem IntermediateField.mul_mem
 -/
 

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

@@ -2,16 +2,13 @@
 Copyright (c) 2020 Anne Baanen. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Anne Baanen
-
-! This file was ported from Lean 3 source module field_theory.intermediate_field
-! leanprover-community/mathlib commit 61db041ab8e4aaf8cb5c7dc10a7d4ff261997536
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.FieldTheory.Minpoly.Field
 import Mathbin.FieldTheory.Subfield
 import Mathbin.FieldTheory.Tower
 
+#align_import field_theory.intermediate_field from "leanprover-community/mathlib"@"61db041ab8e4aaf8cb5c7dc10a7d4ff261997536"
+
 /-!
 # Intermediate fields
 

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

@@ -85,26 +85,34 @@ instance : SubfieldClass (IntermediateField K L) L
   one_mem s := s.one_mem'
   inv_mem := inv_mem'
 
+#print IntermediateField.mem_carrier /-
 @[simp]
 theorem mem_carrier {s : IntermediateField K L} {x : L} : x ∈ s.carrier ↔ x ∈ s :=
   Iff.rfl
 #align intermediate_field.mem_carrier IntermediateField.mem_carrier
+-/
 
+#print IntermediateField.ext /-
 /-- Two intermediate fields are equal if they have the same elements. -/
 @[ext]
 theorem ext {S T : IntermediateField K L} (h : ∀ x, x ∈ S ↔ x ∈ T) : S = T :=
   SetLike.ext h
 #align intermediate_field.ext IntermediateField.ext
+-/
 
+#print IntermediateField.coe_toSubalgebra /-
 @[simp]
 theorem coe_toSubalgebra : (S.toSubalgebra : Set L) = S :=
   rfl
 #align intermediate_field.coe_to_subalgebra IntermediateField.coe_toSubalgebra
+-/
 
+#print IntermediateField.coe_toSubfield /-
 @[simp]
 theorem coe_toSubfield : (S.toSubfield : Set L) = S :=
   rfl
 #align intermediate_field.coe_to_subfield IntermediateField.coe_toSubfield
+-/
 
 @[simp]
 theorem mem_mk (s : Set L) (hK : ∀ x, algebraMap K L x ∈ s) (ho hm hz ha hn hi) (x : L) :
@@ -112,16 +120,21 @@ theorem mem_mk (s : Set L) (hK : ∀ x, algebraMap K L x ∈ s) (ho hm hz ha hn
   Iff.rfl
 #align intermediate_field.mem_mk IntermediateField.mem_mkₓ
 
+#print IntermediateField.mem_toSubalgebra /-
 @[simp]
 theorem mem_toSubalgebra (s : IntermediateField K L) (x : L) : x ∈ s.toSubalgebra ↔ x ∈ s :=
   Iff.rfl
 #align intermediate_field.mem_to_subalgebra IntermediateField.mem_toSubalgebra
+-/
 
+#print IntermediateField.mem_toSubfield /-
 @[simp]
 theorem mem_toSubfield (s : IntermediateField K L) (x : L) : x ∈ s.toSubfield ↔ x ∈ s :=
   Iff.rfl
 #align intermediate_field.mem_to_subfield IntermediateField.mem_toSubfield
+-/
 
+#print IntermediateField.copy /-
 /-- Copy of an intermediate field with a new `carrier` equal to the old one. Useful to fix
 definitional equalities. -/
 protected def copy (S : IntermediateField K L) (s : Set L) (hs : s = ↑S) : IntermediateField K L
@@ -134,16 +147,21 @@ protected def copy (S : IntermediateField K L) (s : Set L) (hs : s = ↑S) : Int
     have hs' : (S.toSubalgebra.copy s hs).carrier = S.toSubalgebra.carrier := hs
     hs'.symm ▸ S.inv_mem'
 #align intermediate_field.copy IntermediateField.copy
+-/
 
+#print IntermediateField.coe_copy /-
 @[simp]
 theorem coe_copy (S : IntermediateField K L) (s : Set L) (hs : s = ↑S) :
     (S.copy s hs : Set L) = s :=
   rfl
 #align intermediate_field.coe_copy IntermediateField.coe_copy
+-/
 
+#print IntermediateField.copy_eq /-
 theorem copy_eq (S : IntermediateField K L) (s : Set L) (hs : s = ↑S) : S.copy s hs = S :=
   SetLike.coe_injective hs
 #align intermediate_field.copy_eq IntermediateField.copy_eq
+-/
 
 section InheritedLemmas
 
@@ -155,137 +173,192 @@ subobject class.
 -/
 
 
+#print IntermediateField.algebraMap_mem /-
 /-- An intermediate field contains the image of the smaller field. -/
 theorem algebraMap_mem (x : K) : algebraMap K L x ∈ S :=
   S.algebraMap_mem' x
 #align intermediate_field.algebra_map_mem IntermediateField.algebraMap_mem
+-/
 
+#print IntermediateField.smul_mem /-
 /-- An intermediate field is closed under scalar multiplication. -/
 theorem smul_mem {y : L} : y ∈ S → ∀ {x : K}, x • y ∈ S :=
   S.toSubalgebra.smul_mem
 #align intermediate_field.smul_mem IntermediateField.smul_mem
+-/
 
+#print IntermediateField.one_mem /-
 /-- An intermediate field contains the ring's 1. -/
 protected theorem one_mem : (1 : L) ∈ S :=
   one_mem S
 #align intermediate_field.one_mem IntermediateField.one_mem
+-/
 
+#print IntermediateField.zero_mem /-
 /-- An intermediate field contains the ring's 0. -/
 protected theorem zero_mem : (0 : L) ∈ S :=
   zero_mem S
 #align intermediate_field.zero_mem IntermediateField.zero_mem
+-/
 
+#print IntermediateField.mul_mem /-
 /-- An intermediate field is closed under multiplication. -/
 protected theorem mul_mem {x y : L} : x ∈ S → y ∈ S → x * y ∈ S :=
   mul_mem
 #align intermediate_field.mul_mem IntermediateField.mul_mem
+-/
 
+#print IntermediateField.add_mem /-
 /-- An intermediate field is closed under addition. -/
 protected theorem add_mem {x y : L} : x ∈ S → y ∈ S → x + y ∈ S :=
   add_mem
 #align intermediate_field.add_mem IntermediateField.add_mem
+-/
 
+#print IntermediateField.sub_mem /-
 /-- An intermediate field is closed under subtraction -/
 protected theorem sub_mem {x y : L} : x ∈ S → y ∈ S → x - y ∈ S :=
   sub_mem
 #align intermediate_field.sub_mem IntermediateField.sub_mem
+-/
 
+#print IntermediateField.neg_mem /-
 /-- An intermediate field is closed under negation. -/
 protected theorem neg_mem {x : L} : x ∈ S → -x ∈ S :=
   neg_mem
 #align intermediate_field.neg_mem IntermediateField.neg_mem
+-/
 
+#print IntermediateField.inv_mem /-
 /-- An intermediate field is closed under inverses. -/
 protected theorem inv_mem {x : L} : x ∈ S → x⁻¹ ∈ S :=
   inv_mem
 #align intermediate_field.inv_mem IntermediateField.inv_mem
+-/
 
+#print IntermediateField.div_mem /-
 /-- An intermediate field is closed under division. -/
 protected theorem div_mem {x y : L} : x ∈ S → y ∈ S → x / y ∈ S :=
   div_mem
 #align intermediate_field.div_mem IntermediateField.div_mem
+-/
 
+#print IntermediateField.list_prod_mem /-
 /-- Product of a list of elements in an intermediate_field is in the intermediate_field. -/
 protected theorem list_prod_mem {l : List L} : (∀ x ∈ l, x ∈ S) → l.Prod ∈ S :=
   list_prod_mem
 #align intermediate_field.list_prod_mem IntermediateField.list_prod_mem
+-/
 
+#print IntermediateField.list_sum_mem /-
 /-- Sum of a list of elements in an intermediate field is in the intermediate_field. -/
 protected theorem list_sum_mem {l : List L} : (∀ x ∈ l, x ∈ S) → l.Sum ∈ S :=
   list_sum_mem
 #align intermediate_field.list_sum_mem IntermediateField.list_sum_mem
+-/
 
+#print IntermediateField.multiset_prod_mem /-
 /-- Product of a multiset of elements in an intermediate field is in the intermediate_field. -/
 protected theorem multiset_prod_mem (m : Multiset L) : (∀ a ∈ m, a ∈ S) → m.Prod ∈ S :=
   multiset_prod_mem m
 #align intermediate_field.multiset_prod_mem IntermediateField.multiset_prod_mem
+-/
 
+#print IntermediateField.multiset_sum_mem /-
 /-- Sum of a multiset of elements in a `intermediate_field` is in the `intermediate_field`. -/
 protected theorem multiset_sum_mem (m : Multiset L) : (∀ a ∈ m, a ∈ S) → m.Sum ∈ S :=
   multiset_sum_mem m
 #align intermediate_field.multiset_sum_mem IntermediateField.multiset_sum_mem
+-/
 
+#print IntermediateField.prod_mem /-
 /-- Product of elements of an intermediate field indexed by a `finset` is in the intermediate_field.
 -/
 protected theorem prod_mem {ι : Type _} {t : Finset ι} {f : ι → L} (h : ∀ c ∈ t, f c ∈ S) :
     ∏ i in t, f i ∈ S :=
   prod_mem h
 #align intermediate_field.prod_mem IntermediateField.prod_mem
+-/
 
+#print IntermediateField.sum_mem /-
 /-- Sum of elements in a `intermediate_field` indexed by a `finset` is in the `intermediate_field`.
 -/
 protected theorem sum_mem {ι : Type _} {t : Finset ι} {f : ι → L} (h : ∀ c ∈ t, f c ∈ S) :
     ∑ i in t, f i ∈ S :=
   sum_mem h
 #align intermediate_field.sum_mem IntermediateField.sum_mem
+-/
 
+#print IntermediateField.pow_mem /-
 protected theorem pow_mem {x : L} (hx : x ∈ S) (n : ℤ) : x ^ n ∈ S :=
   zpow_mem hx n
 #align intermediate_field.pow_mem IntermediateField.pow_mem
+-/
 
+#print IntermediateField.zsmul_mem /-
 protected theorem zsmul_mem {x : L} (hx : x ∈ S) (n : ℤ) : n • x ∈ S :=
   zsmul_mem hx n
 #align intermediate_field.zsmul_mem IntermediateField.zsmul_mem
+-/
 
+#print IntermediateField.coe_int_mem /-
 protected theorem coe_int_mem (n : ℤ) : (n : L) ∈ S :=
   coe_int_mem S n
 #align intermediate_field.coe_int_mem IntermediateField.coe_int_mem
+-/
 
+#print IntermediateField.coe_add /-
 protected theorem coe_add (x y : S) : (↑(x + y) : L) = ↑x + ↑y :=
   rfl
 #align intermediate_field.coe_add IntermediateField.coe_add
+-/
 
+#print IntermediateField.coe_neg /-
 protected theorem coe_neg (x : S) : (↑(-x) : L) = -↑x :=
   rfl
 #align intermediate_field.coe_neg IntermediateField.coe_neg
+-/
 
+#print IntermediateField.coe_mul /-
 protected theorem coe_mul (x y : S) : (↑(x * y) : L) = ↑x * ↑y :=
   rfl
 #align intermediate_field.coe_mul IntermediateField.coe_mul
+-/
 
+#print IntermediateField.coe_inv /-
 protected theorem coe_inv (x : S) : (↑x⁻¹ : L) = (↑x)⁻¹ :=
   rfl
 #align intermediate_field.coe_inv IntermediateField.coe_inv
+-/
 
+#print IntermediateField.coe_zero /-
 protected theorem coe_zero : ((0 : S) : L) = 0 :=
   rfl
 #align intermediate_field.coe_zero IntermediateField.coe_zero
+-/
 
+#print IntermediateField.coe_one /-
 protected theorem coe_one : ((1 : S) : L) = 1 :=
   rfl
 #align intermediate_field.coe_one IntermediateField.coe_one
+-/
 
+#print IntermediateField.coe_pow /-
 protected theorem coe_pow (x : S) (n : ℕ) : (↑(x ^ n) : L) = ↑x ^ n :=
   SubmonoidClass.coe_pow x n
 #align intermediate_field.coe_pow IntermediateField.coe_pow
+-/
 
 end InheritedLemmas
 
+#print IntermediateField.coe_nat_mem /-
 theorem coe_nat_mem (n : ℕ) : (n : L) ∈ S := by simpa using coe_int_mem S n
 #align intermediate_field.coe_nat_mem IntermediateField.coe_nat_mem
+-/
 
 end IntermediateField
 
+#print Subalgebra.toIntermediateField /-
 /-- Turn a subalgebra closed under inverses into an intermediate field -/
 def Subalgebra.toIntermediateField (S : Subalgebra K L) (inv_mem : ∀ x ∈ S, x⁻¹ ∈ S) :
     IntermediateField K L :=
@@ -293,17 +366,23 @@ def Subalgebra.toIntermediateField (S : Subalgebra K L) (inv_mem : ∀ x ∈ S,
     neg_mem' := fun x => S.neg_mem
     inv_mem' := inv_mem }
 #align subalgebra.to_intermediate_field Subalgebra.toIntermediateField
+-/
 
+#print toSubalgebra_toIntermediateField /-
 @[simp]
 theorem toSubalgebra_toIntermediateField (S : Subalgebra K L) (inv_mem : ∀ x ∈ S, x⁻¹ ∈ S) :
     (S.toIntermediateField inv_mem).toSubalgebra = S := by ext; rfl
 #align to_subalgebra_to_intermediate_field toSubalgebra_toIntermediateField
+-/
 
+#print toIntermediateField_toSubalgebra /-
 @[simp]
 theorem toIntermediateField_toSubalgebra (S : IntermediateField K L) :
     (S.toSubalgebra.toIntermediateField fun x => S.inv_mem) = S := by ext; rfl
 #align to_intermediate_field_to_subalgebra toIntermediateField_toSubalgebra
+-/
 
+#print Subalgebra.toIntermediateField' /-
 /-- Turn a subalgebra satisfying `is_field` into an intermediate_field -/
 def Subalgebra.toIntermediateField' (S : Subalgebra K L) (hS : IsField S) : IntermediateField K L :=
   S.toIntermediateField fun x hx => by
@@ -315,30 +394,40 @@ def Subalgebra.toIntermediateField' (S : Subalgebra K L) (hS : IsField S) : Inte
     rw [Subtype.ext_iff, S.coe_mul, S.coe_one, Subtype.coe_mk, mul_eq_one_iff_inv_eq₀ hx0] at hy 
     exact hy.symm ▸ y.2
 #align subalgebra.to_intermediate_field' Subalgebra.toIntermediateField'
+-/
 
+#print toSubalgebra_toIntermediateField' /-
 @[simp]
 theorem toSubalgebra_toIntermediateField' (S : Subalgebra K L) (hS : IsField S) :
     (S.toIntermediateField' hS).toSubalgebra = S := by ext; rfl
 #align to_subalgebra_to_intermediate_field' toSubalgebra_toIntermediateField'
+-/
 
+#print toIntermediateField'_toSubalgebra /-
 @[simp]
 theorem toIntermediateField'_toSubalgebra (S : IntermediateField K L) :
     S.toSubalgebra.toIntermediateField' (Field.toIsField S) = S := by ext; rfl
 #align to_intermediate_field'_to_subalgebra toIntermediateField'_toSubalgebra
+-/
 
+#print Subfield.toIntermediateField /-
 /-- Turn a subfield of `L` containing the image of `K` into an intermediate field -/
 def Subfield.toIntermediateField (S : Subfield L) (algebra_map_mem : ∀ x, algebraMap K L x ∈ S) :
     IntermediateField K L :=
   { S with algebraMap_mem' := algebra_map_mem }
 #align subfield.to_intermediate_field Subfield.toIntermediateField
+-/
 
 namespace IntermediateField
 
+#print IntermediateField.toField /-
 /-- An intermediate field inherits a field structure -/
 instance toField : Field S :=
   S.toSubfield.toField
 #align intermediate_field.to_field IntermediateField.toField
+-/
 
+#print IntermediateField.coe_sum /-
 @[simp, norm_cast]
 theorem coe_sum {ι : Type _} [Fintype ι] (f : ι → S) : (↑(∑ i, f i) : L) = ∑ i, (f i : L) := by
   classical
@@ -346,7 +435,9 @@ theorem coe_sum {ι : Type _} [Fintype ι] (f : ι → S) : (↑(∑ i, f i) : L
   · simp
   · rw [Finset.sum_insert hi, AddMemClass.coe_add, H, Finset.sum_insert hi]
 #align intermediate_field.coe_sum IntermediateField.coe_sum
+-/
 
+#print IntermediateField.coe_prod /-
 @[simp, norm_cast]
 theorem coe_prod {ι : Type _} [Fintype ι] (f : ι → S) : (↑(∏ i, f i) : L) = ∏ i, (f i : L) := by
   classical
@@ -354,55 +445,76 @@ theorem coe_prod {ι : Type _} [Fintype ι] (f : ι → S) : (↑(∏ i, f i) :
   · simp
   · rw [Finset.prod_insert hi, MulMemClass.coe_mul, H, Finset.prod_insert hi]
 #align intermediate_field.coe_prod IntermediateField.coe_prod
+-/
 
 /-! `intermediate_field`s inherit structure from their `subalgebra` coercions. -/
 
 
+#print IntermediateField.module' /-
 instance module' {R} [Semiring R] [SMul R K] [Module R L] [IsScalarTower R K L] : Module R S :=
   S.toSubalgebra.module'
 #align intermediate_field.module' IntermediateField.module'
+-/
 
+#print IntermediateField.module /-
 instance module : Module K S :=
   S.toSubalgebra.Module
 #align intermediate_field.module IntermediateField.module
+-/
 
+#print IntermediateField.isScalarTower /-
 instance isScalarTower {R} [Semiring R] [SMul R K] [Module R L] [IsScalarTower R K L] :
     IsScalarTower R K S :=
   S.toSubalgebra.IsScalarTower
 #align intermediate_field.is_scalar_tower IntermediateField.isScalarTower
+-/
 
+#print IntermediateField.coe_smul /-
 @[simp]
 theorem coe_smul {R} [Semiring R] [SMul R K] [Module R L] [IsScalarTower R K L] (r : R) (x : S) :
     ↑(r • x) = (r • x : L) :=
   rfl
 #align intermediate_field.coe_smul IntermediateField.coe_smul
+-/
 
+#print IntermediateField.algebra' /-
 instance algebra' {K'} [CommSemiring K'] [SMul K' K] [Algebra K' L] [IsScalarTower K' K L] :
     Algebra K' S :=
   S.toSubalgebra.algebra'
 #align intermediate_field.algebra' IntermediateField.algebra'
+-/
 
+#print IntermediateField.algebra /-
 instance algebra : Algebra K S :=
   S.toSubalgebra.Algebra
 #align intermediate_field.algebra IntermediateField.algebra
+-/
 
+#print IntermediateField.toAlgebra /-
 instance toAlgebra {R : Type _} [Semiring R] [Algebra L R] : Algebra S R :=
   S.toSubalgebra.toAlgebra
 #align intermediate_field.to_algebra IntermediateField.toAlgebra
+-/
 
+#print IntermediateField.isScalarTower_bot /-
 instance isScalarTower_bot {R : Type _} [Semiring R] [Algebra L R] : IsScalarTower S L R :=
   IsScalarTower.subalgebra _ _ _ S.toSubalgebra
 #align intermediate_field.is_scalar_tower_bot IntermediateField.isScalarTower_bot
+-/
 
+#print IntermediateField.isScalarTower_mid /-
 instance isScalarTower_mid {R : Type _} [Semiring R] [Algebra L R] [Algebra K R]
     [IsScalarTower K L R] : IsScalarTower K S R :=
   IsScalarTower.subalgebra' _ _ _ S.toSubalgebra
 #align intermediate_field.is_scalar_tower_mid IntermediateField.isScalarTower_mid
+-/
 
+#print IntermediateField.isScalarTower_mid' /-
 /-- Specialize `is_scalar_tower_mid` to the common case where the top field is `L` -/
 instance isScalarTower_mid' : IsScalarTower K S L :=
   S.isScalarTower_mid
 #align intermediate_field.is_scalar_tower_mid' IntermediateField.isScalarTower_mid'
+-/
 
 #print IntermediateField.map /-
 /-- If `f : L →+* L'` fixes `K`, `S.map f` is the intermediate field between `L'` and `K`
@@ -416,24 +528,31 @@ def map (f : L →ₐ[K] L') (S : IntermediateField K L) : IntermediateField K L
 #align intermediate_field.map IntermediateField.map
 -/
 
+#print IntermediateField.coe_map /-
 @[simp]
 theorem coe_map (f : L →ₐ[K] L') : (S.map f : Set L') = f '' S :=
   rfl
 #align intermediate_field.coe_map IntermediateField.coe_map
+-/
 
+#print IntermediateField.map_map /-
 theorem map_map {K L₁ L₂ L₃ : Type _} [Field K] [Field L₁] [Algebra K L₁] [Field L₂] [Algebra K L₂]
     [Field L₃] [Algebra K L₃] (E : IntermediateField K L₁) (f : L₁ →ₐ[K] L₂) (g : L₂ →ₐ[K] L₃) :
     (E.map f).map g = E.map (g.comp f) :=
   SetLike.coe_injective <| Set.image_image _ _ _
 #align intermediate_field.map_map IntermediateField.map_map
+-/
 
+#print IntermediateField.intermediateFieldMap /-
 /-- Given an equivalence `e : L ≃ₐ[K] L'` of `K`-field extensions and an intermediate
 field `E` of `L/K`, `intermediate_field_equiv_map e E` is the induced equivalence
 between `E` and `E.map e` -/
 def intermediateFieldMap (e : L ≃ₐ[K] L') (E : IntermediateField K L) : E ≃ₐ[K] E.map e.toAlgHom :=
   e.subalgebraMap E.toSubalgebra
 #align intermediate_field.intermediate_field_map IntermediateField.intermediateFieldMap
+-/
 
+#print IntermediateField.intermediateFieldMap_apply_coe /-
 /- We manually add these two simp lemmas because `@[simps]` before `intermediate_field_map`
   led to a timeout. -/
 @[simp]
@@ -441,12 +560,15 @@ theorem intermediateFieldMap_apply_coe (e : L ≃ₐ[K] L') (E : IntermediateFie
     ↑(intermediateFieldMap e E a) = e a :=
   rfl
 #align intermediate_field.intermediate_field_map_apply_coe IntermediateField.intermediateFieldMap_apply_coe
+-/
 
+#print IntermediateField.intermediateFieldMap_symm_apply_coe /-
 @[simp]
 theorem intermediateFieldMap_symm_apply_coe (e : L ≃ₐ[K] L') (E : IntermediateField K L)
     (a : E.map e.toAlgHom) : ↑((intermediateFieldMap e E).symm a) = e.symm a :=
   rfl
 #align intermediate_field.intermediate_field_map_symm_apply_coe IntermediateField.intermediateFieldMap_symm_apply_coe
+-/
 
 end IntermediateField
 
@@ -462,55 +584,74 @@ def fieldRange : IntermediateField K L' :=
 #align alg_hom.field_range AlgHom.fieldRange
 -/
 
+#print AlgHom.coe_fieldRange /-
 @[simp]
 theorem coe_fieldRange : ↑f.fieldRange = Set.range f :=
   rfl
 #align alg_hom.coe_field_range AlgHom.coe_fieldRange
+-/
 
+#print AlgHom.fieldRange_toSubfield /-
 @[simp]
 theorem fieldRange_toSubfield : f.fieldRange.toSubfield = (f : L →+* L').fieldRange :=
   rfl
 #align alg_hom.field_range_to_subfield AlgHom.fieldRange_toSubfield
+-/
 
 variable {f}
 
+#print AlgHom.mem_fieldRange /-
 @[simp]
 theorem mem_fieldRange {y : L'} : y ∈ f.fieldRange ↔ ∃ x, f x = y :=
   Iff.rfl
 #align alg_hom.mem_field_range AlgHom.mem_fieldRange
+-/
 
 end AlgHom
 
 namespace IntermediateField
 
+#print IntermediateField.val /-
 /-- The embedding from an intermediate field of `L / K` to `L`. -/
 def val : S →ₐ[K] L :=
   S.toSubalgebra.val
 #align intermediate_field.val IntermediateField.val
+-/
 
+#print IntermediateField.coe_val /-
 @[simp]
 theorem coe_val : ⇑S.val = coe :=
   rfl
 #align intermediate_field.coe_val IntermediateField.coe_val
+-/
 
+#print IntermediateField.val_mk /-
 @[simp]
 theorem val_mk {x : L} (hx : x ∈ S) : S.val ⟨x, hx⟩ = x :=
   rfl
 #align intermediate_field.val_mk IntermediateField.val_mk
+-/
 
+#print IntermediateField.range_val /-
 theorem range_val : S.val.range = S.toSubalgebra :=
   S.toSubalgebra.range_val
 #align intermediate_field.range_val IntermediateField.range_val
+-/
 
+#print IntermediateField.fieldRange_val /-
 @[simp]
 theorem fieldRange_val : S.val.fieldRange = S :=
   SetLike.ext' Subtype.range_val
 #align intermediate_field.field_range_val IntermediateField.fieldRange_val
+-/
 
+#print IntermediateField.AlgHom.inhabited /-
 instance AlgHom.inhabited : Inhabited (S →ₐ[K] L) :=
   ⟨S.val⟩
 #align intermediate_field.alg_hom.inhabited IntermediateField.AlgHom.inhabited
+-/
 
+#print IntermediateField.aeval_coe /-
 theorem aeval_coe {R : Type _} [CommRing R] [Algebra R K] [Algebra R L] [IsScalarTower R K L]
     (x : S) (P : R[X]) : aeval (x : L) P = aeval x P :=
   by
@@ -519,7 +660,9 @@ theorem aeval_coe {R : Type _} [CommRing R] [Algebra R K] [Algebra R L] [IsScala
   · simp only [MulMemClass.coe_mul, aeval_monomial, SubmonoidClass.coe_pow, mul_eq_mul_right_iff]
     left; rfl
 #align intermediate_field.aeval_coe IntermediateField.aeval_coe
+-/
 
+#print IntermediateField.coe_isIntegral_iff /-
 theorem coe_isIntegral_iff {R : Type _} [CommRing R] [Algebra R K] [Algebra R L]
     [IsScalarTower R K L] {x : S} : IsIntegral R (x : L) ↔ IsIntegral R x :=
   by
@@ -533,78 +676,103 @@ theorem coe_isIntegral_iff {R : Type _} [CommRing R] [Algebra R K] [Algebra R L]
     refine' ⟨P, hPmo, _⟩
     rw [← aeval_def, aeval_coe, aeval_def, hProot, ZeroMemClass.coe_zero]
 #align intermediate_field.coe_is_integral_iff IntermediateField.coe_isIntegral_iff
+-/
 
+#print IntermediateField.inclusion /-
 /-- The map `E → F` when `E` is an intermediate field contained in the intermediate field `F`.
 
 This is the intermediate field version of `subalgebra.inclusion`. -/
 def inclusion {E F : IntermediateField K L} (hEF : E ≤ F) : E →ₐ[K] F :=
   Subalgebra.inclusion hEF
 #align intermediate_field.inclusion IntermediateField.inclusion
+-/
 
+#print IntermediateField.inclusion_injective /-
 theorem inclusion_injective {E F : IntermediateField K L} (hEF : E ≤ F) :
     Function.Injective (inclusion hEF) :=
   Subalgebra.inclusion_injective hEF
 #align intermediate_field.inclusion_injective IntermediateField.inclusion_injective
+-/
 
+#print IntermediateField.inclusion_self /-
 @[simp]
 theorem inclusion_self {E : IntermediateField K L} : inclusion (le_refl E) = AlgHom.id K E :=
   Subalgebra.inclusion_self
 #align intermediate_field.inclusion_self IntermediateField.inclusion_self
+-/
 
+#print IntermediateField.inclusion_inclusion /-
 @[simp]
 theorem inclusion_inclusion {E F G : IntermediateField K L} (hEF : E ≤ F) (hFG : F ≤ G) (x : E) :
     inclusion hFG (inclusion hEF x) = inclusion (le_trans hEF hFG) x :=
   Subalgebra.inclusion_inclusion hEF hFG x
 #align intermediate_field.inclusion_inclusion IntermediateField.inclusion_inclusion
+-/
 
+#print IntermediateField.coe_inclusion /-
 @[simp]
 theorem coe_inclusion {E F : IntermediateField K L} (hEF : E ≤ F) (e : E) :
     (inclusion hEF e : L) = e :=
   rfl
 #align intermediate_field.coe_inclusion IntermediateField.coe_inclusion
+-/
 
 variable {S}
 
+#print IntermediateField.toSubalgebra_injective /-
 theorem toSubalgebra_injective {S S' : IntermediateField K L}
     (h : S.toSubalgebra = S'.toSubalgebra) : S = S' := by ext;
   rw [← mem_to_subalgebra, ← mem_to_subalgebra, h]
 #align intermediate_field.to_subalgebra_injective IntermediateField.toSubalgebra_injective
+-/
 
 variable (S)
 
+#print IntermediateField.set_range_subset /-
 theorem set_range_subset : Set.range (algebraMap K L) ⊆ S :=
   S.toSubalgebra.range_subset
 #align intermediate_field.set_range_subset IntermediateField.set_range_subset
+-/
 
+#print IntermediateField.fieldRange_le /-
 theorem fieldRange_le : (algebraMap K L).fieldRange ≤ S.toSubfield := fun x hx =>
   S.toSubalgebra.range_subset (by rwa [Set.mem_range, ← RingHom.mem_fieldRange])
 #align intermediate_field.field_range_le IntermediateField.fieldRange_le
+-/
 
+#print IntermediateField.toSubalgebra_le_toSubalgebra /-
 @[simp]
 theorem toSubalgebra_le_toSubalgebra {S S' : IntermediateField K L} :
     S.toSubalgebra ≤ S'.toSubalgebra ↔ S ≤ S' :=
   Iff.rfl
 #align intermediate_field.to_subalgebra_le_to_subalgebra IntermediateField.toSubalgebra_le_toSubalgebra
+-/
 
+#print IntermediateField.toSubalgebra_lt_toSubalgebra /-
 @[simp]
 theorem toSubalgebra_lt_toSubalgebra {S S' : IntermediateField K L} :
     S.toSubalgebra < S'.toSubalgebra ↔ S < S' :=
   Iff.rfl
 #align intermediate_field.to_subalgebra_lt_to_subalgebra IntermediateField.toSubalgebra_lt_toSubalgebra
+-/
 
 variable {S}
 
 section Tower
 
+#print IntermediateField.lift /-
 /-- Lift an intermediate_field of an intermediate_field -/
 def lift {F : IntermediateField K L} (E : IntermediateField K F) : IntermediateField K L :=
   E.map (val F)
 #align intermediate_field.lift IntermediateField.lift
+-/
 
+#print IntermediateField.hasLift /-
 instance hasLift {F : IntermediateField K L} :
     HasLiftT (IntermediateField K F) (IntermediateField K L) :=
   ⟨lift⟩
 #align intermediate_field.has_lift IntermediateField.hasLift
+-/
 
 section RestrictScalars
 
@@ -618,11 +786,13 @@ def restrictScalars (E : IntermediateField L' L) : IntermediateField K L :=
 #align intermediate_field.restrict_scalars IntermediateField.restrictScalars
 -/
 
+#print IntermediateField.coe_restrictScalars /-
 @[simp]
 theorem coe_restrictScalars {E : IntermediateField L' L} :
     (restrictScalars K E : Set L) = (E : Set L) :=
   rfl
 #align intermediate_field.coe_restrict_scalars IntermediateField.coe_restrictScalars
+-/
 
 #print IntermediateField.restrictScalars_toSubalgebra /-
 @[simp]
@@ -640,16 +810,20 @@ theorem restrictScalars_toSubfield {E : IntermediateField L' L} :
 #align intermediate_field.restrict_scalars_to_subfield IntermediateField.restrictScalars_toSubfield
 -/
 
+#print IntermediateField.mem_restrictScalars /-
 @[simp]
 theorem mem_restrictScalars {E : IntermediateField L' L} {x : L} :
     x ∈ restrictScalars K E ↔ x ∈ E :=
   Iff.rfl
 #align intermediate_field.mem_restrict_scalars IntermediateField.mem_restrictScalars
+-/
 
+#print IntermediateField.restrictScalars_injective /-
 theorem restrictScalars_injective :
     Function.Injective (restrictScalars K : IntermediateField L' L → IntermediateField K L) :=
   fun U V H => ext fun x => by rw [← mem_restrict_scalars K, H, mem_restrict_scalars]
 #align intermediate_field.restrict_scalars_injective IntermediateField.restrictScalars_injective
+-/
 
 end RestrictScalars
 
@@ -662,13 +836,17 @@ section FiniteDimensional
 
 variable (F E : IntermediateField K L)
 
+#print IntermediateField.finiteDimensional_left /-
 instance finiteDimensional_left [FiniteDimensional K L] : FiniteDimensional K F :=
   left K F L
 #align intermediate_field.finite_dimensional_left IntermediateField.finiteDimensional_left
+-/
 
+#print IntermediateField.finiteDimensional_right /-
 instance finiteDimensional_right [FiniteDimensional K L] : FiniteDimensional F L :=
   right K F L
 #align intermediate_field.finite_dimensional_right IntermediateField.finiteDimensional_right
+-/
 
 #print IntermediateField.rank_eq_rank_subalgebra /-
 @[simp]
@@ -677,10 +855,12 @@ theorem rank_eq_rank_subalgebra : Module.rank K F.toSubalgebra = Module.rank K F
 #align intermediate_field.rank_eq_rank_subalgebra IntermediateField.rank_eq_rank_subalgebra
 -/
 
+#print IntermediateField.finrank_eq_finrank_subalgebra /-
 @[simp]
 theorem finrank_eq_finrank_subalgebra : finrank K F.toSubalgebra = finrank K F :=
   rfl
 #align intermediate_field.finrank_eq_finrank_subalgebra IntermediateField.finrank_eq_finrank_subalgebra
+-/
 
 variable {F} {E}
 
@@ -691,17 +871,22 @@ theorem toSubalgebra_eq_iff : F.toSubalgebra = E.toSubalgebra ↔ F = E := by
 #align intermediate_field.to_subalgebra_eq_iff IntermediateField.toSubalgebra_eq_iff
 -/
 
+#print IntermediateField.eq_of_le_of_finrank_le /-
 theorem eq_of_le_of_finrank_le [FiniteDimensional K L] (h_le : F ≤ E)
     (h_finrank : finrank K E ≤ finrank K F) : F = E :=
   toSubalgebra_injective <|
     Subalgebra.toSubmodule.Injective <| eq_of_le_of_finrank_le h_le h_finrank
 #align intermediate_field.eq_of_le_of_finrank_le IntermediateField.eq_of_le_of_finrank_le
+-/
 
+#print IntermediateField.eq_of_le_of_finrank_eq /-
 theorem eq_of_le_of_finrank_eq [FiniteDimensional K L] (h_le : F ≤ E)
     (h_finrank : finrank K F = finrank K E) : F = E :=
   eq_of_le_of_finrank_le h_le h_finrank.ge
 #align intermediate_field.eq_of_le_of_finrank_eq IntermediateField.eq_of_le_of_finrank_eq
+-/
 
+#print IntermediateField.eq_of_le_of_finrank_le' /-
 theorem eq_of_le_of_finrank_le' [FiniteDimensional K L] (h_le : F ≤ E)
     (h_finrank : finrank F L ≤ finrank E L) : F = E :=
   by
@@ -711,31 +896,41 @@ theorem eq_of_le_of_finrank_le' [FiniteDimensional K L] (h_le : F ≤ E)
   have h3 : 0 < finrank E L := finrank_pos
   nlinarith
 #align intermediate_field.eq_of_le_of_finrank_le' IntermediateField.eq_of_le_of_finrank_le'
+-/
 
+#print IntermediateField.eq_of_le_of_finrank_eq' /-
 theorem eq_of_le_of_finrank_eq' [FiniteDimensional K L] (h_le : F ≤ E)
     (h_finrank : finrank F L = finrank E L) : F = E :=
   eq_of_le_of_finrank_le' h_le h_finrank.le
 #align intermediate_field.eq_of_le_of_finrank_eq' IntermediateField.eq_of_le_of_finrank_eq'
+-/
 
 end FiniteDimensional
 
+#print IntermediateField.isAlgebraic_iff /-
 theorem isAlgebraic_iff {x : S} : IsAlgebraic K x ↔ IsAlgebraic K (x : L) :=
   (isAlgebraic_algebraMap_iff (algebraMap S L).Injective).symm
 #align intermediate_field.is_algebraic_iff IntermediateField.isAlgebraic_iff
+-/
 
+#print IntermediateField.isIntegral_iff /-
 theorem isIntegral_iff {x : S} : IsIntegral K x ↔ IsIntegral K (x : L) := by
   rw [← isAlgebraic_iff_isIntegral, is_algebraic_iff, isAlgebraic_iff_isIntegral]
 #align intermediate_field.is_integral_iff IntermediateField.isIntegral_iff
+-/
 
+#print IntermediateField.minpoly_eq /-
 theorem minpoly_eq (x : S) : minpoly K x = minpoly K (x : L) :=
   by
   by_cases hx : IsIntegral K x
   · exact minpoly.eq_of_algebraMap_eq (algebraMap S L).Injective hx rfl
   · exact (minpoly.eq_zero hx).trans (minpoly.eq_zero (mt is_integral_iff.mpr hx)).symm
 #align intermediate_field.minpoly_eq IntermediateField.minpoly_eq
+-/
 
 end IntermediateField
 
+#print subalgebraEquivIntermediateField /-
 /-- If `L/K` is algebraic, the `K`-subalgebras of `L` are all fields.  -/
 def subalgebraEquivIntermediateField (alg : Algebra.IsAlgebraic K L) :
     Subalgebra K L ≃o IntermediateField K L
@@ -746,17 +941,22 @@ def subalgebraEquivIntermediateField (alg : Algebra.IsAlgebraic K L) :
   right_inv := toIntermediateField_toSubalgebra
   map_rel_iff' S S' := Iff.rfl
 #align subalgebra_equiv_intermediate_field subalgebraEquivIntermediateField
+-/
 
+#print mem_subalgebraEquivIntermediateField /-
 @[simp]
 theorem mem_subalgebraEquivIntermediateField (alg : Algebra.IsAlgebraic K L) {S : Subalgebra K L}
     {x : L} : x ∈ subalgebraEquivIntermediateField alg S ↔ x ∈ S :=
   Iff.rfl
 #align mem_subalgebra_equiv_intermediate_field mem_subalgebraEquivIntermediateField
+-/
 
+#print mem_subalgebraEquivIntermediateField_symm /-
 @[simp]
 theorem mem_subalgebraEquivIntermediateField_symm (alg : Algebra.IsAlgebraic K L)
     {S : IntermediateField K L} {x : L} :
     x ∈ (subalgebraEquivIntermediateField alg).symm S ↔ x ∈ S :=
   Iff.rfl
 #align mem_subalgebra_equiv_intermediate_field_symm mem_subalgebraEquivIntermediateField_symm
+-/
 

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

@@ -228,14 +228,14 @@ protected theorem multiset_sum_mem (m : Multiset L) : (∀ a ∈ m, a ∈ S) →
 /-- Product of elements of an intermediate field indexed by a `finset` is in the intermediate_field.
 -/
 protected theorem prod_mem {ι : Type _} {t : Finset ι} {f : ι → L} (h : ∀ c ∈ t, f c ∈ S) :
-    (∏ i in t, f i) ∈ S :=
+    ∏ i in t, f i ∈ S :=
   prod_mem h
 #align intermediate_field.prod_mem IntermediateField.prod_mem
 
 /-- Sum of elements in a `intermediate_field` indexed by a `finset` is in the `intermediate_field`.
 -/
 protected theorem sum_mem {ι : Type _} {t : Finset ι} {f : ι → L} (h : ∀ c ∈ t, f c ∈ S) :
-    (∑ i in t, f i) ∈ S :=
+    ∑ i in t, f i ∈ S :=
   sum_mem h
 #align intermediate_field.sum_mem IntermediateField.sum_mem
 

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

@@ -342,17 +342,17 @@ instance toField : Field S :=
 @[simp, norm_cast]
 theorem coe_sum {ι : Type _} [Fintype ι] (f : ι → S) : (↑(∑ i, f i) : L) = ∑ i, (f i : L) := by
   classical
-    induction' Finset.univ using Finset.induction_on with i s hi H
-    · simp
-    · rw [Finset.sum_insert hi, AddMemClass.coe_add, H, Finset.sum_insert hi]
+  induction' Finset.univ using Finset.induction_on with i s hi H
+  · simp
+  · rw [Finset.sum_insert hi, AddMemClass.coe_add, H, Finset.sum_insert hi]
 #align intermediate_field.coe_sum IntermediateField.coe_sum
 
 @[simp, norm_cast]
 theorem coe_prod {ι : Type _} [Fintype ι] (f : ι → S) : (↑(∏ i, f i) : L) = ∏ i, (f i : L) := by
   classical
-    induction' Finset.univ using Finset.induction_on with i s hi H
-    · simp
-    · rw [Finset.prod_insert hi, MulMemClass.coe_mul, H, Finset.prod_insert hi]
+  induction' Finset.univ using Finset.induction_on with i s hi H
+  · simp
+  · rw [Finset.prod_insert hi, MulMemClass.coe_mul, H, Finset.prod_insert hi]
 #align intermediate_field.coe_prod IntermediateField.coe_prod
 
 /-! `intermediate_field`s inherit structure from their `subalgebra` coercions. -/

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

@@ -74,7 +74,7 @@ def toSubfield : Subfield L :=
 -/
 
 instance : SetLike (IntermediateField K L) L :=
-  ⟨fun S => S.toSubalgebra.carrier, by rintro ⟨⟨⟩⟩ ⟨⟨⟩⟩ ⟨h⟩; congr ⟩
+  ⟨fun S => S.toSubalgebra.carrier, by rintro ⟨⟨⟩⟩ ⟨⟨⟩⟩ ⟨h⟩; congr⟩
 
 instance : SubfieldClass (IntermediateField K L) L
     where
@@ -312,7 +312,7 @@ def Subalgebra.toIntermediateField' (S : Subalgebra K L) (hS : IsField S) : Inte
       exact S.zero_mem
     letI hS' := hS.to_field
     obtain ⟨y, hy⟩ := hS.mul_inv_cancel (show (⟨x, hx⟩ : S) ≠ 0 from Subtype.ne_of_val_ne hx0)
-    rw [Subtype.ext_iff, S.coe_mul, S.coe_one, Subtype.coe_mk, mul_eq_one_iff_inv_eq₀ hx0] at hy
+    rw [Subtype.ext_iff, S.coe_mul, S.coe_one, Subtype.coe_mk, mul_eq_one_iff_inv_eq₀ hx0] at hy 
     exact hy.symm ▸ y.2
 #align subalgebra.to_intermediate_field' Subalgebra.toIntermediateField'
 

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

@@ -46,7 +46,7 @@ intermediate field, field extension
 
 open FiniteDimensional Polynomial
 
-open BigOperators Polynomial
+open scoped BigOperators Polynomial
 
 variable (K L L' : Type _) [Field K] [Field L] [Field L'] [Algebra K L] [Algebra K L']
 

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

@@ -85,46 +85,22 @@ instance : SubfieldClass (IntermediateField K L) L
   one_mem s := s.one_mem'
   inv_mem := inv_mem'
 
-/- warning: intermediate_field.mem_carrier -> IntermediateField.mem_carrier is a dubious translation:
-lean 3 declaration is
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 @[simp]
 theorem mem_carrier {s : IntermediateField K L} {x : L} : x ∈ s.carrier ↔ x ∈ s :=
   Iff.rfl
 #align intermediate_field.mem_carrier IntermediateField.mem_carrier
 
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 /-- Two intermediate fields are equal if they have the same elements. -/
 @[ext]
 theorem ext {S T : IntermediateField K L} (h : ∀ x, x ∈ S ↔ x ∈ T) : S = T :=
   SetLike.ext h
 #align intermediate_field.ext IntermediateField.ext
 
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 @[simp]
 theorem coe_toSubalgebra : (S.toSubalgebra : Set L) = S :=
   rfl
 #align intermediate_field.coe_to_subalgebra IntermediateField.coe_toSubalgebra
 
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 @[simp]
 theorem coe_toSubfield : (S.toSubfield : Set L) = S :=
   rfl
@@ -136,34 +112,16 @@ theorem mem_mk (s : Set L) (hK : ∀ x, algebraMap K L x ∈ s) (ho hm hz ha hn
   Iff.rfl
 #align intermediate_field.mem_mk IntermediateField.mem_mkₓ
 
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 @[simp]
 theorem mem_toSubalgebra (s : IntermediateField K L) (x : L) : x ∈ s.toSubalgebra ↔ x ∈ s :=
   Iff.rfl
 #align intermediate_field.mem_to_subalgebra IntermediateField.mem_toSubalgebra
 
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 @[simp]
 theorem mem_toSubfield (s : IntermediateField K L) (x : L) : x ∈ s.toSubfield ↔ x ∈ s :=
   Iff.rfl
 #align intermediate_field.mem_to_subfield IntermediateField.mem_toSubfield
 
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 /-- Copy of an intermediate field with a new `carrier` equal to the old one. Useful to fix
 definitional equalities. -/
 protected def copy (S : IntermediateField K L) (s : Set L) (hs : s = ↑S) : IntermediateField K L
@@ -177,24 +135,12 @@ protected def copy (S : IntermediateField K L) (s : Set L) (hs : s = ↑S) : Int
     hs'.symm ▸ S.inv_mem'
 #align intermediate_field.copy IntermediateField.copy
 
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 @[simp]
 theorem coe_copy (S : IntermediateField K L) (s : Set L) (hs : s = ↑S) :
     (S.copy s hs : Set L) = s :=
   rfl
 #align intermediate_field.coe_copy IntermediateField.coe_copy
 
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 theorem copy_eq (S : IntermediateField K L) (s : Set L) (hs : s = ↑S) : S.copy s hs = S :=
   SetLike.coe_injective hs
 #align intermediate_field.copy_eq IntermediateField.copy_eq
@@ -209,166 +155,76 @@ subobject class.
 -/
 
 
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 /-- An intermediate field contains the image of the smaller field. -/
 theorem algebraMap_mem (x : K) : algebraMap K L x ∈ S :=
   S.algebraMap_mem' x
 #align intermediate_field.algebra_map_mem IntermediateField.algebraMap_mem
 
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 /-- An intermediate field is closed under scalar multiplication. -/
 theorem smul_mem {y : L} : y ∈ S → ∀ {x : K}, x • y ∈ S :=
   S.toSubalgebra.smul_mem
 #align intermediate_field.smul_mem IntermediateField.smul_mem
 
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 /-- An intermediate field contains the ring's 1. -/
 protected theorem one_mem : (1 : L) ∈ S :=
   one_mem S
 #align intermediate_field.one_mem IntermediateField.one_mem
 
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 /-- An intermediate field contains the ring's 0. -/
 protected theorem zero_mem : (0 : L) ∈ S :=
   zero_mem S
 #align intermediate_field.zero_mem IntermediateField.zero_mem
 
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 /-- An intermediate field is closed under multiplication. -/
 protected theorem mul_mem {x y : L} : x ∈ S → y ∈ S → x * y ∈ S :=
   mul_mem
 #align intermediate_field.mul_mem IntermediateField.mul_mem
 
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 /-- An intermediate field is closed under addition. -/
 protected theorem add_mem {x y : L} : x ∈ S → y ∈ S → x + y ∈ S :=
   add_mem
 #align intermediate_field.add_mem IntermediateField.add_mem
 
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 /-- An intermediate field is closed under subtraction -/
 protected theorem sub_mem {x y : L} : x ∈ S → y ∈ S → x - y ∈ S :=
   sub_mem
 #align intermediate_field.sub_mem IntermediateField.sub_mem
 
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 /-- An intermediate field is closed under negation. -/
 protected theorem neg_mem {x : L} : x ∈ S → -x ∈ S :=
   neg_mem
 #align intermediate_field.neg_mem IntermediateField.neg_mem
 
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 /-- An intermediate field is closed under inverses. -/
 protected theorem inv_mem {x : L} : x ∈ S → x⁻¹ ∈ S :=
   inv_mem
 #align intermediate_field.inv_mem IntermediateField.inv_mem
 
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 /-- An intermediate field is closed under division. -/
 protected theorem div_mem {x y : L} : x ∈ S → y ∈ S → x / y ∈ S :=
   div_mem
 #align intermediate_field.div_mem IntermediateField.div_mem
 
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 /-- Product of a list of elements in an intermediate_field is in the intermediate_field. -/
 protected theorem list_prod_mem {l : List L} : (∀ x ∈ l, x ∈ S) → l.Prod ∈ S :=
   list_prod_mem
 #align intermediate_field.list_prod_mem IntermediateField.list_prod_mem
 
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 /-- Sum of a list of elements in an intermediate field is in the intermediate_field. -/
 protected theorem list_sum_mem {l : List L} : (∀ x ∈ l, x ∈ S) → l.Sum ∈ S :=
   list_sum_mem
 #align intermediate_field.list_sum_mem IntermediateField.list_sum_mem
 
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 /-- Product of a multiset of elements in an intermediate field is in the intermediate_field. -/
 protected theorem multiset_prod_mem (m : Multiset L) : (∀ a ∈ m, a ∈ S) → m.Prod ∈ S :=
   multiset_prod_mem m
 #align intermediate_field.multiset_prod_mem IntermediateField.multiset_prod_mem
 
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 /-- Sum of a multiset of elements in a `intermediate_field` is in the `intermediate_field`. -/
 protected theorem multiset_sum_mem (m : Multiset L) : (∀ a ∈ m, a ∈ S) → m.Sum ∈ S :=
   multiset_sum_mem m
 #align intermediate_field.multiset_sum_mem IntermediateField.multiset_sum_mem
 
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 /-- Product of elements of an intermediate field indexed by a `finset` is in the intermediate_field.
 -/
 protected theorem prod_mem {ι : Type _} {t : Finset ι} {f : ι → L} (h : ∀ c ∈ t, f c ∈ S) :
@@ -376,12 +232,6 @@ protected theorem prod_mem {ι : Type _} {t : Finset ι} {f : ι → L} (h : ∀
   prod_mem h
 #align intermediate_field.prod_mem IntermediateField.prod_mem
 
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 /-- Sum of elements in a `intermediate_field` indexed by a `finset` is in the `intermediate_field`.
 -/
 protected theorem sum_mem {ι : Type _} {t : Finset ι} {f : ι → L} (h : ∀ c ∈ t, f c ∈ S) :
@@ -389,119 +239,53 @@ protected theorem sum_mem {ι : Type _} {t : Finset ι} {f : ι → L} (h : ∀
   sum_mem h
 #align intermediate_field.sum_mem IntermediateField.sum_mem
 
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 protected theorem pow_mem {x : L} (hx : x ∈ S) (n : ℤ) : x ^ n ∈ S :=
   zpow_mem hx n
 #align intermediate_field.pow_mem IntermediateField.pow_mem
 
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 protected theorem zsmul_mem {x : L} (hx : x ∈ S) (n : ℤ) : n • x ∈ S :=
   zsmul_mem hx n
 #align intermediate_field.zsmul_mem IntermediateField.zsmul_mem
 
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 protected theorem coe_int_mem (n : ℤ) : (n : L) ∈ S :=
   coe_int_mem S n
 #align intermediate_field.coe_int_mem IntermediateField.coe_int_mem
 
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 protected theorem coe_add (x y : S) : (↑(x + y) : L) = ↑x + ↑y :=
   rfl
 #align intermediate_field.coe_add IntermediateField.coe_add
 
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 protected theorem coe_neg (x : S) : (↑(-x) : L) = -↑x :=
   rfl
 #align intermediate_field.coe_neg IntermediateField.coe_neg
 
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 protected theorem coe_mul (x y : S) : (↑(x * y) : L) = ↑x * ↑y :=
   rfl
 #align intermediate_field.coe_mul IntermediateField.coe_mul
 
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 protected theorem coe_inv (x : S) : (↑x⁻¹ : L) = (↑x)⁻¹ :=
   rfl
 #align intermediate_field.coe_inv IntermediateField.coe_inv
 
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 protected theorem coe_zero : ((0 : S) : L) = 0 :=
   rfl
 #align intermediate_field.coe_zero IntermediateField.coe_zero
 
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 protected theorem coe_one : ((1 : S) : L) = 1 :=
   rfl
 #align intermediate_field.coe_one IntermediateField.coe_one
 
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 protected theorem coe_pow (x : S) (n : ℕ) : (↑(x ^ n) : L) = ↑x ^ n :=
   SubmonoidClass.coe_pow x n
 #align intermediate_field.coe_pow IntermediateField.coe_pow
 
 end InheritedLemmas
 
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 theorem coe_nat_mem (n : ℕ) : (n : L) ∈ S := by simpa using coe_int_mem S n
 #align intermediate_field.coe_nat_mem IntermediateField.coe_nat_mem
 
 end IntermediateField
 
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 /-- Turn a subalgebra closed under inverses into an intermediate field -/
 def Subalgebra.toIntermediateField (S : Subalgebra K L) (inv_mem : ∀ x ∈ S, x⁻¹ ∈ S) :
     IntermediateField K L :=
@@ -510,34 +294,16 @@ def Subalgebra.toIntermediateField (S : Subalgebra K L) (inv_mem : ∀ x ∈ S,
     inv_mem' := inv_mem }
 #align subalgebra.to_intermediate_field Subalgebra.toIntermediateField
 
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 @[simp]
 theorem toSubalgebra_toIntermediateField (S : Subalgebra K L) (inv_mem : ∀ x ∈ S, x⁻¹ ∈ S) :
     (S.toIntermediateField inv_mem).toSubalgebra = S := by ext; rfl
 #align to_subalgebra_to_intermediate_field toSubalgebra_toIntermediateField
 
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 @[simp]
 theorem toIntermediateField_toSubalgebra (S : IntermediateField K L) :
     (S.toSubalgebra.toIntermediateField fun x => S.inv_mem) = S := by ext; rfl
 #align to_intermediate_field_to_subalgebra toIntermediateField_toSubalgebra
 
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 /-- Turn a subalgebra satisfying `is_field` into an intermediate_field -/
 def Subalgebra.toIntermediateField' (S : Subalgebra K L) (hS : IsField S) : IntermediateField K L :=
   S.toIntermediateField fun x hx => by
@@ -550,34 +316,16 @@ def Subalgebra.toIntermediateField' (S : Subalgebra K L) (hS : IsField S) : Inte
     exact hy.symm ▸ y.2
 #align subalgebra.to_intermediate_field' Subalgebra.toIntermediateField'
 
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 @[simp]
 theorem toSubalgebra_toIntermediateField' (S : Subalgebra K L) (hS : IsField S) :
     (S.toIntermediateField' hS).toSubalgebra = S := by ext; rfl
 #align to_subalgebra_to_intermediate_field' toSubalgebra_toIntermediateField'
 
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 @[simp]
 theorem toIntermediateField'_toSubalgebra (S : IntermediateField K L) :
     S.toSubalgebra.toIntermediateField' (Field.toIsField S) = S := by ext; rfl
 #align to_intermediate_field'_to_subalgebra toIntermediateField'_toSubalgebra
 
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 /-- Turn a subfield of `L` containing the image of `K` into an intermediate field -/
 def Subfield.toIntermediateField (S : Subfield L) (algebra_map_mem : ∀ x, algebraMap K L x ∈ S) :
     IntermediateField K L :=
@@ -586,20 +334,11 @@ def Subfield.toIntermediateField (S : Subfield L) (algebra_map_mem : ∀ x, alge
 
 namespace IntermediateField
 
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 /-- An intermediate field inherits a field structure -/
 instance toField : Field S :=
   S.toSubfield.toField
 #align intermediate_field.to_field IntermediateField.toField
 
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 @[simp, norm_cast]
 theorem coe_sum {ι : Type _} [Fintype ι] (f : ι → S) : (↑(∑ i, f i) : L) = ∑ i, (f i : L) := by
   classical
@@ -608,12 +347,6 @@ theorem coe_sum {ι : Type _} [Fintype ι] (f : ι → S) : (↑(∑ i, f i) : L
     · rw [Finset.sum_insert hi, AddMemClass.coe_add, H, Finset.sum_insert hi]
 #align intermediate_field.coe_sum IntermediateField.coe_sum
 
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 @[simp, norm_cast]
 theorem coe_prod {ι : Type _} [Fintype ι] (f : ι → S) : (↑(∏ i, f i) : L) = ∏ i, (f i : L) := by
   classical
@@ -625,89 +358,47 @@ theorem coe_prod {ι : Type _} [Fintype ι] (f : ι → S) : (↑(∏ i, f i) :
 /-! `intermediate_field`s inherit structure from their `subalgebra` coercions. -/
 
 
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 instance module' {R} [Semiring R] [SMul R K] [Module R L] [IsScalarTower R K L] : Module R S :=
   S.toSubalgebra.module'
 #align intermediate_field.module' IntermediateField.module'
 
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 instance module : Module K S :=
   S.toSubalgebra.Module
 #align intermediate_field.module IntermediateField.module
 
-/- warning: intermediate_field.is_scalar_tower -> IntermediateField.isScalarTower is a dubious translation:
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 instance isScalarTower {R} [Semiring R] [SMul R K] [Module R L] [IsScalarTower R K L] :
     IsScalarTower R K S :=
   S.toSubalgebra.IsScalarTower
 #align intermediate_field.is_scalar_tower IntermediateField.isScalarTower
 
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 @[simp]
 theorem coe_smul {R} [Semiring R] [SMul R K] [Module R L] [IsScalarTower R K L] (r : R) (x : S) :
     ↑(r • x) = (r • x : L) :=
   rfl
 #align intermediate_field.coe_smul IntermediateField.coe_smul
 
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 instance algebra' {K'} [CommSemiring K'] [SMul K' K] [Algebra K' L] [IsScalarTower K' K L] :
     Algebra K' S :=
   S.toSubalgebra.algebra'
 #align intermediate_field.algebra' IntermediateField.algebra'
 
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 instance algebra : Algebra K S :=
   S.toSubalgebra.Algebra
 #align intermediate_field.algebra IntermediateField.algebra
 
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 instance toAlgebra {R : Type _} [Semiring R] [Algebra L R] : Algebra S R :=
   S.toSubalgebra.toAlgebra
 #align intermediate_field.to_algebra IntermediateField.toAlgebra
 
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 instance isScalarTower_bot {R : Type _} [Semiring R] [Algebra L R] : IsScalarTower S L R :=
   IsScalarTower.subalgebra _ _ _ S.toSubalgebra
 #align intermediate_field.is_scalar_tower_bot IntermediateField.isScalarTower_bot
 
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 instance isScalarTower_mid {R : Type _} [Semiring R] [Algebra L R] [Algebra K R]
     [IsScalarTower K L R] : IsScalarTower K S R :=
   IsScalarTower.subalgebra' _ _ _ S.toSubalgebra
 #align intermediate_field.is_scalar_tower_mid IntermediateField.isScalarTower_mid
 
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 /-- Specialize `is_scalar_tower_mid` to the common case where the top field is `L` -/
 instance isScalarTower_mid' : IsScalarTower K S L :=
   S.isScalarTower_mid
@@ -725,32 +416,17 @@ def map (f : L →ₐ[K] L') (S : IntermediateField K L) : IntermediateField K L
 #align intermediate_field.map IntermediateField.map
 -/
 
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 @[simp]
 theorem coe_map (f : L →ₐ[K] L') : (S.map f : Set L') = f '' S :=
   rfl
 #align intermediate_field.coe_map IntermediateField.coe_map
 
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 theorem map_map {K L₁ L₂ L₃ : Type _} [Field K] [Field L₁] [Algebra K L₁] [Field L₂] [Algebra K L₂]
     [Field L₃] [Algebra K L₃] (E : IntermediateField K L₁) (f : L₁ →ₐ[K] L₂) (g : L₂ →ₐ[K] L₃) :
     (E.map f).map g = E.map (g.comp f) :=
   SetLike.coe_injective <| Set.image_image _ _ _
 #align intermediate_field.map_map IntermediateField.map_map
 
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-Case conversion may be inaccurate. Consider using '#align intermediate_field.intermediate_field_map IntermediateField.intermediateFieldMapₓ'. -/
 /-- Given an equivalence `e : L ≃ₐ[K] L'` of `K`-field extensions and an intermediate
 field `E` of `L/K`, `intermediate_field_equiv_map e E` is the induced equivalence
 between `E` and `E.map e` -/
@@ -758,9 +434,6 @@ def intermediateFieldMap (e : L ≃ₐ[K] L') (E : IntermediateField K L) : E 
   e.subalgebraMap E.toSubalgebra
 #align intermediate_field.intermediate_field_map IntermediateField.intermediateFieldMap
 
-/- warning: intermediate_field.intermediate_field_map_apply_coe -> IntermediateField.intermediateFieldMap_apply_coe is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align intermediate_field.intermediate_field_map_apply_coe IntermediateField.intermediateFieldMap_apply_coeₓ'. -/
 /- We manually add these two simp lemmas because `@[simps]` before `intermediate_field_map`
   led to a timeout. -/
 @[simp]
@@ -769,9 +442,6 @@ theorem intermediateFieldMap_apply_coe (e : L ≃ₐ[K] L') (E : IntermediateFie
   rfl
 #align intermediate_field.intermediate_field_map_apply_coe IntermediateField.intermediateFieldMap_apply_coe
 
-/- warning: intermediate_field.intermediate_field_map_symm_apply_coe -> IntermediateField.intermediateFieldMap_symm_apply_coe is a dubious translation:
-<too large>
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 @[simp]
 theorem intermediateFieldMap_symm_apply_coe (e : L ≃ₐ[K] L') (E : IntermediateField K L)
     (a : E.map e.toAlgHom) : ↑((intermediateFieldMap e E).symm a) = e.symm a :=
@@ -792,17 +462,11 @@ def fieldRange : IntermediateField K L' :=
 #align alg_hom.field_range AlgHom.fieldRange
 -/
 
-/- warning: alg_hom.coe_field_range -> AlgHom.coe_fieldRange is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align alg_hom.coe_field_range AlgHom.coe_fieldRangeₓ'. -/
 @[simp]
 theorem coe_fieldRange : ↑f.fieldRange = Set.range f :=
   rfl
 #align alg_hom.coe_field_range AlgHom.coe_fieldRange
 
-/- warning: alg_hom.field_range_to_subfield -> AlgHom.fieldRange_toSubfield is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align alg_hom.field_range_to_subfield AlgHom.fieldRange_toSubfieldₓ'. -/
 @[simp]
 theorem fieldRange_toSubfield : f.fieldRange.toSubfield = (f : L →+* L').fieldRange :=
   rfl
@@ -810,9 +474,6 @@ theorem fieldRange_toSubfield : f.fieldRange.toSubfield = (f : L →+* L').field
 
 variable {f}
 
-/- warning: alg_hom.mem_field_range -> AlgHom.mem_fieldRange is a dubious translation:
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 @[simp]
 theorem mem_fieldRange {y : L'} : y ∈ f.fieldRange ↔ ∃ x, f x = y :=
   Iff.rfl
@@ -822,67 +483,34 @@ end AlgHom
 
 namespace IntermediateField
 
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 /-- The embedding from an intermediate field of `L / K` to `L`. -/
 def val : S →ₐ[K] L :=
   S.toSubalgebra.val
 #align intermediate_field.val IntermediateField.val
 
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 @[simp]
 theorem coe_val : ⇑S.val = coe :=
   rfl
 #align intermediate_field.coe_val IntermediateField.coe_val
 
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 @[simp]
 theorem val_mk {x : L} (hx : x ∈ S) : S.val ⟨x, hx⟩ = x :=
   rfl
 #align intermediate_field.val_mk IntermediateField.val_mk
 
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 theorem range_val : S.val.range = S.toSubalgebra :=
   S.toSubalgebra.range_val
 #align intermediate_field.range_val IntermediateField.range_val
 
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 @[simp]
 theorem fieldRange_val : S.val.fieldRange = S :=
   SetLike.ext' Subtype.range_val
 #align intermediate_field.field_range_val IntermediateField.fieldRange_val
 
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 instance AlgHom.inhabited : Inhabited (S →ₐ[K] L) :=
   ⟨S.val⟩
 #align intermediate_field.alg_hom.inhabited IntermediateField.AlgHom.inhabited
 
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 theorem aeval_coe {R : Type _} [CommRing R] [Algebra R K] [Algebra R L] [IsScalarTower R K L]
     (x : S) (P : R[X]) : aeval (x : L) P = aeval x P :=
   by
@@ -892,9 +520,6 @@ theorem aeval_coe {R : Type _} [CommRing R] [Algebra R K] [Algebra R L] [IsScala
     left; rfl
 #align intermediate_field.aeval_coe IntermediateField.aeval_coe
 
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 theorem coe_isIntegral_iff {R : Type _} [CommRing R] [Algebra R K] [Algebra R L]
     [IsScalarTower R K L] {x : S} : IsIntegral R (x : L) ↔ IsIntegral R x :=
   by
@@ -909,12 +534,6 @@ theorem coe_isIntegral_iff {R : Type _} [CommRing R] [Algebra R K] [Algebra R L]
     rw [← aeval_def, aeval_coe, aeval_def, hProot, ZeroMemClass.coe_zero]
 #align intermediate_field.coe_is_integral_iff IntermediateField.coe_isIntegral_iff
 
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 /-- The map `E → F` when `E` is an intermediate field contained in the intermediate field `F`.
 
 This is the intermediate field version of `subalgebra.inclusion`. -/
@@ -922,37 +541,22 @@ def inclusion {E F : IntermediateField K L} (hEF : E ≤ F) : E →ₐ[K] F :=
   Subalgebra.inclusion hEF
 #align intermediate_field.inclusion IntermediateField.inclusion
 
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 theorem inclusion_injective {E F : IntermediateField K L} (hEF : E ≤ F) :
     Function.Injective (inclusion hEF) :=
   Subalgebra.inclusion_injective hEF
 #align intermediate_field.inclusion_injective IntermediateField.inclusion_injective
 
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 @[simp]
 theorem inclusion_self {E : IntermediateField K L} : inclusion (le_refl E) = AlgHom.id K E :=
   Subalgebra.inclusion_self
 #align intermediate_field.inclusion_self IntermediateField.inclusion_self
 
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 @[simp]
 theorem inclusion_inclusion {E F G : IntermediateField K L} (hEF : E ≤ F) (hFG : F ≤ G) (x : E) :
     inclusion hFG (inclusion hEF x) = inclusion (le_trans hEF hFG) x :=
   Subalgebra.inclusion_inclusion hEF hFG x
 #align intermediate_field.inclusion_inclusion IntermediateField.inclusion_inclusion
 
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 @[simp]
 theorem coe_inclusion {E F : IntermediateField K L} (hEF : E ≤ F) (e : E) :
     (inclusion hEF e : L) = e :=
@@ -961,12 +565,6 @@ theorem coe_inclusion {E F : IntermediateField K L} (hEF : E ≤ F) (e : E) :
 
 variable {S}
 
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 theorem toSubalgebra_injective {S S' : IntermediateField K L}
     (h : S.toSubalgebra = S'.toSubalgebra) : S = S' := by ext;
   rw [← mem_to_subalgebra, ← mem_to_subalgebra, h]
@@ -974,44 +572,20 @@ theorem toSubalgebra_injective {S S' : IntermediateField K L}
 
 variable (S)
 
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 theorem set_range_subset : Set.range (algebraMap K L) ⊆ S :=
   S.toSubalgebra.range_subset
 #align intermediate_field.set_range_subset IntermediateField.set_range_subset
 
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 theorem fieldRange_le : (algebraMap K L).fieldRange ≤ S.toSubfield := fun x hx =>
   S.toSubalgebra.range_subset (by rwa [Set.mem_range, ← RingHom.mem_fieldRange])
 #align intermediate_field.field_range_le IntermediateField.fieldRange_le
 
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 @[simp]
 theorem toSubalgebra_le_toSubalgebra {S S' : IntermediateField K L} :
     S.toSubalgebra ≤ S'.toSubalgebra ↔ S ≤ S' :=
   Iff.rfl
 #align intermediate_field.to_subalgebra_le_to_subalgebra IntermediateField.toSubalgebra_le_toSubalgebra
 
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 @[simp]
 theorem toSubalgebra_lt_toSubalgebra {S S' : IntermediateField K L} :
     S.toSubalgebra < S'.toSubalgebra ↔ S < S' :=
@@ -1022,23 +596,11 @@ variable {S}
 
 section Tower
 
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 /-- Lift an intermediate_field of an intermediate_field -/
 def lift {F : IntermediateField K L} (E : IntermediateField K F) : IntermediateField K L :=
   E.map (val F)
 #align intermediate_field.lift IntermediateField.lift
 
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 instance hasLift {F : IntermediateField K L} :
     HasLiftT (IntermediateField K F) (IntermediateField K L) :=
   ⟨lift⟩
@@ -1056,9 +618,6 @@ def restrictScalars (E : IntermediateField L' L) : IntermediateField K L :=
 #align intermediate_field.restrict_scalars IntermediateField.restrictScalars
 -/
 
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 @[simp]
 theorem coe_restrictScalars {E : IntermediateField L' L} :
     (restrictScalars K E : Set L) = (E : Set L) :=
@@ -1081,21 +640,12 @@ theorem restrictScalars_toSubfield {E : IntermediateField L' L} :
 #align intermediate_field.restrict_scalars_to_subfield IntermediateField.restrictScalars_toSubfield
 -/
 
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 @[simp]
 theorem mem_restrictScalars {E : IntermediateField L' L} {x : L} :
     x ∈ restrictScalars K E ↔ x ∈ E :=
   Iff.rfl
 #align intermediate_field.mem_restrict_scalars IntermediateField.mem_restrictScalars
 
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(Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) (Algebra.toModule.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_4)))))], Function.Injective.{succ u2, succ u2} (IntermediateField.{u3, u2} L' L _inst_3 _inst_2 _inst_6) (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (IntermediateField.restrictScalars.{u1, u2, u3} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7)
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-Case conversion may be inaccurate. Consider using '#align intermediate_field.restrict_scalars_injective IntermediateField.restrictScalars_injectiveₓ'. -/
 theorem restrictScalars_injective :
     Function.Injective (restrictScalars K : IntermediateField L' L → IntermediateField K L) :=
   fun U V H => ext fun x => by rw [← mem_restrict_scalars K, H, mem_restrict_scalars]
@@ -1112,22 +662,10 @@ section FiniteDimensional
 
 variable (F E : IntermediateField K L)
 
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-Case conversion may be inaccurate. Consider using '#align intermediate_field.finite_dimensional_left IntermediateField.finiteDimensional_leftₓ'. -/
 instance finiteDimensional_left [FiniteDimensional K L] : FiniteDimensional K F :=
   left K F L
 #align intermediate_field.finite_dimensional_left IntermediateField.finiteDimensional_left
 
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 instance finiteDimensional_right [FiniteDimensional K L] : FiniteDimensional F L :=
   right K F L
 #align intermediate_field.finite_dimensional_right IntermediateField.finiteDimensional_right
@@ -1139,9 +677,6 @@ theorem rank_eq_rank_subalgebra : Module.rank K F.toSubalgebra = Module.rank K F
 #align intermediate_field.rank_eq_rank_subalgebra IntermediateField.rank_eq_rank_subalgebra
 -/
 
-/- warning: intermediate_field.finrank_eq_finrank_subalgebra -> IntermediateField.finrank_eq_finrank_subalgebra is a dubious translation:
-<too large>
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 @[simp]
 theorem finrank_eq_finrank_subalgebra : finrank K F.toSubalgebra = finrank K F :=
   rfl
@@ -1156,26 +691,17 @@ theorem toSubalgebra_eq_iff : F.toSubalgebra = E.toSubalgebra ↔ F = E := by
 #align intermediate_field.to_subalgebra_eq_iff IntermediateField.toSubalgebra_eq_iff
 -/
 
-/- warning: intermediate_field.eq_of_le_of_finrank_le -> IntermediateField.eq_of_le_of_finrank_le is a dubious translation:
-<too large>
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 theorem eq_of_le_of_finrank_le [FiniteDimensional K L] (h_le : F ≤ E)
     (h_finrank : finrank K E ≤ finrank K F) : F = E :=
   toSubalgebra_injective <|
     Subalgebra.toSubmodule.Injective <| eq_of_le_of_finrank_le h_le h_finrank
 #align intermediate_field.eq_of_le_of_finrank_le IntermediateField.eq_of_le_of_finrank_le
 
-/- warning: intermediate_field.eq_of_le_of_finrank_eq -> IntermediateField.eq_of_le_of_finrank_eq is a dubious translation:
-<too large>
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 theorem eq_of_le_of_finrank_eq [FiniteDimensional K L] (h_le : F ≤ E)
     (h_finrank : finrank K F = finrank K E) : F = E :=
   eq_of_le_of_finrank_le h_le h_finrank.ge
 #align intermediate_field.eq_of_le_of_finrank_eq IntermediateField.eq_of_le_of_finrank_eq
 
-/- warning: intermediate_field.eq_of_le_of_finrank_le' -> IntermediateField.eq_of_le_of_finrank_le' is a dubious translation:
-<too large>
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 theorem eq_of_le_of_finrank_le' [FiniteDimensional K L] (h_le : F ≤ E)
     (h_finrank : finrank F L ≤ finrank E L) : F = E :=
   by
@@ -1186,9 +712,6 @@ theorem eq_of_le_of_finrank_le' [FiniteDimensional K L] (h_le : F ≤ E)
   nlinarith
 #align intermediate_field.eq_of_le_of_finrank_le' IntermediateField.eq_of_le_of_finrank_le'
 
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-<too large>
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 theorem eq_of_le_of_finrank_eq' [FiniteDimensional K L] (h_le : F ≤ E)
     (h_finrank : finrank F L = finrank E L) : F = E :=
   eq_of_le_of_finrank_le' h_le h_finrank.le
@@ -1196,32 +719,14 @@ theorem eq_of_le_of_finrank_eq' [FiniteDimensional K L] (h_le : F ≤ E)
 
 end FiniteDimensional
 
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 theorem isAlgebraic_iff {x : S} : IsAlgebraic K x ↔ IsAlgebraic K (x : L) :=
   (isAlgebraic_algebraMap_iff (algebraMap S L).Injective).symm
 #align intermediate_field.is_algebraic_iff IntermediateField.isAlgebraic_iff
 
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 theorem isIntegral_iff {x : S} : IsIntegral K x ↔ IsIntegral K (x : L) := by
   rw [← isAlgebraic_iff_isIntegral, is_algebraic_iff, isAlgebraic_iff_isIntegral]
 #align intermediate_field.is_integral_iff IntermediateField.isIntegral_iff
 
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 theorem minpoly_eq (x : S) : minpoly K x = minpoly K (x : L) :=
   by
   by_cases hx : IsIntegral K x
@@ -1231,12 +736,6 @@ theorem minpoly_eq (x : S) : minpoly K x = minpoly K (x : L) :=
 
 end IntermediateField
 
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-Case conversion may be inaccurate. Consider using '#align subalgebra_equiv_intermediate_field subalgebraEquivIntermediateFieldₓ'. -/
 /-- If `L/K` is algebraic, the `K`-subalgebras of `L` are all fields.  -/
 def subalgebraEquivIntermediateField (alg : Algebra.IsAlgebraic K L) :
     Subalgebra K L ≃o IntermediateField K L
@@ -1248,18 +747,12 @@ def subalgebraEquivIntermediateField (alg : Algebra.IsAlgebraic K L) :
   map_rel_iff' S S' := Iff.rfl
 #align subalgebra_equiv_intermediate_field subalgebraEquivIntermediateField
 
-/- warning: mem_subalgebra_equiv_intermediate_field -> mem_subalgebraEquivIntermediateField is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align mem_subalgebra_equiv_intermediate_field mem_subalgebraEquivIntermediateFieldₓ'. -/
 @[simp]
 theorem mem_subalgebraEquivIntermediateField (alg : Algebra.IsAlgebraic K L) {S : Subalgebra K L}
     {x : L} : x ∈ subalgebraEquivIntermediateField alg S ↔ x ∈ S :=
   Iff.rfl
 #align mem_subalgebra_equiv_intermediate_field mem_subalgebraEquivIntermediateField
 
-/- warning: mem_subalgebra_equiv_intermediate_field_symm -> mem_subalgebraEquivIntermediateField_symm is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align mem_subalgebra_equiv_intermediate_field_symm mem_subalgebraEquivIntermediateField_symmₓ'. -/
 @[simp]
 theorem mem_subalgebraEquivIntermediateField_symm (alg : Algebra.IsAlgebraic K L)
     {S : IntermediateField K L} {x : L} :

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

@@ -74,9 +74,7 @@ def toSubfield : Subfield L :=
 -/
 
 instance : SetLike (IntermediateField K L) L :=
-  ⟨fun S => S.toSubalgebra.carrier, by
-    rintro ⟨⟨⟩⟩ ⟨⟨⟩⟩ ⟨h⟩
-    congr ⟩
+  ⟨fun S => S.toSubalgebra.carrier, by rintro ⟨⟨⟩⟩ ⟨⟨⟩⟩ ⟨h⟩; congr ⟩
 
 instance : SubfieldClass (IntermediateField K L) L
     where
@@ -520,10 +518,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align to_subalgebra_to_intermediate_field toSubalgebra_toIntermediateFieldₓ'. -/
 @[simp]
 theorem toSubalgebra_toIntermediateField (S : Subalgebra K L) (inv_mem : ∀ x ∈ S, x⁻¹ ∈ S) :
-    (S.toIntermediateField inv_mem).toSubalgebra = S :=
-  by
-  ext
-  rfl
+    (S.toIntermediateField inv_mem).toSubalgebra = S := by ext; rfl
 #align to_subalgebra_to_intermediate_field toSubalgebra_toIntermediateField
 
 /- warning: to_intermediate_field_to_subalgebra -> toIntermediateField_toSubalgebra is a dubious translation:
@@ -534,10 +529,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align to_intermediate_field_to_subalgebra toIntermediateField_toSubalgebraₓ'. -/
 @[simp]
 theorem toIntermediateField_toSubalgebra (S : IntermediateField K L) :
-    (S.toSubalgebra.toIntermediateField fun x => S.inv_mem) = S :=
-  by
-  ext
-  rfl
+    (S.toSubalgebra.toIntermediateField fun x => S.inv_mem) = S := by ext; rfl
 #align to_intermediate_field_to_subalgebra toIntermediateField_toSubalgebra
 
 /- warning: subalgebra.to_intermediate_field' -> Subalgebra.toIntermediateField' is a dubious translation:
@@ -566,10 +558,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align to_subalgebra_to_intermediate_field' toSubalgebra_toIntermediateField'ₓ'. -/
 @[simp]
 theorem toSubalgebra_toIntermediateField' (S : Subalgebra K L) (hS : IsField S) :
-    (S.toIntermediateField' hS).toSubalgebra = S :=
-  by
-  ext
-  rfl
+    (S.toIntermediateField' hS).toSubalgebra = S := by ext; rfl
 #align to_subalgebra_to_intermediate_field' toSubalgebra_toIntermediateField'
 
 /- warning: to_intermediate_field'_to_subalgebra -> toIntermediateField'_toSubalgebra is a dubious translation:
@@ -580,10 +569,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align to_intermediate_field'_to_subalgebra toIntermediateField'_toSubalgebraₓ'. -/
 @[simp]
 theorem toIntermediateField'_toSubalgebra (S : IntermediateField K L) :
-    S.toSubalgebra.toIntermediateField' (Field.toIsField S) = S :=
-  by
-  ext
-  rfl
+    S.toSubalgebra.toIntermediateField' (Field.toIsField S) = S := by ext; rfl
 #align to_intermediate_field'_to_subalgebra toIntermediateField'_toSubalgebra
 
 /- warning: subfield.to_intermediate_field -> Subfield.toIntermediateField is a dubious translation:
@@ -734,9 +720,7 @@ def map (f : L →ₐ[K] L') (S : IntermediateField K L) : IntermediateField K L
   {
     S.toSubalgebra.map
       f with
-    inv_mem' := by
-      rintro _ ⟨x, hx, rfl⟩
-      exact ⟨x⁻¹, S.inv_mem hx, map_inv₀ f x⟩
+    inv_mem' := by rintro _ ⟨x, hx, rfl⟩; exact ⟨x⁻¹, S.inv_mem hx, map_inv₀ f x⟩
     neg_mem' := fun x hx => (S.toSubalgebra.map f).neg_mem hx }
 #align intermediate_field.map IntermediateField.map
 -/
@@ -905,8 +889,7 @@ theorem aeval_coe {R : Type _} [CommRing R] [Algebra R K] [Algebra R L] [IsScala
   refine' Polynomial.induction_on' P (fun f g hf hg => _) fun n r => _
   · rw [aeval_add, aeval_add, AddMemClass.coe_add, hf, hg]
   · simp only [MulMemClass.coe_mul, aeval_monomial, SubmonoidClass.coe_pow, mul_eq_mul_right_iff]
-    left
-    rfl
+    left; rfl
 #align intermediate_field.aeval_coe IntermediateField.aeval_coe
 
 /- warning: intermediate_field.coe_is_integral_iff -> IntermediateField.coe_isIntegral_iff is a dubious translation:
@@ -985,9 +968,7 @@ but is expected to have type
   forall {K : Type.{u2}} {L : Type.{u1}} [_inst_1 : Field.{u2} K] [_inst_2 : Field.{u1} L] [_inst_4 : Algebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))] {S : IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4} {S' : IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4}, (Eq.{succ u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (IntermediateField.toSubalgebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 S) (IntermediateField.toSubalgebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 S')) -> (Eq.{succ u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) S S')
 Case conversion may be inaccurate. Consider using '#align intermediate_field.to_subalgebra_injective IntermediateField.toSubalgebra_injectiveₓ'. -/
 theorem toSubalgebra_injective {S S' : IntermediateField K L}
-    (h : S.toSubalgebra = S'.toSubalgebra) : S = S' :=
-  by
-  ext
+    (h : S.toSubalgebra = S'.toSubalgebra) : S = S' := by ext;
   rw [← mem_to_subalgebra, ← mem_to_subalgebra, h]
 #align intermediate_field.to_subalgebra_injective IntermediateField.toSubalgebra_injective
 
@@ -1170,10 +1151,8 @@ variable {F} {E}
 
 #print IntermediateField.toSubalgebra_eq_iff /-
 @[simp]
-theorem toSubalgebra_eq_iff : F.toSubalgebra = E.toSubalgebra ↔ F = E :=
-  by
-  rw [SetLike.ext_iff, SetLike.ext'_iff, Set.ext_iff]
-  rfl
+theorem toSubalgebra_eq_iff : F.toSubalgebra = E.toSubalgebra ↔ F = E := by
+  rw [SetLike.ext_iff, SetLike.ext'_iff, Set.ext_iff]; rfl
 #align intermediate_field.to_subalgebra_eq_iff IntermediateField.toSubalgebra_eq_iff
 -/
 

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

@@ -422,10 +422,7 @@ protected theorem coe_int_mem (n : ℤ) : (n : L) ∈ S :=
 #align intermediate_field.coe_int_mem IntermediateField.coe_int_mem
 
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 Case conversion may be inaccurate. Consider using '#align intermediate_field.coe_add IntermediateField.coe_addₓ'. -/
 protected theorem coe_add (x y : S) : (↑(x + y) : L) = ↑x + ↑y :=
   rfl
@@ -442,10 +439,7 @@ protected theorem coe_neg (x : S) : (↑(-x) : L) = -↑x :=
 #align intermediate_field.coe_neg IntermediateField.coe_neg
 
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 Case conversion may be inaccurate. Consider using '#align intermediate_field.coe_mul IntermediateField.coe_mulₓ'. -/
 protected theorem coe_mul (x y : S) : (↑(x * y) : L) = ↑x * ↑y :=
   rfl
@@ -618,10 +612,7 @@ instance toField : Field S :=
 #align intermediate_field.to_field IntermediateField.toField
 
 /- warning: intermediate_field.coe_sum -> IntermediateField.coe_sum is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align intermediate_field.coe_sum IntermediateField.coe_sumₓ'. -/
 @[simp, norm_cast]
 theorem coe_sum {ι : Type _} [Fintype ι] (f : ι → S) : (↑(∑ i, f i) : L) = ∑ i, (f i : L) := by
@@ -649,10 +640,7 @@ theorem coe_prod {ι : Type _} [Fintype ι] (f : ι → S) : (↑(∏ i, f i) :
 
 
 /- warning: intermediate_field.module' -> IntermediateField.module' is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align intermediate_field.module' IntermediateField.module'ₓ'. -/
 instance module' {R} [Semiring R] [SMul R K] [Module R L] [IsScalarTower R K L] : Module R S :=
   S.toSubalgebra.module'
@@ -669,10 +657,7 @@ instance module : Module K S :=
 #align intermediate_field.module IntermediateField.module
 
 /- warning: intermediate_field.is_scalar_tower -> IntermediateField.isScalarTower is a dubious translation:
-lean 3 declaration is
-  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] (S : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) {R : Type.{u3}} [_inst_6 : Semiring.{u3} R] [_inst_7 : SMul.{u3, u1} R K] [_inst_8 : Module.{u3, u2} R L _inst_6 (AddCommGroup.toAddCommMonoid.{u2} L (NonUnitalNonAssocRing.toAddCommGroup.{u2} L (NonAssocRing.toNonUnitalNonAssocRing.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))] [_inst_9 : IsScalarTower.{u3, u1, u2} R K L _inst_7 (SMulZeroClass.toHasSmul.{u1, u2} K L (AddZeroClass.toHasZero.{u2} L (AddMonoid.toAddZeroClass.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} K L (MulZeroClass.toHasZero.{u1} K (MulZeroOneClass.toMulZeroClass.{u1} K (MonoidWithZero.toMulZeroOneClass.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (AddZeroClass.toHasZero.{u2} L (AddMonoid.toAddZeroClass.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} K L (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (AddZeroClass.toHasZero.{u2} L (AddMonoid.toAddZeroClass.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))))) (Module.toMulActionWithZero.{u1, u2} K L (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) (Algebra.toModule.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_4))))) (SMulZeroClass.toHasSmul.{u3, u2} R L (AddZeroClass.toHasZero.{u2} L (AddMonoid.toAddZeroClass.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (AddCommGroup.toAddCommMonoid.{u2} L (NonUnitalNonAssocRing.toAddCommGroup.{u2} L (NonAssocRing.toNonUnitalNonAssocRing.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))))) (SMulWithZero.toSmulZeroClass.{u3, u2} R L (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_6)))) (AddZeroClass.toHasZero.{u2} L (AddMonoid.toAddZeroClass.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (AddCommGroup.toAddCommMonoid.{u2} L (NonUnitalNonAssocRing.toAddCommGroup.{u2} L (NonAssocRing.toNonUnitalNonAssocRing.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))))) (MulActionWithZero.toSMulWithZero.{u3, u2} R L (Semiring.toMonoidWithZero.{u3} R _inst_6) (AddZeroClass.toHasZero.{u2} L (AddMonoid.toAddZeroClass.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (AddCommGroup.toAddCommMonoid.{u2} L (NonUnitalNonAssocRing.toAddCommGroup.{u2} L (NonAssocRing.toNonUnitalNonAssocRing.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))))) (Module.toMulActionWithZero.{u3, u2} R L _inst_6 (AddCommGroup.toAddCommMonoid.{u2} L (NonUnitalNonAssocRing.toAddCommGroup.{u2} L (NonAssocRing.toNonUnitalNonAssocRing.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) _inst_8))))], IsScalarTower.{u3, u1, u2} R K (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) S) _inst_7 (SMulZeroClass.toHasSmul.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} 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S) (AddCommGroup.toAddCommMonoid.{u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) S) (NonUnitalNonAssocRing.toAddCommGroup.{u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) S) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) S) (Ring.toNonAssocRing.{u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L 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(AddCommMonoid.toAddMonoid.{u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) S) (AddCommGroup.toAddCommMonoid.{u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) S) (NonUnitalNonAssocRing.toAddCommGroup.{u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) S) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K 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(IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) S) (IntermediateField.toField.{u1, u2} K L _inst_1 _inst_2 _inst_4 S)))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) S) (Semiring.toMonoidWithZero.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (AddZeroClass.toHasZero.{u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) S) (AddMonoid.toAddZeroClass.{u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} 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(IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) S) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) S) (Ring.toNonAssocRing.{u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) S) (DivisionRing.toRing.{u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) S) (Field.toDivisionRing.{u2} (coeSort.{succ u2, succ 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_inst_2)))))) _inst_8))))], IsScalarTower.{u3, u1, u2} R K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) _inst_7 (Algebra.toSMul.{u1, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S)) (Subalgebra.algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S))) (SMulZeroClass.toSMul.{u3, u2} R (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (ZeroMemClass.zero.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (CommMonoidWithZero.toZero.{u2} L (CommGroupWithZero.toCommMonoidWithZero.{u2} L (Semifield.toCommGroupWithZero.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (AddSubmonoidClass.toZeroMemClass.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (AddMonoid.toAddZeroClass.{u2} L (AddMonoidWithOne.toAddMonoid.{u2} L (AddGroupWithOne.toAddMonoidWithOne.{u2} L (Ring.toAddGroupWithOne.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SubsemiringClass.toAddSubmonoidClass.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SubringClass.toSubsemiringClass.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)) (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SubfieldClass.toSubringClass.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L _inst_2 (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (IntermediateField.instSubfieldClassIntermediateFieldInstSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4))))) S) (SMulWithZero.toSMulZeroClass.{u3, u2} R (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_6)) (ZeroMemClass.zero.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (CommMonoidWithZero.toZero.{u2} L (CommGroupWithZero.toCommMonoidWithZero.{u2} L (Semifield.toCommGroupWithZero.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (AddSubmonoidClass.toZeroMemClass.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (AddMonoid.toAddZeroClass.{u2} L (AddMonoidWithOne.toAddMonoid.{u2} L (AddGroupWithOne.toAddMonoidWithOne.{u2} L (Ring.toAddGroupWithOne.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SubsemiringClass.toAddSubmonoidClass.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SubringClass.toSubsemiringClass.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)) (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SubfieldClass.toSubringClass.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L _inst_2 (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (IntermediateField.instSubfieldClassIntermediateFieldInstSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4))))) S) (MulActionWithZero.toSMulWithZero.{u3, u2} R (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (Semiring.toMonoidWithZero.{u3} R _inst_6) (ZeroMemClass.zero.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (CommMonoidWithZero.toZero.{u2} L (CommGroupWithZero.toCommMonoidWithZero.{u2} L (Semifield.toCommGroupWithZero.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (AddSubmonoidClass.toZeroMemClass.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (AddMonoid.toAddZeroClass.{u2} L (AddMonoidWithOne.toAddMonoid.{u2} L (AddGroupWithOne.toAddMonoidWithOne.{u2} L (Ring.toAddGroupWithOne.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SubsemiringClass.toAddSubmonoidClass.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SubringClass.toSubsemiringClass.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)) (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SubfieldClass.toSubringClass.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L _inst_2 (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (IntermediateField.instSubfieldClassIntermediateFieldInstSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4))))) S) (Module.toMulActionWithZero.{u3, u2} R (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 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(IntermediateField.module'.{u1, u2, u3} K L _inst_1 _inst_2 _inst_4 S R _inst_6 _inst_7 _inst_8 _inst_9)))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align intermediate_field.is_scalar_tower IntermediateField.isScalarTowerₓ'. -/
 instance isScalarTower {R} [Semiring R] [SMul R K] [Module R L] [IsScalarTower R K L] :
     IsScalarTower R K S :=
@@ -680,10 +665,7 @@ instance isScalarTower {R} [Semiring R] [SMul R K] [Module R L] [IsScalarTower R
 #align intermediate_field.is_scalar_tower IntermediateField.isScalarTower
 
 /- warning: intermediate_field.coe_smul -> IntermediateField.coe_smul is a dubious translation:
-lean 3 declaration is
-  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] (S : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) {R : Type.{u3}} [_inst_6 : Semiring.{u3} R] [_inst_7 : SMul.{u3, u1} R K] [_inst_8 : Module.{u3, u2} R L _inst_6 (AddCommGroup.toAddCommMonoid.{u2} L (NonUnitalNonAssocRing.toAddCommGroup.{u2} L (NonAssocRing.toNonUnitalNonAssocRing.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))] [_inst_9 : IsScalarTower.{u3, u1, u2} R K L _inst_7 (SMulZeroClass.toHasSmul.{u1, u2} K L (AddZeroClass.toHasZero.{u2} L (AddMonoid.toAddZeroClass.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L 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-  forall {K : Type.{u2}} {L : Type.{u1}} [_inst_1 : Field.{u2} K] [_inst_2 : Field.{u1} L] [_inst_4 : Algebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))] (S : IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) {R : Type.{u3}} [_inst_6 : Semiring.{u3} R] [_inst_7 : SMul.{u3, u2} R K] [_inst_8 : Module.{u3, u1} R L _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} L (NonAssocRing.toNonUnitalNonAssocRing.{u1} L (Ring.toNonAssocRing.{u1} L (DivisionRing.toRing.{u1} L (Field.toDivisionRing.{u1} L _inst_2))))))] [_inst_9 : IsScalarTower.{u3, u2, u1} R K L _inst_7 (Algebra.toSMul.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) 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+<too large>
 Case conversion may be inaccurate. Consider using '#align intermediate_field.coe_smul IntermediateField.coe_smulₓ'. -/
 @[simp]
 theorem coe_smul {R} [Semiring R] [SMul R K] [Module R L] [IsScalarTower R K L] (r : R) (x : S) :
@@ -723,20 +705,14 @@ instance toAlgebra {R : Type _} [Semiring R] [Algebra L R] : Algebra S R :=
 #align intermediate_field.to_algebra IntermediateField.toAlgebra
 
 /- warning: intermediate_field.is_scalar_tower_bot -> IntermediateField.isScalarTower_bot is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align intermediate_field.is_scalar_tower_bot IntermediateField.isScalarTower_botₓ'. -/
 instance isScalarTower_bot {R : Type _} [Semiring R] [Algebra L R] : IsScalarTower S L R :=
   IsScalarTower.subalgebra _ _ _ S.toSubalgebra
 #align intermediate_field.is_scalar_tower_bot IntermediateField.isScalarTower_bot
 
 /- warning: intermediate_field.is_scalar_tower_mid -> IntermediateField.isScalarTower_mid is a dubious translation:
-lean 3 declaration is
-  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] (S : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) {R : Type.{u3}} [_inst_6 : Semiring.{u3} R] [_inst_7 : Algebra.{u2, u3} L R (Semifield.toCommSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)) _inst_6] [_inst_8 : Algebra.{u1, u3} K R (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) _inst_6] [_inst_9 : IsScalarTower.{u1, u2, u3} K L R (SMulZeroClass.toHasSmul.{u1, u2} K L (AddZeroClass.toHasZero.{u2} L (AddMonoid.toAddZeroClass.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} K L (MulZeroClass.toHasZero.{u1} K (MulZeroOneClass.toMulZeroClass.{u1} K (MonoidWithZero.toMulZeroOneClass.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (AddZeroClass.toHasZero.{u2} L (AddMonoid.toAddZeroClass.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} K L (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (AddZeroClass.toHasZero.{u2} L (AddMonoid.toAddZeroClass.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))))) (Module.toMulActionWithZero.{u1, u2} K L (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) (Algebra.toModule.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_4))))) (SMulZeroClass.toHasSmul.{u2, u3} L R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_6)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} L R (MulZeroClass.toHasZero.{u2} L (MulZeroOneClass.toMulZeroClass.{u2} L (MonoidWithZero.toMulZeroOneClass.{u2} L (Semiring.toMonoidWithZero.{u2} L (CommSemiring.toSemiring.{u2} L (Semifield.toCommSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))))) (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_6)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} L R (Semiring.toMonoidWithZero.{u2} L (CommSemiring.toSemiring.{u2} L (Semifield.toCommSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_6)))))) (Module.toMulActionWithZero.{u2, u3} L R (CommSemiring.toSemiring.{u2} L (Semifield.toCommSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_6))) (Algebra.toModule.{u2, u3} L R (Semifield.toCommSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)) _inst_6 _inst_7))))) (SMulZeroClass.toHasSmul.{u1, u3} K R (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_6)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} K R (MulZeroClass.toHasZero.{u1} K (MulZeroOneClass.toMulZeroClass.{u1} K (MonoidWithZero.toMulZeroOneClass.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_6)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} K R (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_6)))))) (Module.toMulActionWithZero.{u1, u3} K R (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_6))) (Algebra.toModule.{u1, u3} K R (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) _inst_6 _inst_8)))))], IsScalarTower.{u1, u2, u3} K (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) S) R (SMulZeroClass.toHasSmul.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) S) (AddZeroClass.toHasZero.{u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) 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+<too large>
 Case conversion may be inaccurate. Consider using '#align intermediate_field.is_scalar_tower_mid IntermediateField.isScalarTower_midₓ'. -/
 instance isScalarTower_mid {R : Type _} [Semiring R] [Algebra L R] [Algebra K R]
     [IsScalarTower K L R] : IsScalarTower K S R :=
@@ -744,10 +720,7 @@ instance isScalarTower_mid {R : Type _} [Semiring R] [Algebra L R] [Algebra K R]
 #align intermediate_field.is_scalar_tower_mid IntermediateField.isScalarTower_mid
 
 /- warning: intermediate_field.is_scalar_tower_mid' -> IntermediateField.isScalarTower_mid' is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align intermediate_field.is_scalar_tower_mid' IntermediateField.isScalarTower_mid'ₓ'. -/
 /-- Specialize `is_scalar_tower_mid` to the common case where the top field is `L` -/
 instance isScalarTower_mid' : IsScalarTower K S L :=
@@ -769,10 +742,7 @@ def map (f : L →ₐ[K] L') (S : IntermediateField K L) : IntermediateField K L
 -/
 
 /- warning: intermediate_field.coe_map -> IntermediateField.coe_map is a dubious translation:
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(Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 (AlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5) (AlgHom.algHomClass.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5))))) f) (SetLike.coe.{u2, u2} (IntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) S))
+<too large>
 Case conversion may be inaccurate. Consider using '#align intermediate_field.coe_map IntermediateField.coe_mapₓ'. -/
 @[simp]
 theorem coe_map (f : L →ₐ[K] L') : (S.map f : Set L') = f '' S :=
@@ -805,10 +775,7 @@ def intermediateFieldMap (e : L ≃ₐ[K] L') (E : IntermediateField K L) : E 
 #align intermediate_field.intermediate_field_map IntermediateField.intermediateFieldMap
 
 /- warning: intermediate_field.intermediate_field_map_apply_coe -> IntermediateField.intermediateFieldMap_apply_coe is a dubious translation:
-lean 3 declaration is
-  forall {K : Type.{u1}} {L : Type.{u2}} {L' : Type.{u3}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_3 : Field.{u3} L'] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] [_inst_5 : Algebra.{u1, u3} K L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3)))] (e : AlgEquiv.{u1, u2, u3} K L L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3))) _inst_4 _inst_5) (E : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (a : coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} 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_inst_5 e) E))) (AddCommMonoid.toAddMonoid.{u1} (Subtype.{succ u1} L' (fun (x : L') => Membership.mem.{u1, u1} L' (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) (SetLike.instMembership.{u1, u1} (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.instSetLikeIntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5)) x (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Subtype.{succ u1} L' (fun (x : L') => Membership.mem.{u1, u1} L' (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) (SetLike.instMembership.{u1, u1} 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(Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))) (Subalgebra.toSemiring.{u3, u1} K L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_5 (IntermediateField.toSubalgebra.{u3, u1} K L' _inst_1 _inst_3 _inst_5 (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E)))))))) (DistribSMul.toSMulZeroClass.{u3, u1} K (Subtype.{succ u1} L' (fun (x : L') => 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(DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Subtype.{succ u1} L' (fun (x : L') => Membership.mem.{u1, u1} L' (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) (SetLike.instMembership.{u1, u1} (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.instSetLikeIntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5)) x (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} L' (fun (x : L') => Membership.mem.{u1, u1} L' (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) (SetLike.instMembership.{u1, u1} (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.instSetLikeIntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5)) x (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))) (Subalgebra.toSemiring.{u3, u1} K L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_5 (IntermediateField.toSubalgebra.{u3, u1} K L' _inst_1 _inst_3 _inst_5 (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E)))))))) (DistribMulAction.toDistribSMul.{u3, u1} K (Subtype.{succ u1} L' (fun (x : L') => Membership.mem.{u1, u1} L' (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) (SetLike.instMembership.{u1, u1} (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.instSetLikeIntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5)) x (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))) (MonoidWithZero.toMonoid.{u3} K (Semiring.toMonoidWithZero.{u3} K (CommSemiring.toSemiring.{u3} K (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} (Subtype.{succ u1} L' (fun (x : L') => Membership.mem.{u1, u1} L' (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) (SetLike.instMembership.{u1, u1} (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.instSetLikeIntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5)) x (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Subtype.{succ u1} L' (fun (x : L') => Membership.mem.{u1, u1} L' (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) (SetLike.instMembership.{u1, u1} (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.instSetLikeIntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5)) x (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Subtype.{succ u1} L' (fun (x : L') => Membership.mem.{u1, u1} L' (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) (SetLike.instMembership.{u1, u1} (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.instSetLikeIntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5)) x (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} L' (fun (x : L') => Membership.mem.{u1, u1} L' (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) (SetLike.instMembership.{u1, u1} (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.instSetLikeIntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5)) x (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))) (Subalgebra.toSemiring.{u3, u1} K L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_5 (IntermediateField.toSubalgebra.{u3, u1} K L' _inst_1 _inst_3 _inst_5 (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))))))) (Module.toDistribMulAction.{u3, u1} K (Subtype.{succ u1} L' (fun (x : L') => Membership.mem.{u1, u1} L' (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) (SetLike.instMembership.{u1, u1} (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.instSetLikeIntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5)) x (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))) (CommSemiring.toSemiring.{u3} K (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Subtype.{succ u1} L' (fun (x : L') => Membership.mem.{u1, u1} L' (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) (SetLike.instMembership.{u1, u1} (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.instSetLikeIntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5)) x (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Subtype.{succ u1} L' (fun (x : L') => Membership.mem.{u1, u1} L' (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) (SetLike.instMembership.{u1, u1} (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.instSetLikeIntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5)) x (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} L' (fun (x : L') => Membership.mem.{u1, u1} L' (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) (SetLike.instMembership.{u1, u1} (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.instSetLikeIntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5)) x (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))) (Subalgebra.toSemiring.{u3, u1} K L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_5 (IntermediateField.toSubalgebra.{u3, u1} K L' _inst_1 _inst_3 _inst_5 (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E)))))) (Algebra.toModule.{u3, u1} K (Subtype.{succ u1} L' (fun (x : L') => Membership.mem.{u1, u1} L' (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) (SetLike.instMembership.{u1, u1} (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.instSetLikeIntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5)) x (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L 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_inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))) (IntermediateField.algebra.{u3, u1} K L' _inst_1 _inst_3 _inst_5 (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E)))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u3, u2, u1} (AlgEquiv.{u3, u2, u1} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4)) x E)) (Subtype.{succ u1} L' (fun (x : L') => Membership.mem.{u1, u1} L' (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) (SetLike.instMembership.{u1, u1} (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.instSetLikeIntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5)) x (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))) (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (Subalgebra.toSemiring.{u3, u2} K L (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u3, u2} K L _inst_1 _inst_2 _inst_4 E)) (Subalgebra.toSemiring.{u3, u1} K L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_5 (IntermediateField.toSubalgebra.{u3, u1} K L' _inst_1 _inst_3 _inst_5 (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))) (IntermediateField.algebra.{u3, u2} K L _inst_1 _inst_2 _inst_4 E) (IntermediateField.algebra.{u3, u1} K L' _inst_1 _inst_3 _inst_5 (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))) K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4)) x E)) (Subtype.{succ u1} L' (fun (x : L') => Membership.mem.{u1, u1} L' (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) (SetLike.instMembership.{u1, u1} (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.instSetLikeIntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5)) x (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))) (MonoidWithZero.toMonoid.{u3} K (Semiring.toMonoidWithZero.{u3} K (CommSemiring.toSemiring.{u3} K (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ 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(IntermediateField.toSubalgebra.{u3, u2} K L _inst_1 _inst_2 _inst_4 E)) (Subalgebra.toSemiring.{u3, u1} K L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_5 (IntermediateField.toSubalgebra.{u3, u1} K L' _inst_1 _inst_3 _inst_5 (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))) (IntermediateField.algebra.{u3, u2} K L _inst_1 _inst_2 _inst_4 E) (IntermediateField.algebra.{u3, u1} K L' _inst_1 _inst_3 _inst_5 (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E)) (AlgEquiv.instAlgEquivClassAlgEquiv.{u3, u2, u1} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4)) x E)) (Subtype.{succ u1} L' (fun (x : L') => Membership.mem.{u1, u1} L' (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) (SetLike.instMembership.{u1, u1} (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) L' 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(DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_5 (IntermediateField.toSubalgebra.{u3, u1} K L' _inst_1 _inst_3 _inst_5 (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))) (IntermediateField.algebra.{u3, u2} K L _inst_1 _inst_2 _inst_4 E) (IntermediateField.algebra.{u3, u1} K L' _inst_1 _inst_3 _inst_5 (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E)))))))) (IntermediateField.intermediateFieldMap.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 e E) a)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AlgEquiv.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5) L (fun (_x : L) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : L) => L') _x) (SMulHomClass.toFunLike.{max u2 u1, u3, u2, u1} (AlgEquiv.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5) K L L' (SMulZeroClass.toSMul.{u3, u2} K L (AddMonoid.toZero.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))))) (DistribSMul.toSMulZeroClass.{u3, u2} K L (AddMonoid.toAddZeroClass.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))))) (DistribMulAction.toDistribSMul.{u3, u2} K L (MonoidWithZero.toMonoid.{u3} K 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L' (Semiring.toNonAssocSemiring.{u1} L' (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))))) (Module.toDistribMulAction.{u3, u2} K L (CommSemiring.toSemiring.{u3} K (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (Algebra.toModule.{u3, u2} K L (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4)) (Module.toDistribMulAction.{u3, u1} K L' (CommSemiring.toSemiring.{u3} K (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L' (Semiring.toNonAssocSemiring.{u1} L' (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3)))))) (Algebra.toModule.{u3, u1} K L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, u2, u1, max u2 u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 (AlgEquiv.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5) (AlgEquivClass.toAlgHomClass.{max u2 u1, u3, u2, u1} (AlgEquiv.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5) K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 (AlgEquiv.instAlgEquivClassAlgEquiv.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5)))))) e (Subtype.val.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Set.{u2} L) (Set.instMembershipSet.{u2} L) x (SetLike.coe.{u2, u2} (IntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) E)) a))
+<too large>
 Case conversion may be inaccurate. Consider using '#align intermediate_field.intermediate_field_map_apply_coe IntermediateField.intermediateFieldMap_apply_coeₓ'. -/
 /- We manually add these two simp lemmas because `@[simps]` before `intermediate_field_map`
   led to a timeout. -/
@@ -819,10 +786,7 @@ theorem intermediateFieldMap_apply_coe (e : L ≃ₐ[K] L') (E : IntermediateFie
 #align intermediate_field.intermediate_field_map_apply_coe IntermediateField.intermediateFieldMap_apply_coe
 
 /- warning: intermediate_field.intermediate_field_map_symm_apply_coe -> IntermediateField.intermediateFieldMap_symm_apply_coe is a dubious translation:
-lean 3 declaration is
-  forall {K : Type.{u1}} {L : Type.{u2}} {L' : Type.{u3}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_3 : Field.{u3} L'] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] [_inst_5 : Algebra.{u1, u3} K L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3)))] (e : AlgEquiv.{u1, u2, u3} K L L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3))) _inst_4 _inst_5) (E : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (a : coeSort.{succ u3, succ (succ u3)} (IntermediateField.{u1, u3} K L' _inst_1 _inst_3 _inst_5) 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(DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E)))))))) (DistribMulAction.toDistribSMul.{u3, u1} K (Subtype.{succ u1} L' (fun (x : L') => Membership.mem.{u1, u1} L' (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) (SetLike.instMembership.{u1, u1} (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.instSetLikeIntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5)) x (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))) (MonoidWithZero.toMonoid.{u3} K (Semiring.toMonoidWithZero.{u3} K 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e) E))) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} L' (fun (x : L') => Membership.mem.{u1, u1} L' (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) (SetLike.instMembership.{u1, u1} (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.instSetLikeIntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5)) x (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))) (Subalgebra.toSemiring.{u3, u1} K L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' 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_inst_5 e) E)) (IntermediateField.algebra.{u3, u2} K L _inst_1 _inst_2 _inst_4 E)) K (Subtype.{succ u1} L' (fun (x : L') => Membership.mem.{u1, u1} L' (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) (SetLike.instMembership.{u1, u1} (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.instSetLikeIntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5)) x (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))) (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} 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_inst_2 _inst_4)) x E)) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4)) x E)) (Subalgebra.toSemiring.{u3, u2} K L (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u3, u2} K L _inst_1 _inst_2 _inst_4 E)))) (Module.toDistribMulAction.{u3, u1} K (Subtype.{succ u1} L' (fun (x : L') => Membership.mem.{u1, u1} L' (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) (SetLike.instMembership.{u1, u1} (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.instSetLikeIntermediateField.{u3, u1} K L' _inst_1 _inst_3 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+<too large>
 Case conversion may be inaccurate. Consider using '#align intermediate_field.intermediate_field_map_symm_apply_coe IntermediateField.intermediateFieldMap_symm_apply_coeₓ'. -/
 @[simp]
 theorem intermediateFieldMap_symm_apply_coe (e : L ≃ₐ[K] L') (E : IntermediateField K L)
@@ -845,10 +809,7 @@ def fieldRange : IntermediateField K L' :=
 -/
 
 /- warning: alg_hom.coe_field_range -> AlgHom.coe_fieldRange is a dubious translation:
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-but is expected to have type
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+<too large>
 Case conversion may be inaccurate. Consider using '#align alg_hom.coe_field_range AlgHom.coe_fieldRangeₓ'. -/
 @[simp]
 theorem coe_fieldRange : ↑f.fieldRange = Set.range f :=
@@ -856,10 +817,7 @@ theorem coe_fieldRange : ↑f.fieldRange = Set.range f :=
 #align alg_hom.coe_field_range AlgHom.coe_fieldRange
 
 /- warning: alg_hom.field_range_to_subfield -> AlgHom.fieldRange_toSubfield is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align alg_hom.field_range_to_subfield AlgHom.fieldRange_toSubfieldₓ'. -/
 @[simp]
 theorem fieldRange_toSubfield : f.fieldRange.toSubfield = (f : L →+* L').fieldRange :=
@@ -869,10 +827,7 @@ theorem fieldRange_toSubfield : f.fieldRange.toSubfield = (f : L →+* L').field
 variable {f}
 
 /- warning: alg_hom.mem_field_range -> AlgHom.mem_fieldRange is a dubious translation:
-lean 3 declaration is
-  forall {K : Type.{u1}} {L : Type.{u2}} {L' : Type.{u3}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_3 : Field.{u3} L'] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] [_inst_5 : Algebra.{u1, u3} K L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3)))] {f : AlgHom.{u1, u2, u3} K L L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3))) _inst_4 _inst_5} {y : L'}, Iff (Membership.Mem.{u3, u3} L' (IntermediateField.{u1, u3} K L' _inst_1 _inst_3 _inst_5) (SetLike.hasMem.{u3, u3} (IntermediateField.{u1, u3} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.setLike.{u1, u3} K L' _inst_1 _inst_3 _inst_5)) y (AlgHom.fieldRange.{u1, u2, u3} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 f)) (Exists.{succ u2} L (fun (x : L) => Eq.{succ u3} L' (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} K L L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3))) _inst_4 _inst_5) (fun (_x : AlgHom.{u1, u2, u3} K L L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3))) _inst_4 _inst_5) => L -> L') ([anonymous].{u1, u2, u3} K L L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3))) _inst_4 _inst_5) f x) y))
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_inst_5))))) f x) y))
+<too large>
 Case conversion may be inaccurate. Consider using '#align alg_hom.mem_field_range AlgHom.mem_fieldRangeₓ'. -/
 @[simp]
 theorem mem_fieldRange {y : L'} : y ∈ f.fieldRange ↔ ∃ x, f x = y :=
@@ -895,10 +850,7 @@ def val : S →ₐ[K] L :=
 #align intermediate_field.val IntermediateField.val
 
 /- warning: intermediate_field.coe_val -> IntermediateField.coe_val is a dubious translation:
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_inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S))))) (Algebra.toModule.{u1, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S)) (IntermediateField.algebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S)))))) (SMulZeroClass.toSMul.{u1, u2} K L (AddMonoid.toZero.{u2} L (AddCommMonoid.toAddMonoid.{u2} L 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(IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (IntermediateField.algebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S) _inst_4) K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) L (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (Algebra.toModule.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (IntermediateField.algebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S) _inst_4) K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) L (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K 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 Case conversion may be inaccurate. Consider using '#align intermediate_field.coe_val IntermediateField.coe_valₓ'. -/
 @[simp]
 theorem coe_val : ⇑S.val = coe :=
@@ -906,10 +858,7 @@ theorem coe_val : ⇑S.val = coe :=
 #align intermediate_field.coe_val IntermediateField.coe_val
 
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_inst_4)) x S)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S)))))) (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))))) (Module.toDistribMulAction.{u1, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S))))) (Algebra.toModule.{u1, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S)) (IntermediateField.algebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S))) (Module.toDistribMulAction.{u1, u2} K L (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K 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(Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (IntermediateField.algebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S) _inst_4) K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) L (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (Module.toDistribMulAction.{u1, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S))))) (Algebra.toModule.{u1, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S)) (IntermediateField.algebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S))) (Module.toDistribMulAction.{u1, u2} K L (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (Algebra.toModule.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u2, u2, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (IntermediateField.algebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S) _inst_4 (AlgHom.{u1, u2, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (IntermediateField.algebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S) _inst_4) (AlgHom.algHomClass.{u1, u2, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (IntermediateField.algebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S) _inst_4))))) (IntermediateField.val.{u1, u2} K L _inst_1 _inst_2 _inst_4 S) (Subtype.mk.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S) x hx)) x
+<too large>
 Case conversion may be inaccurate. Consider using '#align intermediate_field.val_mk IntermediateField.val_mkₓ'. -/
 @[simp]
 theorem val_mk {x : L} (hx : x ∈ S) : S.val ⟨x, hx⟩ = x :=
@@ -948,10 +897,7 @@ instance AlgHom.inhabited : Inhabited (S →ₐ[K] L) :=
 #align intermediate_field.alg_hom.inhabited IntermediateField.AlgHom.inhabited
 
 /- warning: intermediate_field.aeval_coe -> IntermediateField.aeval_coe is a dubious translation:
-lean 3 declaration is
-  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] (S : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) {R : Type.{u3}} [_inst_6 : CommRing.{u3} R] [_inst_7 : Algebra.{u3, u1} R K (CommRing.toCommSemiring.{u3} R _inst_6) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))] [_inst_8 : Algebra.{u3, u2} R L (CommRing.toCommSemiring.{u3} R _inst_6) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] [_inst_9 : IsScalarTower.{u3, u1, u2} R K L (SMulZeroClass.toHasSmul.{u3, u1} R K (AddZeroClass.toHasZero.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))))) (SMulWithZero.toSmulZeroClass.{u3, u1} R K (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6)))))) (AddZeroClass.toHasZero.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))))) (MulActionWithZero.toSMulWithZero.{u3, u1} R K (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (AddZeroClass.toHasZero.{u1} K 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_inst_1 _inst_2 _inst_4 S))))))) (DistribMulAction.toDistribSMul.{u3, u1} R (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x S)) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6)))) (AddCommMonoid.toAddMonoid.{u1} (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x S)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K 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_inst_6)))) (AddCommMonoid.toAddMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))))))) (AddCommMonoid.toAddMonoid.{u1} (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x S)) 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(Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) _inst_7) _inst_8 _inst_9)) (AlgHom.algHomClass.{u3, u3, u1} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x S)) (CommRing.toCommSemiring.{u3} R _inst_6) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (Subalgebra.toSemiring.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 S)) 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(Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 S)) (IntermediateField.algebra'.{u2, u1, u3} K L _inst_1 _inst_2 _inst_4 S R (CommRing.toCommSemiring.{u3} R _inst_6) (Algebra.toSMul.{u3, u2} R K (CommRing.toCommSemiring.{u3} R _inst_6) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) _inst_7) _inst_8 _inst_9) x) P))
+<too large>
 Case conversion may be inaccurate. Consider using '#align intermediate_field.aeval_coe IntermediateField.aeval_coeₓ'. -/
 theorem aeval_coe {R : Type _} [CommRing R] [Algebra R K] [Algebra R L] [IsScalarTower R K L]
     (x : S) (P : R[X]) : aeval (x : L) P = aeval x P :=
@@ -964,10 +910,7 @@ theorem aeval_coe {R : Type _} [CommRing R] [Algebra R K] [Algebra R L] [IsScala
 #align intermediate_field.aeval_coe IntermediateField.aeval_coe
 
 /- warning: intermediate_field.coe_is_integral_iff -> IntermediateField.coe_isIntegral_iff is a dubious translation:
-lean 3 declaration is
-  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] (S : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) {R : Type.{u3}} [_inst_6 : CommRing.{u3} R] [_inst_7 : Algebra.{u3, u1} R K (CommRing.toCommSemiring.{u3} R _inst_6) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))] [_inst_8 : Algebra.{u3, u2} R L (CommRing.toCommSemiring.{u3} R _inst_6) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] [_inst_9 : IsScalarTower.{u3, u1, u2} R K L (SMulZeroClass.toHasSmul.{u3, u1} R K (AddZeroClass.toHasZero.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K 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_inst_1))) _inst_7))))) _inst_8 _inst_9) x)
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 Case conversion may be inaccurate. Consider using '#align intermediate_field.coe_is_integral_iff IntermediateField.coe_isIntegral_iffₓ'. -/
 theorem coe_isIntegral_iff {R : Type _} [CommRing R] [Algebra R K] [Algebra R L]
     [IsScalarTower R K L] {x : S} : IsIntegral R (x : L) ↔ IsIntegral R x :=
@@ -997,10 +940,7 @@ def inclusion {E F : IntermediateField K L} (hEF : E ≤ F) : E →ₐ[K] F :=
 #align intermediate_field.inclusion IntermediateField.inclusion
 
 /- warning: intermediate_field.inclusion_injective -> IntermediateField.inclusion_injective is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align intermediate_field.inclusion_injective IntermediateField.inclusion_injectiveₓ'. -/
 theorem inclusion_injective {E F : IntermediateField K L} (hEF : E ≤ F) :
     Function.Injective (inclusion hEF) :=
@@ -1019,10 +959,7 @@ theorem inclusion_self {E : IntermediateField K L} : inclusion (le_refl E) = Alg
 #align intermediate_field.inclusion_self IntermediateField.inclusion_self
 
 /- warning: intermediate_field.inclusion_inclusion -> IntermediateField.inclusion_inclusion is a dubious translation:
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K L _inst_1 _inst_2 _inst_4) (PartialOrder.toPreorder.{u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.partialOrder.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)))) F G) (x : coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) E), Eq.{succ u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) G) (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} K (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} 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(IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (PartialOrder.toPreorder.{u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instPartialOrder.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4))) E F G hEF hFG)) x)
+<too large>
 Case conversion may be inaccurate. Consider using '#align intermediate_field.inclusion_inclusion IntermediateField.inclusion_inclusionₓ'. -/
 @[simp]
 theorem inclusion_inclusion {E F G : IntermediateField K L} (hEF : E ≤ F) (hFG : F ≤ G) (x : E) :
@@ -1031,10 +968,7 @@ theorem inclusion_inclusion {E F G : IntermediateField K L} (hEF : E ≤ F) (hFG
 #align intermediate_field.inclusion_inclusion IntermediateField.inclusion_inclusion
 
 /- warning: intermediate_field.coe_inclusion -> IntermediateField.coe_inclusion is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align intermediate_field.coe_inclusion IntermediateField.coe_inclusionₓ'. -/
 @[simp]
 theorem coe_inclusion {E F : IntermediateField K L} (hEF : E ≤ F) (e : E) :
@@ -1142,10 +1076,7 @@ def restrictScalars (E : IntermediateField L' L) : IntermediateField K L :=
 -/
 
 /- warning: intermediate_field.coe_restrict_scalars -> IntermediateField.coe_restrictScalars is a dubious translation:
-lean 3 declaration is
-  forall (K : Type.{u1}) {L : Type.{u2}} {L' : Type.{u3}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_3 : Field.{u3} L'] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] [_inst_5 : Algebra.{u1, u3} K L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3)))] [_inst_6 : Algebra.{u3, u2} L' L (Semifield.toCommSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] [_inst_7 : IsScalarTower.{u1, u3, u2} K L' L (SMulZeroClass.toHasSmul.{u1, u3} K L' (AddZeroClass.toHasZero.{u3} L' (AddMonoid.toAddZeroClass.{u3} L' (AddCommMonoid.toAddMonoid.{u3} L' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} L' (Semiring.toNonAssocSemiring.{u3} L' (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3))))))))) (SMulWithZero.toSmulZeroClass.{u1, u3} K L' (MulZeroClass.toHasZero.{u1} K (MulZeroOneClass.toMulZeroClass.{u1} K (MonoidWithZero.toMulZeroOneClass.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (AddZeroClass.toHasZero.{u3} L' (AddMonoid.toAddZeroClass.{u3} L' (AddCommMonoid.toAddMonoid.{u3} L' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} L' (Semiring.toNonAssocSemiring.{u3} L' (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3))))))))) (MulActionWithZero.toSMulWithZero.{u1, u3} K L' (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (AddZeroClass.toHasZero.{u3} L' (AddMonoid.toAddZeroClass.{u3} L' (AddCommMonoid.toAddMonoid.{u3} L' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} L' (Semiring.toNonAssocSemiring.{u3} L' (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3))))))))) (Module.toMulActionWithZero.{u1, u3} K L' (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} L' (Semiring.toNonAssocSemiring.{u3} L' (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3)))))) (Algebra.toModule.{u1, u3} K L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3))) _inst_5))))) (SMulZeroClass.toHasSmul.{u3, u2} L' L (AddZeroClass.toHasZero.{u2} L (AddMonoid.toAddZeroClass.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))))) (SMulWithZero.toSmulZeroClass.{u3, u2} L' L (MulZeroClass.toHasZero.{u3} L' (MulZeroOneClass.toMulZeroClass.{u3} L' (MonoidWithZero.toMulZeroOneClass.{u3} L' (Semiring.toMonoidWithZero.{u3} L' (CommSemiring.toSemiring.{u3} L' (Semifield.toCommSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))))))) (AddZeroClass.toHasZero.{u2} L (AddMonoid.toAddZeroClass.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))))) (MulActionWithZero.toSMulWithZero.{u3, u2} L' L (Semiring.toMonoidWithZero.{u3} L' (CommSemiring.toSemiring.{u3} L' (Semifield.toCommSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3)))) (AddZeroClass.toHasZero.{u2} L (AddMonoid.toAddZeroClass.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))))) (Module.toMulActionWithZero.{u3, u2} L' L (CommSemiring.toSemiring.{u3} L' (Semifield.toCommSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) (Algebra.toModule.{u3, u2} L' L (Semifield.toCommSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_6))))) (SMulZeroClass.toHasSmul.{u1, u2} K L (AddZeroClass.toHasZero.{u2} L (AddMonoid.toAddZeroClass.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} K L (MulZeroClass.toHasZero.{u1} K (MulZeroOneClass.toMulZeroClass.{u1} K (MonoidWithZero.toMulZeroOneClass.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (AddZeroClass.toHasZero.{u2} L (AddMonoid.toAddZeroClass.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} K L (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (AddZeroClass.toHasZero.{u2} L (AddMonoid.toAddZeroClass.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))))) (Module.toMulActionWithZero.{u1, u2} K L (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) (Algebra.toModule.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_4)))))] {E : IntermediateField.{u3, u2} L' L _inst_3 _inst_2 _inst_6}, Eq.{succ u2} (Set.{u2} L) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (Set.{u2} L) (HasLiftT.mk.{succ u2, succ u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (Set.{u2} L) (CoeTCₓ.coe.{succ u2, succ u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (Set.{u2} L) (SetLike.Set.hasCoeT.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)))) (IntermediateField.restrictScalars.{u1, u2, u3} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 E)) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (IntermediateField.{u3, u2} L' L _inst_3 _inst_2 _inst_6) (Set.{u2} L) (HasLiftT.mk.{succ u2, succ u2} (IntermediateField.{u3, u2} L' L _inst_3 _inst_2 _inst_6) (Set.{u2} L) (CoeTCₓ.coe.{succ u2, succ u2} (IntermediateField.{u3, u2} L' L _inst_3 _inst_2 _inst_6) (Set.{u2} L) (SetLike.Set.hasCoeT.{u2, u2} (IntermediateField.{u3, u2} L' L _inst_3 _inst_2 _inst_6) L (IntermediateField.setLike.{u3, u2} L' L _inst_3 _inst_2 _inst_6)))) E)
-but is expected to have type
-  forall (K : Type.{u1}) {L : Type.{u2}} {L' : Type.{u3}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_3 : Field.{u3} L'] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))] [_inst_5 : Algebra.{u1, u3} K L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3)))] [_inst_6 : Algebra.{u3, u2} L' L (Semifield.toCommSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))] [_inst_7 : IsScalarTower.{u1, u3, u2} K L' L (Algebra.toSMul.{u1, u3} K L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))) _inst_5) (Algebra.toSMul.{u3, u2} L' L (Semifield.toCommSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_6) (Algebra.toSMul.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4)] {E : IntermediateField.{u3, u2} L' L _inst_3 _inst_2 _inst_6}, Eq.{succ u2} (Set.{u2} L) (SetLike.coe.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (IntermediateField.restrictScalars.{u1, u2, u3} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 E)) (SetLike.coe.{u2, u2} (IntermediateField.{u3, u2} L' L _inst_3 _inst_2 _inst_6) L (IntermediateField.instSetLikeIntermediateField.{u3, u2} L' L _inst_3 _inst_2 _inst_6) E)
+<too large>
 Case conversion may be inaccurate. Consider using '#align intermediate_field.coe_restrict_scalars IntermediateField.coe_restrictScalarsₓ'. -/
 @[simp]
 theorem coe_restrictScalars {E : IntermediateField L' L} :
@@ -1170,10 +1101,7 @@ theorem restrictScalars_toSubfield {E : IntermediateField L' L} :
 -/
 
 /- warning: intermediate_field.mem_restrict_scalars -> IntermediateField.mem_restrictScalars is a dubious translation:
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-  forall (K : Type.{u1}) {L : Type.{u2}} {L' : Type.{u3}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_3 : Field.{u3} L'] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] [_inst_5 : Algebra.{u1, u3} K L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3)))] [_inst_6 : Algebra.{u3, u2} L' L (Semifield.toCommSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] [_inst_7 : IsScalarTower.{u1, u3, u2} K L' L (SMulZeroClass.toHasSmul.{u1, u3} K L' (AddZeroClass.toHasZero.{u3} L' (AddMonoid.toAddZeroClass.{u3} L' (AddCommMonoid.toAddMonoid.{u3} L' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} L' (Semiring.toNonAssocSemiring.{u3} L' (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3))))))))) (SMulWithZero.toSmulZeroClass.{u1, u3} K L' (MulZeroClass.toHasZero.{u1} K (MulZeroOneClass.toMulZeroClass.{u1} K (MonoidWithZero.toMulZeroOneClass.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (AddZeroClass.toHasZero.{u3} L' (AddMonoid.toAddZeroClass.{u3} L' (AddCommMonoid.toAddMonoid.{u3} L' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} L' (Semiring.toNonAssocSemiring.{u3} L' (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3))))))))) (MulActionWithZero.toSMulWithZero.{u1, u3} K L' (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (AddZeroClass.toHasZero.{u3} L' (AddMonoid.toAddZeroClass.{u3} L' (AddCommMonoid.toAddMonoid.{u3} L' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} L' (Semiring.toNonAssocSemiring.{u3} L' (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3))))))))) (Module.toMulActionWithZero.{u1, u3} K L' (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} L' (Semiring.toNonAssocSemiring.{u3} L' (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3)))))) (Algebra.toModule.{u1, u3} K L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3))) _inst_5))))) (SMulZeroClass.toHasSmul.{u3, u2} L' L (AddZeroClass.toHasZero.{u2} L (AddMonoid.toAddZeroClass.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))))) (SMulWithZero.toSmulZeroClass.{u3, u2} L' L (MulZeroClass.toHasZero.{u3} L' (MulZeroOneClass.toMulZeroClass.{u3} L' (MonoidWithZero.toMulZeroOneClass.{u3} L' (Semiring.toMonoidWithZero.{u3} L' (CommSemiring.toSemiring.{u3} L' (Semifield.toCommSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))))))) (AddZeroClass.toHasZero.{u2} L (AddMonoid.toAddZeroClass.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))))) (MulActionWithZero.toSMulWithZero.{u3, u2} L' L (Semiring.toMonoidWithZero.{u3} L' (CommSemiring.toSemiring.{u3} L' (Semifield.toCommSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3)))) (AddZeroClass.toHasZero.{u2} L (AddMonoid.toAddZeroClass.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))))) (Module.toMulActionWithZero.{u3, u2} L' L (CommSemiring.toSemiring.{u3} L' (Semifield.toCommSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) (Algebra.toModule.{u3, u2} L' L (Semifield.toCommSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_6))))) (SMulZeroClass.toHasSmul.{u1, u2} K L (AddZeroClass.toHasZero.{u2} L (AddMonoid.toAddZeroClass.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} K L (MulZeroClass.toHasZero.{u1} K (MulZeroOneClass.toMulZeroClass.{u1} K (MonoidWithZero.toMulZeroOneClass.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (AddZeroClass.toHasZero.{u2} L (AddMonoid.toAddZeroClass.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} K L (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (AddZeroClass.toHasZero.{u2} L (AddMonoid.toAddZeroClass.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))))) (Module.toMulActionWithZero.{u1, u2} K L (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) (Algebra.toModule.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_4)))))] {E : IntermediateField.{u3, u2} L' L _inst_3 _inst_2 _inst_6} {x : L}, Iff (Membership.Mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.hasMem.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x (IntermediateField.restrictScalars.{u1, u2, u3} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 E)) (Membership.Mem.{u2, u2} L (IntermediateField.{u3, u2} L' L _inst_3 _inst_2 _inst_6) (SetLike.hasMem.{u2, u2} (IntermediateField.{u3, u2} L' L _inst_3 _inst_2 _inst_6) L (IntermediateField.setLike.{u3, u2} L' L _inst_3 _inst_2 _inst_6)) x E)
-but is expected to have type
-  forall (K : Type.{u1}) {L : Type.{u2}} {L' : Type.{u3}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_3 : Field.{u3} L'] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))] [_inst_5 : Algebra.{u1, u3} K L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3)))] [_inst_6 : Algebra.{u3, u2} L' L (Semifield.toCommSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))] [_inst_7 : IsScalarTower.{u1, u3, u2} K L' L (Algebra.toSMul.{u1, u3} K L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))) _inst_5) (Algebra.toSMul.{u3, u2} L' L (Semifield.toCommSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_6) (Algebra.toSMul.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4)] {E : IntermediateField.{u3, u2} L' L _inst_3 _inst_2 _inst_6} {x : L}, Iff (Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x (IntermediateField.restrictScalars.{u1, u2, u3} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 E)) (Membership.mem.{u2, u2} L (IntermediateField.{u3, u2} L' L _inst_3 _inst_2 _inst_6) (SetLike.instMembership.{u2, u2} (IntermediateField.{u3, u2} L' L _inst_3 _inst_2 _inst_6) L (IntermediateField.instSetLikeIntermediateField.{u3, u2} L' L _inst_3 _inst_2 _inst_6)) x E)
+<too large>
 Case conversion may be inaccurate. Consider using '#align intermediate_field.mem_restrict_scalars IntermediateField.mem_restrictScalarsₓ'. -/
 @[simp]
 theorem mem_restrictScalars {E : IntermediateField L' L} {x : L} :
@@ -1231,10 +1159,7 @@ theorem rank_eq_rank_subalgebra : Module.rank K F.toSubalgebra = Module.rank K F
 -/
 
 /- warning: intermediate_field.finrank_eq_finrank_subalgebra -> IntermediateField.finrank_eq_finrank_subalgebra is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align intermediate_field.finrank_eq_finrank_subalgebra IntermediateField.finrank_eq_finrank_subalgebraₓ'. -/
 @[simp]
 theorem finrank_eq_finrank_subalgebra : finrank K F.toSubalgebra = finrank K F :=
@@ -1253,10 +1178,7 @@ theorem toSubalgebra_eq_iff : F.toSubalgebra = E.toSubalgebra ↔ F = E :=
 -/
 
 /- warning: intermediate_field.eq_of_le_of_finrank_le -> IntermediateField.eq_of_le_of_finrank_le is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align intermediate_field.eq_of_le_of_finrank_le IntermediateField.eq_of_le_of_finrank_leₓ'. -/
 theorem eq_of_le_of_finrank_le [FiniteDimensional K L] (h_le : F ≤ E)
     (h_finrank : finrank K E ≤ finrank K F) : F = E :=
@@ -1265,10 +1187,7 @@ theorem eq_of_le_of_finrank_le [FiniteDimensional K L] (h_le : F ≤ E)
 #align intermediate_field.eq_of_le_of_finrank_le IntermediateField.eq_of_le_of_finrank_le
 
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 Case conversion may be inaccurate. Consider using '#align intermediate_field.eq_of_le_of_finrank_eq IntermediateField.eq_of_le_of_finrank_eqₓ'. -/
 theorem eq_of_le_of_finrank_eq [FiniteDimensional K L] (h_le : F ≤ E)
     (h_finrank : finrank K F = finrank K E) : F = E :=
@@ -1276,10 +1195,7 @@ theorem eq_of_le_of_finrank_eq [FiniteDimensional K L] (h_le : F ≤ E)
 #align intermediate_field.eq_of_le_of_finrank_eq IntermediateField.eq_of_le_of_finrank_eq
 
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 Case conversion may be inaccurate. Consider using '#align intermediate_field.eq_of_le_of_finrank_le' IntermediateField.eq_of_le_of_finrank_le'ₓ'. -/
 theorem eq_of_le_of_finrank_le' [FiniteDimensional K L] (h_le : F ≤ E)
     (h_finrank : finrank F L ≤ finrank E L) : F = E :=
@@ -1292,10 +1208,7 @@ theorem eq_of_le_of_finrank_le' [FiniteDimensional K L] (h_le : F ≤ E)
 #align intermediate_field.eq_of_le_of_finrank_le' IntermediateField.eq_of_le_of_finrank_le'
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align intermediate_field.eq_of_le_of_finrank_eq' IntermediateField.eq_of_le_of_finrank_eq'ₓ'. -/
 theorem eq_of_le_of_finrank_eq' [FiniteDimensional K L] (h_le : F ≤ E)
     (h_finrank : finrank F L = finrank E L) : F = E :=
@@ -1357,10 +1270,7 @@ def subalgebraEquivIntermediateField (alg : Algebra.IsAlgebraic K L) :
 #align subalgebra_equiv_intermediate_field subalgebraEquivIntermediateField
 
 /- warning: mem_subalgebra_equiv_intermediate_field -> mem_subalgebraEquivIntermediateField is a dubious translation:
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(Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (Algebra.instCompleteLatticeSubalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) => LE.le.{u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (Preorder.toLE.{u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (PartialOrder.toPreorder.{u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instPartialOrder.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (fun (_x : Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) => IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (RelHomClass.toFunLike.{u1, u1, u1} (RelIso.{u1, u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) => LE.le.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (Algebra.instCompleteLatticeSubalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) => LE.le.{u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (Preorder.toLE.{u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (PartialOrder.toPreorder.{u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instPartialOrder.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) => LE.le.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (Algebra.instCompleteLatticeSubalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) => LE.le.{u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (Preorder.toLE.{u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (PartialOrder.toPreorder.{u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instPartialOrder.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{u1, u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) => LE.le.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (Algebra.instCompleteLatticeSubalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) => LE.le.{u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (Preorder.toLE.{u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (PartialOrder.toPreorder.{u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instPartialOrder.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) (subalgebraEquivIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4 alg) S)) (Membership.mem.{u1, u1} L (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) L (Subalgebra.instSetLikeSubalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4)) x S)
+<too large>
 Case conversion may be inaccurate. Consider using '#align mem_subalgebra_equiv_intermediate_field mem_subalgebraEquivIntermediateFieldₓ'. -/
 @[simp]
 theorem mem_subalgebraEquivIntermediateField (alg : Algebra.IsAlgebraic K L) {S : Subalgebra K L}
@@ -1369,10 +1279,7 @@ theorem mem_subalgebraEquivIntermediateField (alg : Algebra.IsAlgebraic K L) {S
 #align mem_subalgebra_equiv_intermediate_field mem_subalgebraEquivIntermediateField
 
 /- warning: mem_subalgebra_equiv_intermediate_field_symm -> mem_subalgebraEquivIntermediateField_symm is a dubious translation:
-lean 3 declaration is
-  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] (alg : Algebra.IsAlgebraic.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)) _inst_4) {S : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4} {x : L}, Iff (Membership.Mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_4) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_4) L (Subalgebra.setLike.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_4)) x (coeFn.{succ u2, succ u2} (OrderIso.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_4) (Preorder.toHasLe.{u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (PartialOrder.toPreorder.{u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.partialOrder.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)))) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_4) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_4) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_4) L (Subalgebra.setLike.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_4))))) (fun (_x : RelIso.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_4) (LE.le.{u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (Preorder.toHasLe.{u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (PartialOrder.toPreorder.{u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.partialOrder.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4))))) (LE.le.{u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_4) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_4) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L 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(Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_4) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_4) L (Subalgebra.setLike.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_4)))))) (OrderIso.symm.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_4) (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L 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K L _inst_1 _inst_2 _inst_4)))) (subalgebraEquivIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4 alg)) S)) (Membership.Mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.hasMem.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)
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(DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) 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(DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) => LE.le.{u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (Preorder.toLE.{u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (PartialOrder.toPreorder.{u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instPartialOrder.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) => LE.le.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (Algebra.instCompleteLatticeSubalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) => LE.le.{u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (Preorder.toLE.{u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (PartialOrder.toPreorder.{u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instPartialOrder.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) => LE.le.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (Algebra.instCompleteLatticeSubalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) => LE.le.{u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (Preorder.toLE.{u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (PartialOrder.toPreorder.{u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instPartialOrder.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) => LE.le.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (Algebra.instCompleteLatticeSubalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) (OrderIso.symm.{u1, u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (Algebra.instCompleteLatticeSubalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4))))) (Preorder.toLE.{u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (PartialOrder.toPreorder.{u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instPartialOrder.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)))) (subalgebraEquivIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4 alg)) S)) (Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x S)
+<too large>
 Case conversion may be inaccurate. Consider using '#align mem_subalgebra_equiv_intermediate_field_symm mem_subalgebraEquivIntermediateField_symmₓ'. -/
 @[simp]
 theorem mem_subalgebraEquivIntermediateField_symm (alg : Algebra.IsAlgebraic K L)

mathlib commit https://github.com/leanprover-community/mathlib/commit/ef95945cd48c932c9e034872bd25c3c220d9c946

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Anne Baanen
 
 ! This file was ported from Lean 3 source module field_theory.intermediate_field
-! leanprover-community/mathlib commit c596622fccd6e0321979d94931c964054dea2d26
+! leanprover-community/mathlib commit 61db041ab8e4aaf8cb5c7dc10a7d4ff261997536
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -15,6 +15,9 @@ import Mathbin.FieldTheory.Tower
 /-!
 # Intermediate fields
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 Let `L / K` be a field extension, given as an instance `algebra K L`.
 This file defines the type of fields in between `K` and `L`, `intermediate_field K L`.
 An `intermediate_field K L` is a subfield of `L` which contains (the image of) `K`,

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

@@ -769,7 +769,7 @@ def map (f : L →ₐ[K] L') (S : IntermediateField K L) : IntermediateField K L
 lean 3 declaration is
   forall {K : Type.{u1}} {L : Type.{u2}} {L' : Type.{u3}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_3 : Field.{u3} L'] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] [_inst_5 : Algebra.{u1, u3} K L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3)))] (S : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (f : AlgHom.{u1, u2, u3} K L L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3))) _inst_4 _inst_5), Eq.{succ u3} (Set.{u3} L') ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (IntermediateField.{u1, u3} K L' _inst_1 _inst_3 _inst_5) (Set.{u3} L') (HasLiftT.mk.{succ u3, succ u3} (IntermediateField.{u1, u3} K L' _inst_1 _inst_3 _inst_5) (Set.{u3} L') (CoeTCₓ.coe.{succ u3, succ u3} (IntermediateField.{u1, u3} K L' _inst_1 _inst_3 _inst_5) (Set.{u3} L') (SetLike.Set.hasCoeT.{u3, u3} (IntermediateField.{u1, u3} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.setLike.{u1, u3} K L' _inst_1 _inst_3 _inst_5)))) (IntermediateField.map.{u1, u2, u3} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 f S)) (Set.image.{u2, u3} L L' (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} K L L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3))) _inst_4 _inst_5) (fun (_x : AlgHom.{u1, u2, u3} K L L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3))) _inst_4 _inst_5) => L -> L') ([anonymous].{u1, u2, u3} K L L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3))) _inst_4 _inst_5) f) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (Set.{u2} L) (HasLiftT.mk.{succ u2, succ u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (Set.{u2} L) (CoeTCₓ.coe.{succ u2, succ u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (Set.{u2} L) (SetLike.Set.hasCoeT.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)))) S))
 but is expected to have type
-  forall {K : Type.{u3}} {L : Type.{u2}} {L' : Type.{u1}} [_inst_1 : Field.{u3} K] [_inst_2 : Field.{u2} L] [_inst_3 : Field.{u1} L'] [_inst_4 : Algebra.{u3, u2} K L (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))] [_inst_5 : Algebra.{u3, u1} K L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3)))] (S : IntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) (f : AlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5), Eq.{succ u1} (Set.{u1} L') (SetLike.coe.{u1, u1} (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.instSetLikeIntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 f S)) (Set.image.{u2, u1} L L' (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5) L (fun (_x : L) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : L) => L') _x) (SMulHomClass.toFunLike.{max u2 u1, u3, u2, u1} (AlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5) K L L' (SMulZeroClass.toSMul.{u3, u2} K L (AddMonoid.toZero.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))))) (DistribSMul.toSMulZeroClass.{u3, u2} K L (AddMonoid.toAddZeroClass.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))))) (DistribMulAction.toDistribSMul.{u3, u2} K L (MonoidWithZero.toMonoid.{u3} K (Semiring.toMonoidWithZero.{u3} K (CommSemiring.toSemiring.{u3} K (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))))) (Module.toDistribMulAction.{u3, u2} K L (CommSemiring.toSemiring.{u3} K (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (Algebra.toModule.{u3, u2} K L (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4))))) (SMulZeroClass.toSMul.{u3, u1} K L' (AddMonoid.toZero.{u1} L' (AddCommMonoid.toAddMonoid.{u1} L' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L' (Semiring.toNonAssocSemiring.{u1} L' (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3)))))))) (DistribSMul.toSMulZeroClass.{u3, u1} K L' (AddMonoid.toAddZeroClass.{u1} L' (AddCommMonoid.toAddMonoid.{u1} L' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L' (Semiring.toNonAssocSemiring.{u1} L' (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3)))))))) (DistribMulAction.toDistribSMul.{u3, u1} K L' (MonoidWithZero.toMonoid.{u3} K (Semiring.toMonoidWithZero.{u3} K (CommSemiring.toSemiring.{u3} K (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} L' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L' (Semiring.toNonAssocSemiring.{u1} L' (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))))))) (Module.toDistribMulAction.{u3, u1} K L' (CommSemiring.toSemiring.{u3} K (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L' (Semiring.toNonAssocSemiring.{u1} L' (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3)))))) (Algebra.toModule.{u3, u1} K L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u3, u2, u1} (AlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5) K L L' (MonoidWithZero.toMonoid.{u3} K (Semiring.toMonoidWithZero.{u3} K (CommSemiring.toSemiring.{u3} K (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))))) (AddCommMonoid.toAddMonoid.{u1} L' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L' (Semiring.toNonAssocSemiring.{u1} L' (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))))))) (Module.toDistribMulAction.{u3, u2} K L (CommSemiring.toSemiring.{u3} K (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (Algebra.toModule.{u3, u2} K L (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4)) (Module.toDistribMulAction.{u3, u1} K L' (CommSemiring.toSemiring.{u3} K (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L' (Semiring.toNonAssocSemiring.{u1} L' (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3)))))) (Algebra.toModule.{u3, u1} K L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_5)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u3, u2, u1} (AlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5) K L L' (MonoidWithZero.toMonoid.{u3} K (Semiring.toMonoidWithZero.{u3} K (CommSemiring.toSemiring.{u3} K (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L' (Semiring.toNonAssocSemiring.{u1} L' (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))))) (Module.toDistribMulAction.{u3, u2} K L (CommSemiring.toSemiring.{u3} K (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (Algebra.toModule.{u3, u2} K L (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4)) (Module.toDistribMulAction.{u3, u1} K L' (CommSemiring.toSemiring.{u3} K (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L' (Semiring.toNonAssocSemiring.{u1} L' (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3)))))) (Algebra.toModule.{u3, u1} K L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, u2, u1, max u2 u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 (AlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5) (AlgHom.algHomClass.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5))))) f) (SetLike.coe.{u2, u2} (IntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) S))
+  forall {K : Type.{u3}} {L : Type.{u2}} {L' : Type.{u1}} [_inst_1 : Field.{u3} K] [_inst_2 : Field.{u2} L] [_inst_3 : Field.{u1} L'] [_inst_4 : Algebra.{u3, u2} K L (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))] [_inst_5 : Algebra.{u3, u1} K L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3)))] (S : IntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) (f : AlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5), Eq.{succ u1} (Set.{u1} L') (SetLike.coe.{u1, u1} (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.instSetLikeIntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 f S)) (Set.image.{u2, u1} L L' (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5) L (fun (_x : L) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : L) => L') _x) (SMulHomClass.toFunLike.{max u2 u1, u3, u2, u1} (AlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5) K L L' (SMulZeroClass.toSMul.{u3, u2} K L (AddMonoid.toZero.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))))) (DistribSMul.toSMulZeroClass.{u3, u2} K L (AddMonoid.toAddZeroClass.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))))) (DistribMulAction.toDistribSMul.{u3, u2} K L (MonoidWithZero.toMonoid.{u3} K (Semiring.toMonoidWithZero.{u3} K (CommSemiring.toSemiring.{u3} K (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))))) (Module.toDistribMulAction.{u3, u2} K L (CommSemiring.toSemiring.{u3} K (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (Algebra.toModule.{u3, u2} K L (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4))))) (SMulZeroClass.toSMul.{u3, u1} K L' (AddMonoid.toZero.{u1} L' (AddCommMonoid.toAddMonoid.{u1} L' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L' (Semiring.toNonAssocSemiring.{u1} L' (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3)))))))) (DistribSMul.toSMulZeroClass.{u3, u1} K L' (AddMonoid.toAddZeroClass.{u1} L' (AddCommMonoid.toAddMonoid.{u1} L' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L' (Semiring.toNonAssocSemiring.{u1} L' (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3)))))))) (DistribMulAction.toDistribSMul.{u3, u1} K L' (MonoidWithZero.toMonoid.{u3} K (Semiring.toMonoidWithZero.{u3} K (CommSemiring.toSemiring.{u3} K (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} L' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L' (Semiring.toNonAssocSemiring.{u1} L' (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))))))) (Module.toDistribMulAction.{u3, u1} K L' (CommSemiring.toSemiring.{u3} K (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L' (Semiring.toNonAssocSemiring.{u1} L' (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3)))))) (Algebra.toModule.{u3, u1} K L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u3, u2, u1} (AlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5) K L L' (MonoidWithZero.toMonoid.{u3} K (Semiring.toMonoidWithZero.{u3} K (CommSemiring.toSemiring.{u3} K (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))))) (AddCommMonoid.toAddMonoid.{u1} L' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L' (Semiring.toNonAssocSemiring.{u1} L' (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))))))) (Module.toDistribMulAction.{u3, u2} K L (CommSemiring.toSemiring.{u3} K (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (Algebra.toModule.{u3, u2} K L (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4)) (Module.toDistribMulAction.{u3, u1} K L' (CommSemiring.toSemiring.{u3} K (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L' (Semiring.toNonAssocSemiring.{u1} L' (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3)))))) (Algebra.toModule.{u3, u1} K L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_5)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u3, u2, u1} (AlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5) K L L' (MonoidWithZero.toMonoid.{u3} K (Semiring.toMonoidWithZero.{u3} K (CommSemiring.toSemiring.{u3} K (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L' (Semiring.toNonAssocSemiring.{u1} L' (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))))) (Module.toDistribMulAction.{u3, u2} K L (CommSemiring.toSemiring.{u3} K (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (Algebra.toModule.{u3, u2} K L (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4)) (Module.toDistribMulAction.{u3, u1} K L' (CommSemiring.toSemiring.{u3} K (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L' (Semiring.toNonAssocSemiring.{u1} L' (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3)))))) (Algebra.toModule.{u3, u1} K L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, u2, u1, max u2 u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 (AlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5) (AlgHom.algHomClass.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5))))) f) (SetLike.coe.{u2, u2} (IntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) S))
 Case conversion may be inaccurate. Consider using '#align intermediate_field.coe_map IntermediateField.coe_mapₓ'. -/
 @[simp]
 theorem coe_map (f : L →ₐ[K] L') : (S.map f : Set L') = f '' S :=
@@ -805,7 +805,7 @@ def intermediateFieldMap (e : L ≃ₐ[K] L') (E : IntermediateField K L) : E 
 lean 3 declaration is
   forall {K : Type.{u1}} {L : Type.{u2}} {L' : Type.{u3}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_3 : Field.{u3} L'] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] [_inst_5 : Algebra.{u1, u3} K L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3)))] (e : AlgEquiv.{u1, u2, u3} K L L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3))) _inst_4 _inst_5) (E : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (a : coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) E), Eq.{succ u3} L' ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (coeSort.{succ u3, succ (succ u3)} (IntermediateField.{u1, u3} K L' _inst_1 _inst_3 _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (IntermediateField.{u1, u3} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.setLike.{u1, u3} K L' _inst_1 _inst_3 _inst_5)) (IntermediateField.map.{u1, u2, u3} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u1, u2, u3} K L L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3))) _inst_4 _inst_5 e) E)) L' (HasLiftT.mk.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (IntermediateField.{u1, u3} K L' _inst_1 _inst_3 _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (IntermediateField.{u1, u3} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.setLike.{u1, u3} K L' _inst_1 _inst_3 _inst_5)) (IntermediateField.map.{u1, u2, u3} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u1, u2, u3} K L L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3))) _inst_4 _inst_5 e) E)) L' (CoeTCₓ.coe.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (IntermediateField.{u1, u3} K L' _inst_1 _inst_3 _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (IntermediateField.{u1, u3} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.setLike.{u1, u3} K L' _inst_1 _inst_3 _inst_5)) (IntermediateField.map.{u1, u2, u3} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u1, u2, u3} K L L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3))) _inst_4 _inst_5 e) E)) L' (coeBase.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (IntermediateField.{u1, u3} K L' _inst_1 _inst_3 _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (IntermediateField.{u1, u3} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.setLike.{u1, u3} K L' _inst_1 _inst_3 _inst_5)) (IntermediateField.map.{u1, u2, u3} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u1, u2, u3} K L L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3))) _inst_4 _inst_5 e) E)) L' (coeSubtype.{succ u3} L' (fun (x : L') => Membership.Mem.{u3, u3} L' (IntermediateField.{u1, u3} K L' _inst_1 _inst_3 _inst_5) (SetLike.hasMem.{u3, u3} (IntermediateField.{u1, u3} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.setLike.{u1, u3} K L' _inst_1 _inst_3 _inst_5)) x (IntermediateField.map.{u1, u2, u3} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u1, u2, u3} K L L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3))) _inst_4 _inst_5 e) E)))))) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgEquiv.{u1, u2, u3} K (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) E) (coeSort.{succ u3, succ (succ u3)} (IntermediateField.{u1, u3} K L' _inst_1 _inst_3 _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (IntermediateField.{u1, u3} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.setLike.{u1, u3} K L' _inst_1 _inst_3 _inst_5)) (IntermediateField.map.{u1, u2, u3} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u1, u2, u3} K L L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3))) _inst_4 _inst_5 e) E)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) E) (DivisionRing.toRing.{u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) E) (Field.toDivisionRing.{u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) E) (IntermediateField.toField.{u1, u2} K L _inst_1 _inst_2 _inst_4 E)))) (Ring.toSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (IntermediateField.{u1, u3} K L' _inst_1 _inst_3 _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (IntermediateField.{u1, u3} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.setLike.{u1, u3} K L' _inst_1 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(IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) E) L (coeSubtype.{succ u2} L (fun (x : L) => Membership.Mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.hasMem.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x E))))) a))
 but is expected to have type
-  forall {K : Type.{u3}} {L : Type.{u2}} {L' : Type.{u1}} [_inst_1 : Field.{u3} K] [_inst_2 : Field.{u2} L] [_inst_3 : Field.{u1} L'] [_inst_4 : Algebra.{u3, u2} K L (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))] [_inst_5 : Algebra.{u3, u1} K L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3)))] (e : AlgEquiv.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5) (E : IntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) (a : Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4)) x E)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : L) => L') (Subtype.val.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Set.{u2} L) (Set.instMembershipSet.{u2} L) x (SetLike.coe.{u2, u2} (IntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) E)) a)) (Subtype.val.{succ u1} L' (fun (x : L') => Membership.mem.{u1, u1} L' (Set.{u1} L') (Set.instMembershipSet.{u1} L') x (SetLike.coe.{u1, u1} (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.instSetLikeIntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AlgEquiv.{u3, u2, u1} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4)) x E)) (Subtype.{succ u1} L' (fun (x : L') => Membership.mem.{u1, u1} L' (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) (SetLike.instMembership.{u1, u1} (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.instSetLikeIntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5)) x (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))) (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (Subalgebra.toSemiring.{u3, u2} K L (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u3, u2} K L _inst_1 _inst_2 _inst_4 E)) (Subalgebra.toSemiring.{u3, u1} K L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_5 (IntermediateField.toSubalgebra.{u3, u1} K L' _inst_1 _inst_3 _inst_5 (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))) (IntermediateField.algebra.{u3, u2} K L _inst_1 _inst_2 _inst_4 E) (IntermediateField.algebra.{u3, u1} K L' _inst_1 _inst_3 _inst_5 (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))) (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4)) x E)) (fun (_x : Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4)) x E)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4)) x E)) => Subtype.{succ u1} L' (fun (x : L') => Membership.mem.{u1, u1} L' (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) (SetLike.instMembership.{u1, u1} (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.instSetLikeIntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5)) x (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))) _x) (SMulHomClass.toFunLike.{max u2 u1, u3, u2, u1} (AlgEquiv.{u3, u2, u1} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4)) x E)) (Subtype.{succ u1} L' (fun (x : L') => Membership.mem.{u1, u1} L' (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) (SetLike.instMembership.{u1, u1} (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.instSetLikeIntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5)) x (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))) (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (Subalgebra.toSemiring.{u3, u2} K L (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u3, u2} K L _inst_1 _inst_2 _inst_4 E)) (Subalgebra.toSemiring.{u3, u1} K L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_5 (IntermediateField.toSubalgebra.{u3, u1} K L' _inst_1 _inst_3 _inst_5 (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))) (IntermediateField.algebra.{u3, u2} K L _inst_1 _inst_2 _inst_4 E) (IntermediateField.algebra.{u3, u1} K L' _inst_1 _inst_3 _inst_5 (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))) K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4)) x E)) (Subtype.{succ u1} L' (fun (x : L') => Membership.mem.{u1, u1} L' (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) (SetLike.instMembership.{u1, u1} (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.instSetLikeIntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5)) x (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))) (SMulZeroClass.toSMul.{u3, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4)) x E)) (AddMonoid.toZero.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4)) x E)) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4)) x E)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4)) x E)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4)) x E)) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4)) x E)) (Subalgebra.toSemiring.{u3, u2} K L (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u3, u2} K L _inst_1 _inst_2 _inst_4 E))))))) (DistribSMul.toSMulZeroClass.{u3, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4)) x E)) (AddMonoid.toAddZeroClass.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4)) x E)) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L 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_inst_5 e) E))) (AddCommMonoid.toAddMonoid.{u1} (Subtype.{succ u1} L' (fun (x : L') => Membership.mem.{u1, u1} L' (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) (SetLike.instMembership.{u1, u1} (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.instSetLikeIntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5)) x (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Subtype.{succ u1} L' (fun (x : L') => Membership.mem.{u1, u1} L' (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) (SetLike.instMembership.{u1, u1} 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_inst_3 _inst_5 (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E)))))))) (DistribMulAction.toDistribSMul.{u3, u1} K (Subtype.{succ u1} L' (fun (x : L') => Membership.mem.{u1, u1} L' (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) (SetLike.instMembership.{u1, u1} (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.instSetLikeIntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5)) x (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))) (MonoidWithZero.toMonoid.{u3} K (Semiring.toMonoidWithZero.{u3} K (CommSemiring.toSemiring.{u3} K (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} (Subtype.{succ u1} L' (fun (x : L') => Membership.mem.{u1, u1} L' (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) (SetLike.instMembership.{u1, u1} (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.instSetLikeIntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5)) x (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L 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E))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Subtype.{succ u1} L' (fun (x : L') => Membership.mem.{u1, u1} L' (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) (SetLike.instMembership.{u1, u1} (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.instSetLikeIntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5)) x (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} L' (fun (x : L') => Membership.mem.{u1, u1} L' (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) (SetLike.instMembership.{u1, u1} (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.instSetLikeIntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5)) x (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))) (Subalgebra.toSemiring.{u3, u1} K L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_5 (IntermediateField.toSubalgebra.{u3, u1} K L' _inst_1 _inst_3 _inst_5 (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))))))) (Module.toDistribMulAction.{u3, u1} K (Subtype.{succ u1} L' (fun (x : L') => Membership.mem.{u1, u1} L' (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) (SetLike.instMembership.{u1, u1} (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.instSetLikeIntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5)) x (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))) (CommSemiring.toSemiring.{u3} K (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Subtype.{succ u1} L' (fun (x : L') => Membership.mem.{u1, u1} L' (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) (SetLike.instMembership.{u1, u1} (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.instSetLikeIntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5)) x (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' 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(IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))) (Subalgebra.toSemiring.{u3, u1} K L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_5 (IntermediateField.toSubalgebra.{u3, u1} K L' _inst_1 _inst_3 _inst_5 (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L 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L' _inst_3))) _inst_4 _inst_5 e) E))) (Subalgebra.toSemiring.{u3, u1} K L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_5 (IntermediateField.toSubalgebra.{u3, u1} K L' _inst_1 _inst_3 _inst_5 (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E)))))) (Algebra.toModule.{u3, u1} K (Subtype.{succ u1} L' (fun (x : L') => Membership.mem.{u1, u1} L' (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) (SetLike.instMembership.{u1, u1} (IntermediateField.{u3, u1} K L' 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_inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))) (IntermediateField.algebra.{u3, u1} K L' _inst_1 _inst_3 _inst_5 (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E)))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u3, u2, u1} (AlgEquiv.{u3, u2, u1} K (Subtype.{succ u2} L (fun (x : L) 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_inst_5 e) E))) (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (Subalgebra.toSemiring.{u3, u2} K L (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u3, u2} K L _inst_1 _inst_2 _inst_4 E)) (Subalgebra.toSemiring.{u3, u1} K L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_5 (IntermediateField.toSubalgebra.{u3, u1} K L' _inst_1 _inst_3 _inst_5 (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) 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_inst_4)) x E)) (Subtype.{succ u1} L' (fun (x : L') => Membership.mem.{u1, u1} L' (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) (SetLike.instMembership.{u1, u1} (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.instSetLikeIntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5)) x (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))) (MonoidWithZero.toMonoid.{u3} K (Semiring.toMonoidWithZero.{u3} K (CommSemiring.toSemiring.{u3} K (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ 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(AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} L' (fun (x : L') => Membership.mem.{u1, u1} L' (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) (SetLike.instMembership.{u1, u1} (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.instSetLikeIntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5)) x (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))) (Subalgebra.toSemiring.{u3, u1} K L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_5 (IntermediateField.toSubalgebra.{u3, u1} K L' _inst_1 _inst_3 _inst_5 (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E)))))) (Algebra.toModule.{u3, u1} K (Subtype.{succ u1} L' (fun (x : L') => Membership.mem.{u1, u1} L' (IntermediateField.{u3, u1} K 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(DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_5 (IntermediateField.toSubalgebra.{u3, u1} K L' _inst_1 _inst_3 _inst_5 (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))) (IntermediateField.algebra.{u3, u2} K L _inst_1 _inst_2 _inst_4 E) (IntermediateField.algebra.{u3, u1} K L' _inst_1 _inst_3 _inst_5 (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E)))))))) (IntermediateField.intermediateFieldMap.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 e E) a)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AlgEquiv.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5) L (fun (_x : L) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : L) => L') _x) (SMulHomClass.toFunLike.{max u2 u1, u3, u2, u1} (AlgEquiv.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5) K L L' (SMulZeroClass.toSMul.{u3, u2} K L (AddMonoid.toZero.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))))) (DistribSMul.toSMulZeroClass.{u3, u2} K L (AddMonoid.toAddZeroClass.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))))) (DistribMulAction.toDistribSMul.{u3, u2} K L (MonoidWithZero.toMonoid.{u3} K (Semiring.toMonoidWithZero.{u3} K (CommSemiring.toSemiring.{u3} K (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))))) (Module.toDistribMulAction.{u3, u2} K L (CommSemiring.toSemiring.{u3} K (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (Algebra.toModule.{u3, u2} K L (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4))))) (SMulZeroClass.toSMul.{u3, u1} K L' (AddMonoid.toZero.{u1} L' (AddCommMonoid.toAddMonoid.{u1} L' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L' (Semiring.toNonAssocSemiring.{u1} L' (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3)))))))) (DistribSMul.toSMulZeroClass.{u3, u1} K L' (AddMonoid.toAddZeroClass.{u1} L' (AddCommMonoid.toAddMonoid.{u1} L' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L' (Semiring.toNonAssocSemiring.{u1} L' (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3)))))))) (DistribMulAction.toDistribSMul.{u3, u1} K L' (MonoidWithZero.toMonoid.{u3} K (Semiring.toMonoidWithZero.{u3} K (CommSemiring.toSemiring.{u3} K (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} L' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L' (Semiring.toNonAssocSemiring.{u1} L' (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))))))) (Module.toDistribMulAction.{u3, u1} K L' (CommSemiring.toSemiring.{u3} K (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L' (Semiring.toNonAssocSemiring.{u1} L' (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3)))))) (Algebra.toModule.{u3, u1} K L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u3, u2, u1} (AlgEquiv.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5) K L L' (MonoidWithZero.toMonoid.{u3} K (Semiring.toMonoidWithZero.{u3} K (CommSemiring.toSemiring.{u3} K (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))))) (AddCommMonoid.toAddMonoid.{u1} L' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L' (Semiring.toNonAssocSemiring.{u1} L' (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))))))) (Module.toDistribMulAction.{u3, u2} K L (CommSemiring.toSemiring.{u3} K (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (Algebra.toModule.{u3, u2} K L (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4)) (Module.toDistribMulAction.{u3, u1} K L' (CommSemiring.toSemiring.{u3} K (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L' (Semiring.toNonAssocSemiring.{u1} L' (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3)))))) (Algebra.toModule.{u3, u1} K L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_5)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u3, u2, u1} (AlgEquiv.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5) K L L' (MonoidWithZero.toMonoid.{u3} K (Semiring.toMonoidWithZero.{u3} K (CommSemiring.toSemiring.{u3} K (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L' (Semiring.toNonAssocSemiring.{u1} L' (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))))) (Module.toDistribMulAction.{u3, u2} K L (CommSemiring.toSemiring.{u3} K (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (Algebra.toModule.{u3, u2} K L (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4)) (Module.toDistribMulAction.{u3, u1} K L' (CommSemiring.toSemiring.{u3} K (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L' (Semiring.toNonAssocSemiring.{u1} L' (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3)))))) (Algebra.toModule.{u3, u1} K L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, u2, u1, max u2 u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 (AlgEquiv.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5) (AlgEquivClass.toAlgHomClass.{max u2 u1, u3, u2, u1} (AlgEquiv.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5) K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 (AlgEquiv.instAlgEquivClassAlgEquiv.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5)))))) e (Subtype.val.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Set.{u2} L) (Set.instMembershipSet.{u2} L) x (SetLike.coe.{u2, u2} (IntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) E)) a))
+  forall {K : Type.{u3}} {L : Type.{u2}} {L' : Type.{u1}} [_inst_1 : Field.{u3} K] [_inst_2 : Field.{u2} L] [_inst_3 : Field.{u1} L'] [_inst_4 : Algebra.{u3, u2} K L (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))] [_inst_5 : Algebra.{u3, u1} K L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3)))] (e : AlgEquiv.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5) (E : IntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) (a : Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4)) x E)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : L) => L') (Subtype.val.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Set.{u2} L) (Set.instMembershipSet.{u2} L) x (SetLike.coe.{u2, u2} (IntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) E)) a)) (Subtype.val.{succ u1} L' (fun (x : L') => Membership.mem.{u1, u1} L' (Set.{u1} L') (Set.instMembershipSet.{u1} L') x (SetLike.coe.{u1, u1} (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.instSetLikeIntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AlgEquiv.{u3, u2, u1} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4)) x E)) (Subtype.{succ u1} L' (fun (x : L') => Membership.mem.{u1, u1} L' (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) (SetLike.instMembership.{u1, u1} (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) L' 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_inst_5 e) E))) (AddCommMonoid.toAddMonoid.{u1} (Subtype.{succ u1} L' (fun (x : L') => Membership.mem.{u1, u1} L' (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) (SetLike.instMembership.{u1, u1} (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.instSetLikeIntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5)) x (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Subtype.{succ u1} L' (fun (x : L') => Membership.mem.{u1, u1} L' (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) (SetLike.instMembership.{u1, u1} 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_inst_3 _inst_5 (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E)))))))) (DistribMulAction.toDistribSMul.{u3, u1} K (Subtype.{succ u1} L' (fun (x : L') => Membership.mem.{u1, u1} L' (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) (SetLike.instMembership.{u1, u1} (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.instSetLikeIntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5)) x (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) 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(IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))) (Subalgebra.toSemiring.{u3, u1} K L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_5 (IntermediateField.toSubalgebra.{u3, u1} K L' _inst_1 _inst_3 _inst_5 (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L 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L' _inst_3))) _inst_4 _inst_5 e) E))) (Subalgebra.toSemiring.{u3, u1} K L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_5 (IntermediateField.toSubalgebra.{u3, u1} K L' _inst_1 _inst_3 _inst_5 (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E)))))) (Algebra.toModule.{u3, u1} K (Subtype.{succ u1} L' (fun (x : L') => Membership.mem.{u1, u1} L' (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) (SetLike.instMembership.{u1, u1} (IntermediateField.{u3, u1} K L' 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_inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))) (IntermediateField.algebra.{u3, u1} K L' _inst_1 _inst_3 _inst_5 (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E)))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u3, u2, u1} (AlgEquiv.{u3, u2, u1} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4)) x E)) (Subtype.{succ u1} L' (fun (x : L') => Membership.mem.{u1, u1} L' (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) (SetLike.instMembership.{u1, u1} (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.instSetLikeIntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5)) x (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))) (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (Subalgebra.toSemiring.{u3, u2} K L (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u3, u2} K L _inst_1 _inst_2 _inst_4 E)) (Subalgebra.toSemiring.{u3, u1} K L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_5 (IntermediateField.toSubalgebra.{u3, u1} K L' _inst_1 _inst_3 _inst_5 (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) 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(Semiring.toMonoidWithZero.{u3} K (CommSemiring.toSemiring.{u3} K (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))))) (Module.toDistribMulAction.{u3, u2} K L (CommSemiring.toSemiring.{u3} K (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (Algebra.toModule.{u3, u2} K L (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4))))) (SMulZeroClass.toSMul.{u3, u1} K L' (AddMonoid.toZero.{u1} L' (AddCommMonoid.toAddMonoid.{u1} L' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L' (Semiring.toNonAssocSemiring.{u1} L' (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3)))))))) (DistribSMul.toSMulZeroClass.{u3, u1} K L' (AddMonoid.toAddZeroClass.{u1} L' (AddCommMonoid.toAddMonoid.{u1} L' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L' (Semiring.toNonAssocSemiring.{u1} L' (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3)))))))) (DistribMulAction.toDistribSMul.{u3, u1} K L' (MonoidWithZero.toMonoid.{u3} K (Semiring.toMonoidWithZero.{u3} K (CommSemiring.toSemiring.{u3} K (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} L' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L' (Semiring.toNonAssocSemiring.{u1} L' (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))))))) (Module.toDistribMulAction.{u3, u1} K L' (CommSemiring.toSemiring.{u3} K (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L' (Semiring.toNonAssocSemiring.{u1} L' (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3)))))) (Algebra.toModule.{u3, u1} K L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u3, u2, u1} (AlgEquiv.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5) K L L' (MonoidWithZero.toMonoid.{u3} K (Semiring.toMonoidWithZero.{u3} K (CommSemiring.toSemiring.{u3} K (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))))) (AddCommMonoid.toAddMonoid.{u1} L' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L' (Semiring.toNonAssocSemiring.{u1} L' (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))))))) (Module.toDistribMulAction.{u3, u2} K L (CommSemiring.toSemiring.{u3} K (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (Algebra.toModule.{u3, u2} K L (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4)) (Module.toDistribMulAction.{u3, u1} K L' (CommSemiring.toSemiring.{u3} K (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L' (Semiring.toNonAssocSemiring.{u1} L' (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3)))))) (Algebra.toModule.{u3, u1} K L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_5)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u3, u2, u1} (AlgEquiv.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5) K L L' (MonoidWithZero.toMonoid.{u3} K (Semiring.toMonoidWithZero.{u3} K (CommSemiring.toSemiring.{u3} K (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L' (Semiring.toNonAssocSemiring.{u1} L' (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))))) (Module.toDistribMulAction.{u3, u2} K L (CommSemiring.toSemiring.{u3} K (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (Algebra.toModule.{u3, u2} K L (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4)) (Module.toDistribMulAction.{u3, u1} K L' (CommSemiring.toSemiring.{u3} K (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L' (Semiring.toNonAssocSemiring.{u1} L' (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3)))))) (Algebra.toModule.{u3, u1} K L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, u2, u1, max u2 u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 (AlgEquiv.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5) (AlgEquivClass.toAlgHomClass.{max u2 u1, u3, u2, u1} (AlgEquiv.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5) K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 (AlgEquiv.instAlgEquivClassAlgEquiv.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5)))))) e (Subtype.val.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Set.{u2} L) (Set.instMembershipSet.{u2} L) x (SetLike.coe.{u2, u2} (IntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) E)) a))
 Case conversion may be inaccurate. Consider using '#align intermediate_field.intermediate_field_map_apply_coe IntermediateField.intermediateFieldMap_apply_coeₓ'. -/
 /- We manually add these two simp lemmas because `@[simps]` before `intermediate_field_map`
   led to a timeout. -/
@@ -819,7 +819,7 @@ theorem intermediateFieldMap_apply_coe (e : L ≃ₐ[K] L') (E : IntermediateFie
 lean 3 declaration is
   forall {K : Type.{u1}} {L : Type.{u2}} {L' : Type.{u3}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_3 : Field.{u3} L'] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] [_inst_5 : Algebra.{u1, u3} K L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3)))] (e : AlgEquiv.{u1, u2, u3} K L L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3))) _inst_4 _inst_5) (E : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (a : coeSort.{succ u3, succ (succ u3)} (IntermediateField.{u1, u3} K L' _inst_1 _inst_3 _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (IntermediateField.{u1, u3} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.setLike.{u1, u3} K L' _inst_1 _inst_3 _inst_5)) (IntermediateField.map.{u1, u2, u3} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u1, u2, u3} K L L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3))) _inst_4 _inst_5 e) E)), Eq.{succ u2} L ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) E) L (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) E) L (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) E) L (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) E) L (coeSubtype.{succ u2} L (fun (x : L) => Membership.Mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.hasMem.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x E))))) (coeFn.{max (succ u3) (succ u2), max (succ u3) (succ u2)} (AlgEquiv.{u1, u3, u2} K (coeSort.{succ u3, succ (succ u3)} (IntermediateField.{u1, u3} K L' _inst_1 _inst_3 _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (IntermediateField.{u1, u3} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.setLike.{u1, u3} K L' _inst_1 _inst_3 _inst_5)) (IntermediateField.map.{u1, u2, u3} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u1, u2, u3} K L L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3))) _inst_4 _inst_5 e) E)) (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} 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(Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_5 _inst_4) => L' -> L) (AlgEquiv.hasCoeToFun.{u1, u3, u2} K L' L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3))) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_5 _inst_4) (AlgEquiv.symm.{u1, u2, u3} K L L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3))) _inst_4 _inst_5 e) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (coeSort.{succ u3, succ (succ u3)} (IntermediateField.{u1, u3} K L' _inst_1 _inst_3 _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (IntermediateField.{u1, u3} K 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(Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3))) _inst_4 _inst_5 e) E)) L' (CoeTCₓ.coe.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (IntermediateField.{u1, u3} K L' _inst_1 _inst_3 _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (IntermediateField.{u1, u3} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.setLike.{u1, u3} K L' _inst_1 _inst_3 _inst_5)) (IntermediateField.map.{u1, u2, u3} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u1, u2, u3} K L L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3))) _inst_4 _inst_5 e) E)) L' (coeBase.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (IntermediateField.{u1, u3} K L' _inst_1 _inst_3 _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (IntermediateField.{u1, u3} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.setLike.{u1, u3} K L' _inst_1 _inst_3 _inst_5)) (IntermediateField.map.{u1, u2, u3} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u1, u2, u3} K L L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3))) _inst_4 _inst_5 e) E)) L' (coeSubtype.{succ u3} L' (fun (x : L') => Membership.Mem.{u3, u3} L' (IntermediateField.{u1, u3} K L' _inst_1 _inst_3 _inst_5) (SetLike.hasMem.{u3, u3} (IntermediateField.{u1, u3} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.setLike.{u1, u3} K L' _inst_1 _inst_3 _inst_5)) x (IntermediateField.map.{u1, u2, u3} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u1, u2, u3} K L L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3))) _inst_4 _inst_5 e) E)))))) a))
 but is expected to have type
-  forall {K : Type.{u3}} {L : Type.{u2}} {L' : Type.{u1}} [_inst_1 : Field.{u3} K] [_inst_2 : Field.{u2} L] [_inst_3 : Field.{u1} L'] [_inst_4 : Algebra.{u3, u2} K L (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))] [_inst_5 : Algebra.{u3, u1} K L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3)))] (e : AlgEquiv.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5) (E : IntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) (a : Subtype.{succ u1} L' (fun (x : L') => Membership.mem.{u1, u1} L' (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) (SetLike.instMembership.{u1, u1} (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.instSetLikeIntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5)) x (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : L') => L) (Subtype.val.{succ u1} L' (fun (x : L') => Membership.mem.{u1, u1} L' (Set.{u1} L') (Set.instMembershipSet.{u1} L') x (SetLike.coe.{u1, u1} (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.instSetLikeIntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))) a)) (Subtype.val.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Set.{u2} L) (Set.instMembershipSet.{u2} L) x (SetLike.coe.{u2, u2} (IntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) E)) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (AlgEquiv.{u3, u1, u2} K (Subtype.{succ u1} L' (fun (x : L') => Membership.mem.{u1, u1} L' (IntermediateField.{u3, u1} K L' 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(DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))) (IntermediateField.algebra.{u3, u1} K L' _inst_1 _inst_3 _inst_5 (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E)))) (Module.toDistribMulAction.{u3, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4)) x E)) 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_inst_5 e) E)) (IntermediateField.algebra.{u3, u2} K L _inst_1 _inst_2 _inst_4 E)) K (Subtype.{succ u1} L' (fun (x : L') => Membership.mem.{u1, u1} L' (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) (SetLike.instMembership.{u1, u1} (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.instSetLikeIntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5)) x (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))) (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} 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_inst_1)) (Subalgebra.toSemiring.{u3, u2} K L (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u3, u2} K L _inst_1 _inst_2 _inst_4 E)) (IntermediateField.algebra.{u3, u2} K L _inst_1 _inst_2 _inst_4 E))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, u1, u2, max u2 u1} K (Subtype.{succ u1} L' (fun (x : L') => Membership.mem.{u1, u1} L' (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) (SetLike.instMembership.{u1, u1} (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.instSetLikeIntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5)) x (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 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u1} K L' _inst_1 _inst_3 _inst_5) (SetLike.instMembership.{u1, u1} (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.instSetLikeIntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5)) x (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))) (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (Subalgebra.toSemiring.{u3, u2} K L (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u3, u2} K L _inst_1 _inst_2 _inst_4 E)) (Subalgebra.toSemiring.{u3, u1} K L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_5 (IntermediateField.toSubalgebra.{u3, u1} K L' _inst_1 _inst_3 _inst_5 (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))) (IntermediateField.algebra.{u3, u2} K L _inst_1 _inst_2 _inst_4 E) (IntermediateField.algebra.{u3, u1} K L' _inst_1 _inst_3 _inst_5 (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E)) (IntermediateField.intermediateFieldMap.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 e E)) a)) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (AlgEquiv.{u3, u1, u2} K L' L (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_5 _inst_4) L' (fun (_x : L') => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : L') => L) _x) (SMulHomClass.toFunLike.{max u2 u1, u3, u1, u2} (AlgEquiv.{u3, u1, u2} K L' L (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_5 _inst_4) K L' L (SMulZeroClass.toSMul.{u3, u1} K L' (AddMonoid.toZero.{u1} L' (AddCommMonoid.toAddMonoid.{u1} L' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L' (Semiring.toNonAssocSemiring.{u1} L' (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3)))))))) (DistribSMul.toSMulZeroClass.{u3, u1} K L' (AddMonoid.toAddZeroClass.{u1} L' (AddCommMonoid.toAddMonoid.{u1} L' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L' (Semiring.toNonAssocSemiring.{u1} L' (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3)))))))) (DistribMulAction.toDistribSMul.{u3, u1} K L' (MonoidWithZero.toMonoid.{u3} K (Semiring.toMonoidWithZero.{u3} K (CommSemiring.toSemiring.{u3} K (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} L' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L' (Semiring.toNonAssocSemiring.{u1} L' (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))))))) (Module.toDistribMulAction.{u3, u1} K L' (CommSemiring.toSemiring.{u3} K (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L' (Semiring.toNonAssocSemiring.{u1} L' (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3)))))) (Algebra.toModule.{u3, u1} K L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_5))))) (SMulZeroClass.toSMul.{u3, u2} K L (AddMonoid.toZero.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))))) (DistribSMul.toSMulZeroClass.{u3, u2} K L (AddMonoid.toAddZeroClass.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))))) (DistribMulAction.toDistribSMul.{u3, u2} K L (MonoidWithZero.toMonoid.{u3} K (Semiring.toMonoidWithZero.{u3} K (CommSemiring.toSemiring.{u3} K (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))))) (Module.toDistribMulAction.{u3, u2} K L (CommSemiring.toSemiring.{u3} K (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (Algebra.toModule.{u3, u2} K L (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u3, u1, u2} (AlgEquiv.{u3, u1, u2} K L' L (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_5 _inst_4) K L' L (MonoidWithZero.toMonoid.{u3} K (Semiring.toMonoidWithZero.{u3} K (CommSemiring.toSemiring.{u3} K (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} L' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L' (Semiring.toNonAssocSemiring.{u1} L' (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))))))) (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))))) (Module.toDistribMulAction.{u3, u1} K L' (CommSemiring.toSemiring.{u3} K (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L' (Semiring.toNonAssocSemiring.{u1} L' (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3)))))) (Algebra.toModule.{u3, u1} K L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_5)) (Module.toDistribMulAction.{u3, u2} K L (CommSemiring.toSemiring.{u3} K (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (Algebra.toModule.{u3, u2} K L (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u3, u1, u2} (AlgEquiv.{u3, u1, u2} K L' L (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_5 _inst_4) K L' L (MonoidWithZero.toMonoid.{u3} K (Semiring.toMonoidWithZero.{u3} K (CommSemiring.toSemiring.{u3} K (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L' (Semiring.toNonAssocSemiring.{u1} L' (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (Module.toDistribMulAction.{u3, u1} K L' (CommSemiring.toSemiring.{u3} K (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L' (Semiring.toNonAssocSemiring.{u1} L' (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3)))))) (Algebra.toModule.{u3, u1} K L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_5)) (Module.toDistribMulAction.{u3, u2} K L (CommSemiring.toSemiring.{u3} K (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (Algebra.toModule.{u3, u2} K L (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, u1, u2, max u2 u1} K L' L (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_5 _inst_4 (AlgEquiv.{u3, u1, u2} K L' L (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_5 _inst_4) (AlgEquivClass.toAlgHomClass.{max u2 u1, u3, u1, u2} (AlgEquiv.{u3, u1, u2} K L' L (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_5 _inst_4) K L' L (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_5 _inst_4 (AlgEquiv.instAlgEquivClassAlgEquiv.{u3, u1, u2} K L' L (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_5 _inst_4)))))) (AlgEquiv.symm.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) (Subtype.val.{succ u1} L' (fun (x : L') => Membership.mem.{u1, u1} L' (Set.{u1} L') (Set.instMembershipSet.{u1} L') x (SetLike.coe.{u1, u1} (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.instSetLikeIntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))) a))
+  forall {K : Type.{u3}} {L : Type.{u2}} {L' : Type.{u1}} [_inst_1 : Field.{u3} K] [_inst_2 : Field.{u2} L] [_inst_3 : Field.{u1} L'] [_inst_4 : Algebra.{u3, u2} K L (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))] [_inst_5 : Algebra.{u3, u1} K L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3)))] (e : AlgEquiv.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5) (E : IntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) (a : Subtype.{succ u1} L' (fun (x : L') => Membership.mem.{u1, u1} L' (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) (SetLike.instMembership.{u1, u1} (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.instSetLikeIntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5)) x (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : L') => L) (Subtype.val.{succ u1} L' (fun (x : L') => Membership.mem.{u1, u1} L' (Set.{u1} L') (Set.instMembershipSet.{u1} L') x (SetLike.coe.{u1, u1} (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.instSetLikeIntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))) a)) (Subtype.val.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Set.{u2} L) (Set.instMembershipSet.{u2} L) x (SetLike.coe.{u2, u2} (IntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) E)) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (AlgEquiv.{u3, u1, u2} K (Subtype.{succ u1} L' (fun (x : L') => Membership.mem.{u1, u1} L' (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) (SetLike.instMembership.{u1, u1} (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.instSetLikeIntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5)) x (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))) (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4)) x E)) (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (Subalgebra.toSemiring.{u3, u1} K L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_5 (IntermediateField.toSubalgebra.{u3, u1} K L' _inst_1 _inst_3 _inst_5 (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))) (Subalgebra.toSemiring.{u3, u2} K L (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u3, u2} K L _inst_1 _inst_2 _inst_4 E)) (IntermediateField.algebra.{u3, u1} K L' _inst_1 _inst_3 _inst_5 (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E)) (IntermediateField.algebra.{u3, u2} K L _inst_1 _inst_2 _inst_4 E)) (Subtype.{succ u1} L' (fun (x : L') => Membership.mem.{u1, u1} L' (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) (SetLike.instMembership.{u1, u1} (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.instSetLikeIntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5)) x (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))) (fun (_x : Subtype.{succ u1} L' (fun (x : L') => Membership.mem.{u1, u1} L' (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) (SetLike.instMembership.{u1, u1} (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.instSetLikeIntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5)) x (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Subtype.{succ u1} L' (fun (x : L') => Membership.mem.{u1, u1} L' (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) (SetLike.instMembership.{u1, u1} (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.instSetLikeIntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5)) x (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))) => Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4)) x E)) _x) (SMulHomClass.toFunLike.{max u2 u1, u3, u1, u2} (AlgEquiv.{u3, u1, u2} K (Subtype.{succ u1} L' (fun (x : L') => Membership.mem.{u1, u1} L' (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) (SetLike.instMembership.{u1, u1} (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.instSetLikeIntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5)) x (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))) (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4)) x E)) (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (Subalgebra.toSemiring.{u3, u1} K L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_5 (IntermediateField.toSubalgebra.{u3, u1} K L' _inst_1 _inst_3 _inst_5 (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))) (Subalgebra.toSemiring.{u3, u2} K L (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u3, u2} K L _inst_1 _inst_2 _inst_4 E)) (IntermediateField.algebra.{u3, u1} K L' _inst_1 _inst_3 _inst_5 (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E)) (IntermediateField.algebra.{u3, u2} K L _inst_1 _inst_2 _inst_4 E)) K (Subtype.{succ u1} L' (fun (x : L') => Membership.mem.{u1, u1} L' (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) (SetLike.instMembership.{u1, u1} (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.instSetLikeIntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5)) x (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))) (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4)) x E)) (SMulZeroClass.toSMul.{u3, u1} K (Subtype.{succ u1} L' (fun (x : L') => Membership.mem.{u1, u1} L' (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) (SetLike.instMembership.{u1, u1} (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.instSetLikeIntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5)) x (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))) (AddMonoid.toZero.{u1} (Subtype.{succ u1} L' (fun (x : L') => 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(IntermediateField.instSetLikeIntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5)) x (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Subtype.{succ u1} L' (fun (x : L') => Membership.mem.{u1, u1} L' (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) (SetLike.instMembership.{u1, u1} (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.instSetLikeIntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5)) x (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Subtype.{succ u1} L' (fun (x : L') => Membership.mem.{u1, u1} L' (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) (SetLike.instMembership.{u1, u1} (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.instSetLikeIntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5)) x (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} L' (fun (x : L') => Membership.mem.{u1, u1} L' (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) (SetLike.instMembership.{u1, u1} (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.instSetLikeIntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5)) x (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))) (Subalgebra.toSemiring.{u3, u1} K L' (Semifield.toCommSemiring.{u3} K 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_inst_4 _inst_5 e) E))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Subtype.{succ u1} L' (fun (x : L') => Membership.mem.{u1, u1} L' (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) (SetLike.instMembership.{u1, u1} (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.instSetLikeIntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5)) x (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Subtype.{succ u1} L' (fun (x : L') => Membership.mem.{u1, u1} L' (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) 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K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))) (Subalgebra.toSemiring.{u3, u1} K L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_5 (IntermediateField.toSubalgebra.{u3, u1} K L' _inst_1 _inst_3 _inst_5 (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E)))))))) (DistribMulAction.toDistribSMul.{u3, u1} K (Subtype.{succ u1} L' (fun (x : L') => Membership.mem.{u1, u1} L' (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) (SetLike.instMembership.{u1, u1} (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.instSetLikeIntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5)) x (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))) (MonoidWithZero.toMonoid.{u3} K (Semiring.toMonoidWithZero.{u3} K 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(Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))))))) (Module.toDistribMulAction.{u3, u1} K (Subtype.{succ u1} L' (fun (x : L') => Membership.mem.{u1, u1} L' (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) (SetLike.instMembership.{u1, u1} (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.instSetLikeIntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5)) x (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))) (CommSemiring.toSemiring.{u3} K (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 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_inst_3 _inst_5) L' (IntermediateField.instSetLikeIntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5)) x (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} L' (fun (x : L') => Membership.mem.{u1, u1} L' (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) (SetLike.instMembership.{u1, u1} (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.instSetLikeIntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5)) x (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, 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(DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))) (IntermediateField.algebra.{u3, u1} K L' _inst_1 _inst_3 _inst_5 (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E)))) (Module.toDistribMulAction.{u3, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4)) x E)) 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_inst_5 e) E)) (IntermediateField.algebra.{u3, u2} K L _inst_1 _inst_2 _inst_4 E)) K (Subtype.{succ u1} L' (fun (x : L') => Membership.mem.{u1, u1} L' (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) (SetLike.instMembership.{u1, u1} (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.instSetLikeIntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5)) x (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))) (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} 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_inst_2 _inst_4)) x E)) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4)) x E)) (Subalgebra.toSemiring.{u3, u2} K L (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u3, u2} K L _inst_1 _inst_2 _inst_4 E)))) (Module.toDistribMulAction.{u3, u1} K (Subtype.{succ u1} L' (fun (x : L') => Membership.mem.{u1, u1} L' (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) (SetLike.instMembership.{u1, u1} (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.instSetLikeIntermediateField.{u3, u1} K L' _inst_1 _inst_3 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(IntermediateField.algebra.{u3, u1} K L' _inst_1 _inst_3 _inst_5 (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E)) (IntermediateField.algebra.{u3, u2} K L _inst_1 _inst_2 _inst_4 E))))))) (AlgEquiv.symm.{u3, u2, u1} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4)) x E)) (Subtype.{succ u1} L' (fun (x : L') => Membership.mem.{u1, u1} L' (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) (SetLike.instMembership.{u1, u1} (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.instSetLikeIntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5)) x (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))) (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (Subalgebra.toSemiring.{u3, u2} K L (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u3, u2} K L _inst_1 _inst_2 _inst_4 E)) (Subalgebra.toSemiring.{u3, u1} K L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_5 (IntermediateField.toSubalgebra.{u3, u1} K L' _inst_1 _inst_3 _inst_5 (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))) (IntermediateField.algebra.{u3, u2} K L _inst_1 _inst_2 _inst_4 E) (IntermediateField.algebra.{u3, u1} K L' _inst_1 _inst_3 _inst_5 (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E)) (IntermediateField.intermediateFieldMap.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 e E)) a)) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (AlgEquiv.{u3, u1, u2} K L' L (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_5 _inst_4) L' (fun (_x : L') => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : L') => L) _x) (SMulHomClass.toFunLike.{max u2 u1, u3, u1, u2} (AlgEquiv.{u3, u1, u2} K L' L 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(CommSemiring.toSemiring.{u3} K (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L' (Semiring.toNonAssocSemiring.{u1} L' (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (Module.toDistribMulAction.{u3, u1} K L' (CommSemiring.toSemiring.{u3} K (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L' (Semiring.toNonAssocSemiring.{u1} L' (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3)))))) (Algebra.toModule.{u3, u1} K L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_5)) (Module.toDistribMulAction.{u3, u2} K L (CommSemiring.toSemiring.{u3} K (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (Algebra.toModule.{u3, u2} K L (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, u1, u2, max u2 u1} K L' L (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_5 _inst_4 (AlgEquiv.{u3, u1, u2} K L' L (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_5 _inst_4) (AlgEquivClass.toAlgHomClass.{max u2 u1, u3, u1, u2} (AlgEquiv.{u3, u1, u2} K L' L (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_5 _inst_4) K L' L (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_5 _inst_4 (AlgEquiv.instAlgEquivClassAlgEquiv.{u3, u1, u2} K L' L (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_5 _inst_4)))))) (AlgEquiv.symm.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) (Subtype.val.{succ u1} L' (fun (x : L') => Membership.mem.{u1, u1} L' (Set.{u1} L') (Set.instMembershipSet.{u1} L') x (SetLike.coe.{u1, u1} (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.instSetLikeIntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))) a))
 Case conversion may be inaccurate. Consider using '#align intermediate_field.intermediate_field_map_symm_apply_coe IntermediateField.intermediateFieldMap_symm_apply_coeₓ'. -/
 @[simp]
 theorem intermediateFieldMap_symm_apply_coe (e : L ≃ₐ[K] L') (E : IntermediateField K L)
@@ -845,7 +845,7 @@ def fieldRange : IntermediateField K L' :=
 lean 3 declaration is
   forall {K : Type.{u1}} {L : Type.{u2}} {L' : Type.{u3}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_3 : Field.{u3} L'] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] [_inst_5 : Algebra.{u1, u3} K L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3)))] (f : AlgHom.{u1, u2, u3} K L L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3))) _inst_4 _inst_5), Eq.{succ u3} (Set.{u3} L') ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (IntermediateField.{u1, u3} K L' _inst_1 _inst_3 _inst_5) (Set.{u3} L') (HasLiftT.mk.{succ u3, succ u3} (IntermediateField.{u1, u3} K L' _inst_1 _inst_3 _inst_5) (Set.{u3} L') (CoeTCₓ.coe.{succ u3, succ u3} (IntermediateField.{u1, u3} K L' _inst_1 _inst_3 _inst_5) (Set.{u3} L') (SetLike.Set.hasCoeT.{u3, u3} (IntermediateField.{u1, u3} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.setLike.{u1, u3} K L' _inst_1 _inst_3 _inst_5)))) (AlgHom.fieldRange.{u1, u2, u3} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 f)) (Set.range.{u3, succ u2} L' L (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} K L L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3))) _inst_4 _inst_5) (fun (_x : AlgHom.{u1, u2, u3} K L L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3))) _inst_4 _inst_5) => L -> L') ([anonymous].{u1, u2, u3} K L L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3))) _inst_4 _inst_5) f))
 but is expected to have type
-  forall {K : Type.{u2}} {L : Type.{u1}} {L' : Type.{u3}} [_inst_1 : Field.{u2} K] [_inst_2 : Field.{u1} L] [_inst_3 : Field.{u3} L'] [_inst_4 : Algebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))] [_inst_5 : Algebra.{u2, u3} K L' (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3)))] (f : AlgHom.{u2, u1, u3} K L L' (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))) _inst_4 _inst_5), Eq.{succ u3} (Set.{u3} L') (SetLike.coe.{u3, u3} (IntermediateField.{u2, u3} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.instSetLikeIntermediateField.{u2, u3} K L' _inst_1 _inst_3 _inst_5) (AlgHom.fieldRange.{u2, u1, u3} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 f)) (Set.range.{u3, succ u1} L' L (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (AlgHom.{u2, u1, u3} K L L' (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))) _inst_4 _inst_5) L (fun (_x : L) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : L) => L') _x) (SMulHomClass.toFunLike.{max u1 u3, u2, u1, u3} (AlgHom.{u2, u1, u3} K L L' (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))) _inst_4 _inst_5) K L L' (SMulZeroClass.toSMul.{u2, u1} K L (AddMonoid.toZero.{u1} L (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))))) (DistribSMul.toSMulZeroClass.{u2, u1} K L (AddMonoid.toAddZeroClass.{u1} L (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))))) (DistribMulAction.toDistribSMul.{u2, u1} K L (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))))))) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4))))) (SMulZeroClass.toSMul.{u2, u3} K L' (AddMonoid.toZero.{u3} L' (AddCommMonoid.toAddMonoid.{u3} L' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} L' (Semiring.toNonAssocSemiring.{u3} L' (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3)))))))) (DistribSMul.toSMulZeroClass.{u2, u3} K L' (AddMonoid.toAddZeroClass.{u3} L' (AddCommMonoid.toAddMonoid.{u3} L' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} L' (Semiring.toNonAssocSemiring.{u3} L' (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3)))))))) (DistribMulAction.toDistribSMul.{u2, u3} K L' (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u3} L' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} L' (Semiring.toNonAssocSemiring.{u3} L' (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))))))) (Module.toDistribMulAction.{u2, u3} K L' (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} L' (Semiring.toNonAssocSemiring.{u3} L' (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3)))))) (Algebra.toModule.{u2, u3} K L' (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))) _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u3, u2, u1, u3} (AlgHom.{u2, u1, u3} K L L' (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))) _inst_4 _inst_5) K L L' (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))))))) (AddCommMonoid.toAddMonoid.{u3} L' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} L' (Semiring.toNonAssocSemiring.{u3} L' (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))))))) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4)) (Module.toDistribMulAction.{u2, u3} K L' (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} L' (Semiring.toNonAssocSemiring.{u3} L' (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3)))))) (Algebra.toModule.{u2, u3} K L' (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))) _inst_5)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u3, u2, u1, u3} (AlgHom.{u2, u1, u3} K L L' (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))) _inst_4 _inst_5) K L L' (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} L' (Semiring.toNonAssocSemiring.{u3} L' (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))))) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4)) (Module.toDistribMulAction.{u2, u3} K L' (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} L' (Semiring.toNonAssocSemiring.{u3} L' (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3)))))) (Algebra.toModule.{u2, u3} K L' (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))) _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u1, u3, max u1 u3} K L L' (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))) _inst_4 _inst_5 (AlgHom.{u2, u1, u3} K L L' (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))) _inst_4 _inst_5) (AlgHom.algHomClass.{u2, u1, u3} K L L' (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))) _inst_4 _inst_5))))) f))
+  forall {K : Type.{u2}} {L : Type.{u1}} {L' : Type.{u3}} [_inst_1 : Field.{u2} K] [_inst_2 : Field.{u1} L] [_inst_3 : Field.{u3} L'] [_inst_4 : Algebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))] [_inst_5 : Algebra.{u2, u3} K L' (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3)))] (f : AlgHom.{u2, u1, u3} K L L' (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))) _inst_4 _inst_5), Eq.{succ u3} (Set.{u3} L') (SetLike.coe.{u3, u3} (IntermediateField.{u2, u3} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.instSetLikeIntermediateField.{u2, u3} K L' _inst_1 _inst_3 _inst_5) (AlgHom.fieldRange.{u2, u1, u3} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 f)) (Set.range.{u3, succ u1} L' L (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (AlgHom.{u2, u1, u3} K L L' (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))) _inst_4 _inst_5) L (fun (_x : L) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : L) => L') _x) (SMulHomClass.toFunLike.{max u1 u3, u2, u1, u3} (AlgHom.{u2, u1, u3} K L L' (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))) _inst_4 _inst_5) K L L' (SMulZeroClass.toSMul.{u2, u1} K L (AddMonoid.toZero.{u1} L (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))))) (DistribSMul.toSMulZeroClass.{u2, u1} K L (AddMonoid.toAddZeroClass.{u1} L (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))))) (DistribMulAction.toDistribSMul.{u2, u1} K L (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))))))) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4))))) (SMulZeroClass.toSMul.{u2, u3} K L' (AddMonoid.toZero.{u3} L' (AddCommMonoid.toAddMonoid.{u3} L' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} L' (Semiring.toNonAssocSemiring.{u3} L' (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3)))))))) (DistribSMul.toSMulZeroClass.{u2, u3} K L' (AddMonoid.toAddZeroClass.{u3} L' (AddCommMonoid.toAddMonoid.{u3} L' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} L' (Semiring.toNonAssocSemiring.{u3} L' (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3)))))))) (DistribMulAction.toDistribSMul.{u2, u3} K L' (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u3} L' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} L' (Semiring.toNonAssocSemiring.{u3} L' (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))))))) (Module.toDistribMulAction.{u2, u3} K L' (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} L' (Semiring.toNonAssocSemiring.{u3} L' (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3)))))) (Algebra.toModule.{u2, u3} K L' (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))) _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u3, u2, u1, u3} (AlgHom.{u2, u1, u3} K L L' (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))) _inst_4 _inst_5) K L L' (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))))))) (AddCommMonoid.toAddMonoid.{u3} L' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} L' (Semiring.toNonAssocSemiring.{u3} L' (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))))))) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4)) (Module.toDistribMulAction.{u2, u3} K L' (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} L' (Semiring.toNonAssocSemiring.{u3} L' (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3)))))) (Algebra.toModule.{u2, u3} K L' (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))) _inst_5)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u3, u2, u1, u3} (AlgHom.{u2, u1, u3} K L L' (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))) _inst_4 _inst_5) K L L' (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} L' (Semiring.toNonAssocSemiring.{u3} L' (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))))) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4)) (Module.toDistribMulAction.{u2, u3} K L' (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} L' (Semiring.toNonAssocSemiring.{u3} L' (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3)))))) (Algebra.toModule.{u2, u3} K L' (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))) _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u1, u3, max u1 u3} K L L' (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))) _inst_4 _inst_5 (AlgHom.{u2, u1, u3} K L L' (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))) _inst_4 _inst_5) (AlgHom.algHomClass.{u2, u1, u3} K L L' (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))) _inst_4 _inst_5))))) f))
 Case conversion may be inaccurate. Consider using '#align alg_hom.coe_field_range AlgHom.coe_fieldRangeₓ'. -/
 @[simp]
 theorem coe_fieldRange : ↑f.fieldRange = Set.range f :=
@@ -869,7 +869,7 @@ variable {f}
 lean 3 declaration is
   forall {K : Type.{u1}} {L : Type.{u2}} {L' : Type.{u3}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_3 : Field.{u3} L'] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] [_inst_5 : Algebra.{u1, u3} K L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3)))] {f : AlgHom.{u1, u2, u3} K L L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3))) _inst_4 _inst_5} {y : L'}, Iff (Membership.Mem.{u3, u3} L' (IntermediateField.{u1, u3} K L' _inst_1 _inst_3 _inst_5) (SetLike.hasMem.{u3, u3} (IntermediateField.{u1, u3} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.setLike.{u1, u3} K L' _inst_1 _inst_3 _inst_5)) y (AlgHom.fieldRange.{u1, u2, u3} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 f)) (Exists.{succ u2} L (fun (x : L) => Eq.{succ u3} L' (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} K L L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3))) _inst_4 _inst_5) (fun (_x : AlgHom.{u1, u2, u3} K L L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3))) _inst_4 _inst_5) => L -> L') ([anonymous].{u1, u2, u3} K L L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3))) _inst_4 _inst_5) f x) y))
 but is expected to have type
-  forall {K : Type.{u2}} {L : Type.{u1}} {L' : Type.{u3}} [_inst_1 : Field.{u2} K] [_inst_2 : Field.{u1} L] [_inst_3 : Field.{u3} L'] [_inst_4 : Algebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))] [_inst_5 : Algebra.{u2, u3} K L' (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3)))] {f : AlgHom.{u2, u1, u3} K L L' (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))) _inst_4 _inst_5} {y : L'}, Iff (Membership.mem.{u3, u3} L' (IntermediateField.{u2, u3} K L' _inst_1 _inst_3 _inst_5) (SetLike.instMembership.{u3, u3} (IntermediateField.{u2, u3} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.instSetLikeIntermediateField.{u2, u3} K L' _inst_1 _inst_3 _inst_5)) y (AlgHom.fieldRange.{u2, u1, u3} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 f)) (Exists.{succ u1} L (fun (x : L) => Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : L) => L') x) (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (AlgHom.{u2, u1, u3} K L L' (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))) _inst_4 _inst_5) L (fun (_x : L) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : L) => L') _x) (SMulHomClass.toFunLike.{max u1 u3, u2, u1, u3} (AlgHom.{u2, u1, u3} K L L' (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))) _inst_4 _inst_5) K L L' (SMulZeroClass.toSMul.{u2, u1} K L (AddMonoid.toZero.{u1} L (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))))) (DistribSMul.toSMulZeroClass.{u2, u1} K L (AddMonoid.toAddZeroClass.{u1} L (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))))) (DistribMulAction.toDistribSMul.{u2, u1} K L (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))))))) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4))))) (SMulZeroClass.toSMul.{u2, u3} K L' (AddMonoid.toZero.{u3} L' (AddCommMonoid.toAddMonoid.{u3} L' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} L' (Semiring.toNonAssocSemiring.{u3} L' (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3)))))))) (DistribSMul.toSMulZeroClass.{u2, u3} K L' (AddMonoid.toAddZeroClass.{u3} L' (AddCommMonoid.toAddMonoid.{u3} L' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} L' (Semiring.toNonAssocSemiring.{u3} L' (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3)))))))) (DistribMulAction.toDistribSMul.{u2, u3} K L' (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u3} L' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} L' (Semiring.toNonAssocSemiring.{u3} L' (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))))))) (Module.toDistribMulAction.{u2, u3} K L' (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} L' (Semiring.toNonAssocSemiring.{u3} L' (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3)))))) (Algebra.toModule.{u2, u3} K L' (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))) _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u3, u2, u1, u3} (AlgHom.{u2, u1, u3} K L L' (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))) _inst_4 _inst_5) K L L' (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))))))) (AddCommMonoid.toAddMonoid.{u3} L' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} L' (Semiring.toNonAssocSemiring.{u3} L' (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))))))) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4)) (Module.toDistribMulAction.{u2, u3} K L' (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} L' (Semiring.toNonAssocSemiring.{u3} L' (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3)))))) (Algebra.toModule.{u2, u3} K L' (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))) _inst_5)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u3, u2, u1, u3} (AlgHom.{u2, u1, u3} K L L' (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))) _inst_4 _inst_5) K L L' (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} L' (Semiring.toNonAssocSemiring.{u3} L' (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))))) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4)) (Module.toDistribMulAction.{u2, u3} K L' (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} L' (Semiring.toNonAssocSemiring.{u3} L' (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3)))))) (Algebra.toModule.{u2, u3} K L' (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))) _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u1, u3, max u1 u3} K L L' (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))) _inst_4 _inst_5 (AlgHom.{u2, u1, u3} K L L' (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))) _inst_4 _inst_5) (AlgHom.algHomClass.{u2, u1, u3} K L L' (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))) _inst_4 _inst_5))))) f x) y))
+  forall {K : Type.{u2}} {L : Type.{u1}} {L' : Type.{u3}} [_inst_1 : Field.{u2} K] [_inst_2 : Field.{u1} L] [_inst_3 : Field.{u3} L'] [_inst_4 : Algebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))] [_inst_5 : Algebra.{u2, u3} K L' (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3)))] {f : AlgHom.{u2, u1, u3} K L L' (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))) _inst_4 _inst_5} {y : L'}, Iff (Membership.mem.{u3, u3} L' (IntermediateField.{u2, u3} K L' _inst_1 _inst_3 _inst_5) (SetLike.instMembership.{u3, u3} (IntermediateField.{u2, u3} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.instSetLikeIntermediateField.{u2, u3} K L' _inst_1 _inst_3 _inst_5)) y (AlgHom.fieldRange.{u2, u1, u3} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 f)) (Exists.{succ u1} L (fun (x : L) => Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : L) => L') x) (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (AlgHom.{u2, u1, u3} K L L' (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))) _inst_4 _inst_5) L (fun (_x : L) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : L) => L') _x) (SMulHomClass.toFunLike.{max u1 u3, u2, u1, u3} (AlgHom.{u2, u1, u3} K L L' (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))) _inst_4 _inst_5) K L L' (SMulZeroClass.toSMul.{u2, u1} K L (AddMonoid.toZero.{u1} L (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))))) (DistribSMul.toSMulZeroClass.{u2, u1} K L (AddMonoid.toAddZeroClass.{u1} L (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))))) (DistribMulAction.toDistribSMul.{u2, u1} K L (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))))))) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4))))) (SMulZeroClass.toSMul.{u2, u3} K L' (AddMonoid.toZero.{u3} L' (AddCommMonoid.toAddMonoid.{u3} L' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} L' (Semiring.toNonAssocSemiring.{u3} L' (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3)))))))) (DistribSMul.toSMulZeroClass.{u2, u3} K L' (AddMonoid.toAddZeroClass.{u3} L' (AddCommMonoid.toAddMonoid.{u3} L' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} L' (Semiring.toNonAssocSemiring.{u3} L' (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3)))))))) (DistribMulAction.toDistribSMul.{u2, u3} K L' (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u3} L' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} L' (Semiring.toNonAssocSemiring.{u3} L' (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))))))) (Module.toDistribMulAction.{u2, u3} K L' (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} L' (Semiring.toNonAssocSemiring.{u3} L' (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3)))))) (Algebra.toModule.{u2, u3} K L' (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))) _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u3, u2, u1, u3} (AlgHom.{u2, u1, u3} K L L' (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))) _inst_4 _inst_5) K L L' (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))))))) (AddCommMonoid.toAddMonoid.{u3} L' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} L' (Semiring.toNonAssocSemiring.{u3} L' (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))))))) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4)) (Module.toDistribMulAction.{u2, u3} K L' (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} L' (Semiring.toNonAssocSemiring.{u3} L' (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3)))))) (Algebra.toModule.{u2, u3} K L' (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))) _inst_5)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u3, u2, u1, u3} (AlgHom.{u2, u1, u3} K L L' (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))) _inst_4 _inst_5) K L L' (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} L' (Semiring.toNonAssocSemiring.{u3} L' (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))))) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4)) (Module.toDistribMulAction.{u2, u3} K L' (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} L' (Semiring.toNonAssocSemiring.{u3} L' (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3)))))) (Algebra.toModule.{u2, u3} K L' (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))) _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u1, u3, max u1 u3} K L L' (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))) _inst_4 _inst_5 (AlgHom.{u2, u1, u3} K L L' (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))) _inst_4 _inst_5) (AlgHom.algHomClass.{u2, u1, u3} K L L' (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))) _inst_4 _inst_5))))) f x) y))
 Case conversion may be inaccurate. Consider using '#align alg_hom.mem_field_range AlgHom.mem_fieldRangeₓ'. -/
 @[simp]
 theorem mem_fieldRange {y : L'} : y ∈ f.fieldRange ↔ ∃ x, f x = y :=
@@ -895,7 +895,7 @@ def val : S →ₐ[K] L :=
 lean 3 declaration is
   forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] (S : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4), Eq.{succ u2} ((coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) S) -> L) (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} K (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) S) L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) S) (DivisionRing.toRing.{u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) S) (Field.toDivisionRing.{u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) S) (IntermediateField.toField.{u1, u2} K L _inst_1 _inst_2 _inst_4 S)))) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (IntermediateField.algebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S) _inst_4) (fun (_x : AlgHom.{u1, u2, u2} K (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) S) L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) S) (DivisionRing.toRing.{u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) S) (Field.toDivisionRing.{u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) S) (IntermediateField.toField.{u1, u2} K L _inst_1 _inst_2 _inst_4 S)))) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (IntermediateField.algebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S) _inst_4) => (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) S) -> L) ([anonymous].{u1, u2, u2} K (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) S) L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) S) (DivisionRing.toRing.{u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) S) (Field.toDivisionRing.{u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) S) (IntermediateField.toField.{u1, u2} K L _inst_1 _inst_2 _inst_4 S)))) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (IntermediateField.algebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S) _inst_4) (IntermediateField.val.{u1, u2} K L _inst_1 _inst_2 _inst_4 S)) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) S) L (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) S) L (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) S) L (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) S) L (coeSubtype.{succ u2} L (fun (x : L) => Membership.Mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.hasMem.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S))))))
 but is expected to have type
-  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))] (S : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4), Eq.{succ u2} (forall (ᾰ : Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)), (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) => L) ᾰ) (FunLike.coe.{succ u2, succ u2, succ u2} (AlgHom.{u1, u2, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (IntermediateField.algebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S) _inst_4) (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (fun (_x : Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) => L) _x) (SMulHomClass.toFunLike.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (IntermediateField.algebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S) _inst_4) K (Subtype.{succ u2} L (fun (x : L) => 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L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S))))))) (DistribSMul.toSMulZeroClass.{u1, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) 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_inst_1 _inst_2 _inst_4)) x S)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S))))))) (DistribMulAction.toDistribSMul.{u1, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L 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(Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S)))))) (Module.toDistribMulAction.{u1, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L 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_inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S))))) (Algebra.toModule.{u1, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S)) (IntermediateField.algebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S)))))) (SMulZeroClass.toSMul.{u1, u2} K L (AddMonoid.toZero.{u2} L (AddCommMonoid.toAddMonoid.{u2} L 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(IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (IntermediateField.algebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S) _inst_4) K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) L (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S)))))) (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))))) (Module.toDistribMulAction.{u1, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S))))) (Algebra.toModule.{u1, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S)) (IntermediateField.algebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S))) (Module.toDistribMulAction.{u1, u2} K L (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (Algebra.toModule.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (IntermediateField.algebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S) _inst_4) K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) L (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (Module.toDistribMulAction.{u1, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S))))) (Algebra.toModule.{u1, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S)) (IntermediateField.algebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S))) (Module.toDistribMulAction.{u1, u2} K L (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (Algebra.toModule.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u2, u2, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (IntermediateField.algebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S) _inst_4 (AlgHom.{u1, u2, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (IntermediateField.algebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S) _inst_4) (AlgHom.algHomClass.{u1, u2, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (IntermediateField.algebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S) _inst_4))))) (IntermediateField.val.{u1, u2} K L _inst_1 _inst_2 _inst_4 S)) (Subtype.val.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Set.{u2} L) (Set.instMembershipSet.{u2} L) x (SetLike.coe.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) S)))
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))] (S : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4), Eq.{succ u2} (forall (ᾰ : Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)), (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) => L) ᾰ) (FunLike.coe.{succ u2, succ u2, succ u2} (AlgHom.{u1, u2, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (IntermediateField.algebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S) _inst_4) (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (fun (_x : Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) => L) _x) (SMulHomClass.toFunLike.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (IntermediateField.algebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S) _inst_4) K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) L (SMulZeroClass.toSMul.{u1, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (AddMonoid.toZero.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S))))))) (DistribSMul.toSMulZeroClass.{u1, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (AddMonoid.toAddZeroClass.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S))))))) (DistribMulAction.toDistribSMul.{u1, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L 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(Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S)))))) (Module.toDistribMulAction.{u1, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S))))) (Algebra.toModule.{u1, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S)) (IntermediateField.algebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S)))))) (SMulZeroClass.toSMul.{u1, u2} K L (AddMonoid.toZero.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))))) (DistribSMul.toSMulZeroClass.{u1, u2} K L (AddMonoid.toAddZeroClass.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))))) (DistribMulAction.toDistribSMul.{u1, u2} K L (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L 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(IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (IntermediateField.algebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S) _inst_4) K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) L (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S)))))) (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))))) (Module.toDistribMulAction.{u1, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S))))) (Algebra.toModule.{u1, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S)) (IntermediateField.algebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S))) (Module.toDistribMulAction.{u1, u2} K L (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (Algebra.toModule.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (IntermediateField.algebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S) _inst_4) K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) L (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (Module.toDistribMulAction.{u1, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S))))) (Algebra.toModule.{u1, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S)) (IntermediateField.algebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S))) (Module.toDistribMulAction.{u1, u2} K L (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (Algebra.toModule.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u2, u2, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (IntermediateField.algebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S) _inst_4 (AlgHom.{u1, u2, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (IntermediateField.algebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S) _inst_4) (AlgHom.algHomClass.{u1, u2, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (IntermediateField.algebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S) _inst_4))))) (IntermediateField.val.{u1, u2} K L _inst_1 _inst_2 _inst_4 S)) (Subtype.val.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Set.{u2} L) (Set.instMembershipSet.{u2} L) x (SetLike.coe.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) S)))
 Case conversion may be inaccurate. Consider using '#align intermediate_field.coe_val IntermediateField.coe_valₓ'. -/
 @[simp]
 theorem coe_val : ⇑S.val = coe :=
@@ -906,7 +906,7 @@ theorem coe_val : ⇑S.val = coe :=
 lean 3 declaration is
   forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] (S : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) {x : L} (hx : Membership.Mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.hasMem.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S), Eq.{succ u2} L (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} K (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) S) L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) S) (DivisionRing.toRing.{u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) S) (Field.toDivisionRing.{u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) S) (IntermediateField.toField.{u1, u2} K L _inst_1 _inst_2 _inst_4 S)))) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (IntermediateField.algebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S) _inst_4) (fun (_x : AlgHom.{u1, u2, u2} K (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) S) L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) S) (DivisionRing.toRing.{u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L 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 but is expected to have type
-  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))] (S : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) {x : L} (hx : Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 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u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) => L) _x) (SMulHomClass.toFunLike.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S)) 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(Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S))))))) (DistribMulAction.toDistribSMul.{u1, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L 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(IntermediateField.algebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S)))))) (SMulZeroClass.toSMul.{u1, u2} K L (AddMonoid.toZero.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))))) (DistribSMul.toSMulZeroClass.{u1, u2} K L (AddMonoid.toAddZeroClass.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))))) (DistribMulAction.toDistribSMul.{u1, u2} K L (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) 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_inst_4)) x S)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S)))))) (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))))) (Module.toDistribMulAction.{u1, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S))))) (Algebra.toModule.{u1, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S)) (IntermediateField.algebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S))) (Module.toDistribMulAction.{u1, u2} K L (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (Algebra.toModule.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (IntermediateField.algebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S) _inst_4) K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) L (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} L 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: L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S)) (IntermediateField.algebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S))) (Module.toDistribMulAction.{u1, u2} K L (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (Algebra.toModule.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u2, u2, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (IntermediateField.algebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S) _inst_4 (AlgHom.{u1, u2, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (IntermediateField.algebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S) _inst_4) (AlgHom.algHomClass.{u1, u2, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (IntermediateField.algebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S) _inst_4))))) (IntermediateField.val.{u1, u2} K L _inst_1 _inst_2 _inst_4 S) (Subtype.mk.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S) x hx)) x
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))] (S : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) {x : L} (hx : Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) => L) (Subtype.mk.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S) x hx)) (FunLike.coe.{succ u2, succ u2, succ u2} (AlgHom.{u1, u2, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (IntermediateField.algebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S) _inst_4) (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (fun (_x : Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) => L) _x) (SMulHomClass.toFunLike.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (IntermediateField.algebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S) _inst_4) K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) L (SMulZeroClass.toSMul.{u1, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (AddMonoid.toZero.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) 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(Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S))))))) (DistribMulAction.toDistribSMul.{u1, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) 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(IntermediateField.algebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S)))))) (SMulZeroClass.toSMul.{u1, u2} K L (AddMonoid.toZero.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))))) (DistribSMul.toSMulZeroClass.{u1, u2} K L (AddMonoid.toAddZeroClass.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))))) (DistribMulAction.toDistribSMul.{u1, u2} K L (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) 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_inst_4)) x S)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S)))))) (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))))) (Module.toDistribMulAction.{u1, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S))))) (Algebra.toModule.{u1, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S)) (IntermediateField.algebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S))) (Module.toDistribMulAction.{u1, u2} K L (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (Algebra.toModule.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (IntermediateField.algebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S) _inst_4) K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) L (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} L 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: L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S)) (IntermediateField.algebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S))) (Module.toDistribMulAction.{u1, u2} K L (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (Algebra.toModule.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u2, u2, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (IntermediateField.algebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S) _inst_4 (AlgHom.{u1, u2, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (IntermediateField.algebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S) _inst_4) (AlgHom.algHomClass.{u1, u2, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (IntermediateField.algebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S) _inst_4))))) (IntermediateField.val.{u1, u2} K L _inst_1 _inst_2 _inst_4 S) (Subtype.mk.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S) x hx)) x
 Case conversion may be inaccurate. Consider using '#align intermediate_field.val_mk IntermediateField.val_mkₓ'. -/
 @[simp]
 theorem val_mk {x : L} (hx : x ∈ S) : S.val ⟨x, hx⟩ = x :=
@@ -948,7 +948,7 @@ instance AlgHom.inhabited : Inhabited (S →ₐ[K] L) :=
 lean 3 declaration is
   forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] (S : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) {R : Type.{u3}} [_inst_6 : CommRing.{u3} R] [_inst_7 : Algebra.{u3, u1} R K (CommRing.toCommSemiring.{u3} R _inst_6) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))] [_inst_8 : Algebra.{u3, u2} R L (CommRing.toCommSemiring.{u3} R _inst_6) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] [_inst_9 : IsScalarTower.{u3, u1, u2} R K L (SMulZeroClass.toHasSmul.{u3, u1} R K (AddZeroClass.toHasZero.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))))) (SMulWithZero.toSmulZeroClass.{u3, u1} R K (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6)))))) (AddZeroClass.toHasZero.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))))) (MulActionWithZero.toSMulWithZero.{u3, u1} R K (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (AddZeroClass.toHasZero.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))))) (Module.toMulActionWithZero.{u3, u1} R K (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Algebra.toModule.{u3, u1} R K (CommRing.toCommSemiring.{u3} R _inst_6) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_7))))) (SMulZeroClass.toHasSmul.{u1, u2} K L (AddZeroClass.toHasZero.{u2} L (AddMonoid.toAddZeroClass.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} K L (MulZeroClass.toHasZero.{u1} K (MulZeroOneClass.toMulZeroClass.{u1} K (MonoidWithZero.toMulZeroOneClass.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (AddZeroClass.toHasZero.{u2} L (AddMonoid.toAddZeroClass.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} K L (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (AddZeroClass.toHasZero.{u2} L (AddMonoid.toAddZeroClass.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))))) (Module.toMulActionWithZero.{u1, u2} K L (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) (Algebra.toModule.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_4))))) (SMulZeroClass.toHasSmul.{u3, u2} R L (AddZeroClass.toHasZero.{u2} L (AddMonoid.toAddZeroClass.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))))) (SMulWithZero.toSmulZeroClass.{u3, u2} R L (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6)))))) (AddZeroClass.toHasZero.{u2} L (AddMonoid.toAddZeroClass.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))))) (MulActionWithZero.toSMulWithZero.{u3, u2} R L (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (AddZeroClass.toHasZero.{u2} L (AddMonoid.toAddZeroClass.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))))) (Module.toMulActionWithZero.{u3, u2} R L (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) (Algebra.toModule.{u3, u2} R L (CommRing.toCommSemiring.{u3} R _inst_6) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_8)))))] (x : coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) S) (P : Polynomial.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_6))), Eq.{succ u2} L (coeFn.{max (succ u3) (succ u2), max (succ u3) (succ u2)} (AlgHom.{u3, u3, u2} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) L (CommRing.toCommSemiring.{u3} R _inst_6) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Polynomial.algebraOfAlgebra.{u3, u3} R R (CommRing.toCommSemiring.{u3} R _inst_6) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6)) (Algebra.id.{u3} R 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(CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (AddZeroClass.toHasZero.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))))) (Module.toMulActionWithZero.{u3, u1} R K (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Algebra.toModule.{u3, u1} R K (CommRing.toCommSemiring.{u3} R _inst_6) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_7))))) _inst_8 _inst_9) x) P))
 but is expected to have type
-  forall {K : Type.{u2}} {L : Type.{u1}} [_inst_1 : Field.{u2} K] [_inst_2 : Field.{u1} L] [_inst_4 : Algebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))] (S : IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) {R : Type.{u3}} [_inst_6 : CommRing.{u3} R] [_inst_7 : Algebra.{u3, u2} R K (CommRing.toCommSemiring.{u3} R _inst_6) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))] [_inst_8 : Algebra.{u3, u1} R L (CommRing.toCommSemiring.{u3} R _inst_6) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))] [_inst_9 : IsScalarTower.{u3, u2, u1} R K L (Algebra.toSMul.{u3, u2} R K (CommRing.toCommSemiring.{u3} R _inst_6) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) _inst_7) (Algebra.toSMul.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (Algebra.toSMul.{u3, u1} R L (CommRing.toCommSemiring.{u3} R _inst_6) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_8)] (x : Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x S)) (P : Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) => L) P) 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_inst_6))) => L) _x) (SMulHomClass.toFunLike.{max u1 u3, u3, u3, u1} (AlgHom.{u3, u3, u1} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) L (CommRing.toCommSemiring.{u3} R _inst_6) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (Polynomial.algebraOfAlgebra.{u3, u3} R R (CommRing.toCommSemiring.{u3} R _inst_6) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) _inst_8) R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) L (SMulZeroClass.toSMul.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (AddMonoid.toZero.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))))))) (Module.toDistribMulAction.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6)))))) (Algebra.toModule.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (CommRing.toCommSemiring.{u3} R _inst_6) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (Polynomial.algebraOfAlgebra.{u3, u3} R R (CommRing.toCommSemiring.{u3} R _inst_6) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6)))))))) (SMulZeroClass.toSMul.{u3, u1} R L (AddMonoid.toZero.{u1} L (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))))) (DistribSMul.toSMulZeroClass.{u3, u1} R L (AddMonoid.toAddZeroClass.{u1} L (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))))) (DistribMulAction.toDistribSMul.{u3, u1} R L (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6)))) (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))))))) (Module.toDistribMulAction.{u3, u1} R L (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))) (Algebra.toModule.{u3, u1} R L (CommRing.toCommSemiring.{u3} R _inst_6) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_8))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u3, u3, u3, u1} (AlgHom.{u3, u3, u1} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) L (CommRing.toCommSemiring.{u3} R _inst_6) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (Polynomial.algebraOfAlgebra.{u3, u3} R R (CommRing.toCommSemiring.{u3} R _inst_6) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) _inst_8) R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) L (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6)))) (AddCommMonoid.toAddMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))))))) (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))))))) (Module.toDistribMulAction.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6)))))) (Algebra.toModule.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (CommRing.toCommSemiring.{u3} R _inst_6) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (Polynomial.algebraOfAlgebra.{u3, u3} R R (CommRing.toCommSemiring.{u3} R _inst_6) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))))) (Module.toDistribMulAction.{u3, u1} R L (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))) (Algebra.toModule.{u3, u1} R L 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(IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x S)) (Subalgebra.toSemiring.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 S)))))) (Module.toDistribMulAction.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} 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(IntermediateField.toSubalgebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 S)) (IntermediateField.algebra'.{u2, u1, u3} K L _inst_1 _inst_2 _inst_4 S R (CommRing.toCommSemiring.{u3} R _inst_6) (Algebra.toSMul.{u3, u2} R K (CommRing.toCommSemiring.{u3} R _inst_6) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) _inst_7) _inst_8 _inst_9))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u3, u3, u3, u1} (AlgHom.{u3, u3, u1} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x S)) (CommRing.toCommSemiring.{u3} R _inst_6) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (Subalgebra.toSemiring.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 S)) (Polynomial.algebraOfAlgebra.{u3, u3} R R (CommRing.toCommSemiring.{u3} R _inst_6) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (IntermediateField.algebra'.{u2, u1, u3} K L _inst_1 _inst_2 _inst_4 S R (CommRing.toCommSemiring.{u3} R _inst_6) (Algebra.toSMul.{u3, u2} R K (CommRing.toCommSemiring.{u3} R _inst_6) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) _inst_7) _inst_8 _inst_9)) R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x S)) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x S)) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x S)) (Subalgebra.toSemiring.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 S)))) (Module.toDistribMulAction.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6)))))) (Algebra.toModule.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (CommRing.toCommSemiring.{u3} R _inst_6) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (Polynomial.algebraOfAlgebra.{u3, u3} R R (CommRing.toCommSemiring.{u3} R _inst_6) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))))) (Module.toDistribMulAction.{u3, u1} R (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x S)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x S)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x S)) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x S)) (Subalgebra.toSemiring.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 S))))) (Algebra.toModule.{u3, u1} R (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x S)) (CommRing.toCommSemiring.{u3} R _inst_6) (Subalgebra.toSemiring.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 S)) (IntermediateField.algebra'.{u2, u1, u3} K L _inst_1 _inst_2 _inst_4 S R (CommRing.toCommSemiring.{u3} R _inst_6) (Algebra.toSMul.{u3, u2} R K (CommRing.toCommSemiring.{u3} R _inst_6) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) _inst_7) _inst_8 _inst_9))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, u3, u1, max u1 u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x S)) (CommRing.toCommSemiring.{u3} R _inst_6) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (Subalgebra.toSemiring.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 S)) (Polynomial.algebraOfAlgebra.{u3, u3} R R (CommRing.toCommSemiring.{u3} R _inst_6) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (IntermediateField.algebra'.{u2, u1, u3} K L _inst_1 _inst_2 _inst_4 S R (CommRing.toCommSemiring.{u3} R _inst_6) (Algebra.toSMul.{u3, u2} R K (CommRing.toCommSemiring.{u3} R _inst_6) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) _inst_7) _inst_8 _inst_9) (AlgHom.{u3, u3, u1} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x S)) (CommRing.toCommSemiring.{u3} R _inst_6) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (Subalgebra.toSemiring.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 S)) (Polynomial.algebraOfAlgebra.{u3, u3} R R (CommRing.toCommSemiring.{u3} R _inst_6) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (IntermediateField.algebra'.{u2, u1, u3} K L _inst_1 _inst_2 _inst_4 S R (CommRing.toCommSemiring.{u3} R _inst_6) (Algebra.toSMul.{u3, u2} R K (CommRing.toCommSemiring.{u3} R _inst_6) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) _inst_7) _inst_8 _inst_9)) (AlgHom.algHomClass.{u3, u3, u1} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x S)) (CommRing.toCommSemiring.{u3} R _inst_6) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (Subalgebra.toSemiring.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 S)) (Polynomial.algebraOfAlgebra.{u3, u3} R R (CommRing.toCommSemiring.{u3} R _inst_6) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (IntermediateField.algebra'.{u2, u1, u3} K L _inst_1 _inst_2 _inst_4 S R (CommRing.toCommSemiring.{u3} R _inst_6) (Algebra.toSMul.{u3, u2} R K (CommRing.toCommSemiring.{u3} R _inst_6) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) _inst_7) _inst_8 _inst_9)))))) (Polynomial.aeval.{u3, u1} R (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x S)) (CommRing.toCommSemiring.{u3} R _inst_6) (Subalgebra.toSemiring.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 S)) (IntermediateField.algebra'.{u2, u1, u3} K L _inst_1 _inst_2 _inst_4 S R (CommRing.toCommSemiring.{u3} R _inst_6) (Algebra.toSMul.{u3, u2} R K (CommRing.toCommSemiring.{u3} R _inst_6) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) _inst_7) _inst_8 _inst_9) x) P))
+  forall {K : Type.{u2}} {L : Type.{u1}} [_inst_1 : Field.{u2} K] [_inst_2 : Field.{u1} L] [_inst_4 : Algebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))] (S : IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) {R : Type.{u3}} [_inst_6 : CommRing.{u3} R] [_inst_7 : Algebra.{u3, u2} R K (CommRing.toCommSemiring.{u3} R _inst_6) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))] [_inst_8 : Algebra.{u3, u1} R L (CommRing.toCommSemiring.{u3} R _inst_6) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))] [_inst_9 : IsScalarTower.{u3, u2, u1} R K L (Algebra.toSMul.{u3, u2} R K (CommRing.toCommSemiring.{u3} R _inst_6) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) _inst_7) (Algebra.toSMul.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (Algebra.toSMul.{u3, u1} R L (CommRing.toCommSemiring.{u3} R _inst_6) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_8)] (x : Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x S)) (P : Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) => L) P) 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_inst_6)))) (AddCommMonoid.toAddMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))))))) (AddCommMonoid.toAddMonoid.{u1} (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x S)) 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(IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x S)) (Subalgebra.toSemiring.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 S)))))) (Module.toDistribMulAction.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} 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_inst_6))))) (Module.toDistribMulAction.{u3, u1} R (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x S)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x S)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} 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K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x S)) (CommRing.toCommSemiring.{u3} R _inst_6) (Subalgebra.toSemiring.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 S)) (IntermediateField.algebra'.{u2, u1, u3} K L _inst_1 _inst_2 _inst_4 S R (CommRing.toCommSemiring.{u3} R _inst_6) (Algebra.toSMul.{u3, u2} R K (CommRing.toCommSemiring.{u3} R _inst_6) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) _inst_7) _inst_8 _inst_9))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, u3, u1, max u1 u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x S)) (CommRing.toCommSemiring.{u3} R _inst_6) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (Subalgebra.toSemiring.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 S)) (Polynomial.algebraOfAlgebra.{u3, u3} R R (CommRing.toCommSemiring.{u3} R _inst_6) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (IntermediateField.algebra'.{u2, u1, u3} K L _inst_1 _inst_2 _inst_4 S R (CommRing.toCommSemiring.{u3} R _inst_6) (Algebra.toSMul.{u3, u2} R K (CommRing.toCommSemiring.{u3} R _inst_6) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) _inst_7) _inst_8 _inst_9) (AlgHom.{u3, u3, u1} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x S)) (CommRing.toCommSemiring.{u3} R _inst_6) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (Subalgebra.toSemiring.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 S)) (Polynomial.algebraOfAlgebra.{u3, u3} R R (CommRing.toCommSemiring.{u3} R _inst_6) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (IntermediateField.algebra'.{u2, u1, u3} K L _inst_1 _inst_2 _inst_4 S R (CommRing.toCommSemiring.{u3} R _inst_6) (Algebra.toSMul.{u3, u2} R K (CommRing.toCommSemiring.{u3} R _inst_6) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) _inst_7) _inst_8 _inst_9)) (AlgHom.algHomClass.{u3, u3, u1} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x S)) (CommRing.toCommSemiring.{u3} R _inst_6) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (Subalgebra.toSemiring.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 S)) (Polynomial.algebraOfAlgebra.{u3, u3} R R (CommRing.toCommSemiring.{u3} R _inst_6) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (IntermediateField.algebra'.{u2, u1, u3} K L _inst_1 _inst_2 _inst_4 S R (CommRing.toCommSemiring.{u3} R _inst_6) (Algebra.toSMul.{u3, u2} R K (CommRing.toCommSemiring.{u3} R _inst_6) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) _inst_7) _inst_8 _inst_9)))))) (Polynomial.aeval.{u3, u1} R (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x S)) (CommRing.toCommSemiring.{u3} R _inst_6) (Subalgebra.toSemiring.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 S)) (IntermediateField.algebra'.{u2, u1, u3} K L _inst_1 _inst_2 _inst_4 S R (CommRing.toCommSemiring.{u3} R _inst_6) (Algebra.toSMul.{u3, u2} R K (CommRing.toCommSemiring.{u3} R _inst_6) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) _inst_7) _inst_8 _inst_9) x) P))
 Case conversion may be inaccurate. Consider using '#align intermediate_field.aeval_coe IntermediateField.aeval_coeₓ'. -/
 theorem aeval_coe {R : Type _} [CommRing R] [Algebra R K] [Algebra R L] [IsScalarTower R K L]
     (x : S) (P : R[X]) : aeval (x : L) P = aeval x P :=
@@ -997,7 +997,7 @@ def inclusion {E F : IntermediateField K L} (hEF : E ≤ F) : E →ₐ[K] F :=
 lean 3 declaration is
   forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] {E : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4} {F : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4} (hEF : LE.le.{u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (Preorder.toHasLe.{u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (PartialOrder.toPreorder.{u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.partialOrder.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)))) E F), Function.Injective.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} 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_inst_1 _inst_2 _inst_4 F)) (fun (_x : AlgHom.{u1, u2, u2} K (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) E) (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) F) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) E) (DivisionRing.toRing.{u2} (coeSort.{succ u2, succ (succ u2)} 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 but is expected to have type
-  forall {K : Type.{u2}} {L : Type.{u1}} [_inst_1 : Field.{u2} K] [_inst_2 : Field.{u1} L] [_inst_4 : Algebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))] {E : IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4} {F : IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4} (hEF : LE.le.{u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (Preorder.toLE.{u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (PartialOrder.toPreorder.{u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instPartialOrder.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)))) E F), Function.Injective.{succ u1, succ u1} (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 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(AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u1, u1, u1} K (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x E)) (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x F)) (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (Subalgebra.toSemiring.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 E)) (Subalgebra.toSemiring.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 F)) (IntermediateField.algebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 E) (IntermediateField.algebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 F) (AlgHom.{u2, u1, u1} K (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x E)) (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x F)) (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (Subalgebra.toSemiring.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 E)) (Subalgebra.toSemiring.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 F)) 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(Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 E)) (Subalgebra.toSemiring.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 F)) (IntermediateField.algebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 E) (IntermediateField.algebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 F)))))) (IntermediateField.inclusion.{u2, u1} K L _inst_1 _inst_2 _inst_4 E F hEF))
+  forall {K : Type.{u2}} {L : Type.{u1}} [_inst_1 : Field.{u2} K] [_inst_2 : Field.{u1} L] [_inst_4 : Algebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))] {E : IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4} {F : IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4} (hEF : LE.le.{u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (Preorder.toLE.{u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (PartialOrder.toPreorder.{u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instPartialOrder.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)))) E F), Function.Injective.{succ u1, succ u1} (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 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L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x E)) (fun (_x : Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x E)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x E)) => Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x F)) _x) (SMulHomClass.toFunLike.{u1, u2, u1, u1} (AlgHom.{u2, u1, u1} K (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x E)) (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x F)) (Semifield.toCommSemiring.{u2} K 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(IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x E)) (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x F)) (SMulZeroClass.toSMul.{u2, u1} K (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x E)) (AddMonoid.toZero.{u1} (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L 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(IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x E)) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x E)) (Subalgebra.toSemiring.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 E))))))) (DistribSMul.toSMulZeroClass.{u2, u1} K (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} 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(Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 E)) (IntermediateField.algebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 E))) (Module.toDistribMulAction.{u2, u1} K (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x F)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x F)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x F)) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x F)) (Subalgebra.toSemiring.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 F))))) (Algebra.toModule.{u2, u1} K (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x F)) (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (Subalgebra.toSemiring.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 F)) (IntermediateField.algebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 F))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u1, u1, u1} K (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x E)) (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x F)) (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (Subalgebra.toSemiring.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 E)) (Subalgebra.toSemiring.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 F)) (IntermediateField.algebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 E) (IntermediateField.algebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 F) (AlgHom.{u2, u1, u1} K (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 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(IntermediateField.algebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 E) (IntermediateField.algebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 F)) (AlgHom.algHomClass.{u2, u1, u1} K (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x E)) (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x F)) (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (Subalgebra.toSemiring.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 E)) (Subalgebra.toSemiring.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 F)) (IntermediateField.algebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 E) (IntermediateField.algebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 F)))))) (IntermediateField.inclusion.{u2, u1} K L _inst_1 _inst_2 _inst_4 E F hEF))
 Case conversion may be inaccurate. Consider using '#align intermediate_field.inclusion_injective IntermediateField.inclusion_injectiveₓ'. -/
 theorem inclusion_injective {E F : IntermediateField K L} (hEF : E ≤ F) :
     Function.Injective (inclusion hEF) :=
@@ -1019,7 +1019,7 @@ theorem inclusion_self {E : IntermediateField K L} : inclusion (le_refl E) = Alg
 lean 3 declaration is
   forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] {E : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4} {F : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4} {G : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4} (hEF : LE.le.{u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (Preorder.toHasLe.{u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (PartialOrder.toPreorder.{u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.partialOrder.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)))) E F) (hFG : LE.le.{u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (Preorder.toHasLe.{u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (PartialOrder.toPreorder.{u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.partialOrder.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)))) F G) (x : coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) E), Eq.{succ u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) G) (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} K (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} 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 but is expected to have type
-  forall {K : Type.{u2}} {L : Type.{u1}} [_inst_1 : Field.{u2} K] [_inst_2 : Field.{u1} L] [_inst_4 : Algebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))] {E : IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4} {F : IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4} {G : IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4} (hEF : LE.le.{u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (Preorder.toLE.{u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (PartialOrder.toPreorder.{u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instPartialOrder.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)))) E F) (hFG : LE.le.{u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) 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(Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 G)) (IntermediateField.algebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 E) (IntermediateField.algebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 G)) K (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x E)) (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x G)) (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x E)) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x E)) (Subalgebra.toSemiring.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 E)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x G)) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x G)) (Subalgebra.toSemiring.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 G)))) (Module.toDistribMulAction.{u2, u1} K (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x E)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x E)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x E)) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x E)) (Subalgebra.toSemiring.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 E))))) (Algebra.toModule.{u2, u1} K (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x E)) (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (Subalgebra.toSemiring.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 E)) (IntermediateField.algebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 E))) (Module.toDistribMulAction.{u2, u1} K (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x G)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x G)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x G)) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} L (fun (x : L) => 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u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 G)) (IntermediateField.algebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 G))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u1, u1, u1} K (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x E)) (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x G)) (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (Subalgebra.toSemiring.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 E)) (Subalgebra.toSemiring.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 G)) (IntermediateField.algebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 E) (IntermediateField.algebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 G) (AlgHom.{u2, u1, u1} K (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x E)) (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x G)) (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (Subalgebra.toSemiring.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 E)) (Subalgebra.toSemiring.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 G)) (IntermediateField.algebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 E) (IntermediateField.algebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 G)) (AlgHom.algHomClass.{u2, u1, u1} K (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x E)) (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x G)) (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (Subalgebra.toSemiring.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 E)) (Subalgebra.toSemiring.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 G)) (IntermediateField.algebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 E) (IntermediateField.algebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 G)))))) (IntermediateField.inclusion.{u2, u1} K L _inst_1 _inst_2 _inst_4 E G (le_trans.{u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (PartialOrder.toPreorder.{u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instPartialOrder.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4))) E F G hEF hFG)) x)
+  forall {K : Type.{u2}} {L : Type.{u1}} [_inst_1 : Field.{u2} K] [_inst_2 : Field.{u1} L] [_inst_4 : Algebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))] {E : IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4} {F : IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4} {G : IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4} (hEF : LE.le.{u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (Preorder.toLE.{u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (PartialOrder.toPreorder.{u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instPartialOrder.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)))) E F) (hFG : LE.le.{u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (Preorder.toLE.{u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (PartialOrder.toPreorder.{u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instPartialOrder.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)))) F G) (x : Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x E)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x F)) => Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x G)) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgHom.{u2, u1, u1} K (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x E)) (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x F)) (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (Subalgebra.toSemiring.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 E)) (Subalgebra.toSemiring.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 F)) (IntermediateField.algebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 E) (IntermediateField.algebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 F)) (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L 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(Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 E)) (Subalgebra.toSemiring.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 F)) (IntermediateField.algebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 E) (IntermediateField.algebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 F)) K (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x E)) (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x E)) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x E)) (Subalgebra.toSemiring.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 E))))))) (DistribMulAction.toDistribSMul.{u2, u1} K (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x E)) (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x E)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L 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u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 G)) (IntermediateField.algebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 G))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u1, u1, u1} K (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x E)) (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x G)) (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (Subalgebra.toSemiring.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 E)) (Subalgebra.toSemiring.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 G)) (IntermediateField.algebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 E) (IntermediateField.algebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 G) (AlgHom.{u2, u1, u1} K (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x E)) (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x G)) (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (Subalgebra.toSemiring.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 E)) (Subalgebra.toSemiring.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 G)) (IntermediateField.algebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 E) (IntermediateField.algebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 G)) (AlgHom.algHomClass.{u2, u1, u1} K (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x E)) (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x G)) (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (Subalgebra.toSemiring.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 E)) (Subalgebra.toSemiring.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 G)) (IntermediateField.algebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 E) (IntermediateField.algebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 G)))))) (IntermediateField.inclusion.{u2, u1} K L _inst_1 _inst_2 _inst_4 E G (le_trans.{u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (PartialOrder.toPreorder.{u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instPartialOrder.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4))) E F G hEF hFG)) x)
 Case conversion may be inaccurate. Consider using '#align intermediate_field.inclusion_inclusion IntermediateField.inclusion_inclusionₓ'. -/
 @[simp]
 theorem inclusion_inclusion {E F G : IntermediateField K L} (hEF : E ≤ F) (hFG : F ≤ G) (x : E) :
@@ -1031,7 +1031,7 @@ theorem inclusion_inclusion {E F G : IntermediateField K L} (hEF : E ≤ F) (hFG
 lean 3 declaration is
   forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] {E : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4} {F : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4} (hEF : LE.le.{u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (Preorder.toHasLe.{u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (PartialOrder.toPreorder.{u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.partialOrder.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)))) E F) (e : coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) E), Eq.{succ u2} L ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) F) L (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) F) L (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) F) L (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) F) L (coeSubtype.{succ u2} L (fun (x : L) => Membership.Mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.hasMem.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x F))))) (coeFn.{succ u2, succ u2} (AlgHom.{u1, u2, u2} K (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) E) (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 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(IntermediateField.algebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 F)) (IntermediateField.inclusion.{u1, u2} K L _inst_1 _inst_2 _inst_4 E F hEF) e)) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) E) L (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) E) L (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 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 but is expected to have type
-  forall {K : Type.{u2}} {L : Type.{u1}} [_inst_1 : Field.{u2} K] [_inst_2 : Field.{u1} L] [_inst_4 : Algebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))] {E : IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4} {F : IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4} (hEF : LE.le.{u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (Preorder.toLE.{u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (PartialOrder.toPreorder.{u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instPartialOrder.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)))) E F) (e : Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) 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=> Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x F)) _x) (SMulHomClass.toFunLike.{u1, u2, u1, u1} (AlgHom.{u2, u1, u1} K (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x E)) (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x F)) (Semifield.toCommSemiring.{u2} K 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u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x F)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x F)) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x F)) (Subalgebra.toSemiring.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 F))))) (Algebra.toModule.{u2, u1} K (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x F)) (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (Subalgebra.toSemiring.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 F)) (IntermediateField.algebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 F))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u1, u1, u1} K (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x E)) (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x F)) (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (Subalgebra.toSemiring.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 E)) (Subalgebra.toSemiring.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 F)) (IntermediateField.algebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 E) (IntermediateField.algebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 F) (AlgHom.{u2, u1, u1} K (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x E)) (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x F)) (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (Subalgebra.toSemiring.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 E)) (Subalgebra.toSemiring.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 F)) (IntermediateField.algebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 E) (IntermediateField.algebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 F)) (AlgHom.algHomClass.{u2, u1, u1} K (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x E)) (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x F)) (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (Subalgebra.toSemiring.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 E)) (Subalgebra.toSemiring.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 F)) (IntermediateField.algebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 E) (IntermediateField.algebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 F)))))) (IntermediateField.inclusion.{u2, u1} K L _inst_1 _inst_2 _inst_4 E F hEF) e)) (Subtype.val.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (Set.{u1} L) (Set.instMembershipSet.{u1} L) x (SetLike.coe.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) E)) e)
+  forall {K : Type.{u2}} {L : Type.{u1}} [_inst_1 : Field.{u2} K] [_inst_2 : Field.{u1} L] [_inst_4 : Algebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))] {E : IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4} {F : IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4} (hEF : LE.le.{u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (Preorder.toLE.{u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (PartialOrder.toPreorder.{u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instPartialOrder.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)))) E F) (e : Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x E)), Eq.{succ u1} L (Subtype.val.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (Set.{u1} L) (Set.instMembershipSet.{u1} L) x (SetLike.coe.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) F)) (FunLike.coe.{succ u1, succ u1, succ u1} (AlgHom.{u2, u1, u1} K (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x E)) (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x F)) (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (Subalgebra.toSemiring.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 E)) (Subalgebra.toSemiring.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 F)) (IntermediateField.algebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 E) (IntermediateField.algebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 F)) (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x E)) (fun (_x : Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x E)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x E)) => Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x F)) _x) (SMulHomClass.toFunLike.{u1, u2, u1, u1} (AlgHom.{u2, u1, u1} K (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x E)) (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x F)) (Semifield.toCommSemiring.{u2} K 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(IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x E)) (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x F)) (SMulZeroClass.toSMul.{u2, u1} K (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x E)) (AddMonoid.toZero.{u1} (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L 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(IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x E)) (Subalgebra.toSemiring.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 E))))) (Algebra.toModule.{u2, u1} K (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x E)) (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (Subalgebra.toSemiring.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 E)) (IntermediateField.algebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 E))) (Module.toDistribMulAction.{u2, u1} K (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x F)) (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, 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(Field.toSemifield.{u1} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 F))))) (Algebra.toModule.{u2, u1} K (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x F)) (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (Subalgebra.toSemiring.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 F)) (IntermediateField.algebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 F))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u1, u1, u1} K (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x E)) (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x F)) (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (Subalgebra.toSemiring.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 E)) (Subalgebra.toSemiring.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 F)) (IntermediateField.algebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 E) (IntermediateField.algebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 F) (AlgHom.{u2, u1, u1} K (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x E)) (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x F)) (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (Subalgebra.toSemiring.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 E)) (Subalgebra.toSemiring.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 F)) (IntermediateField.algebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 E) (IntermediateField.algebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 F)) (AlgHom.algHomClass.{u2, u1, u1} K (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x E)) (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x F)) (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (Subalgebra.toSemiring.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 E)) (Subalgebra.toSemiring.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 F)) (IntermediateField.algebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 E) (IntermediateField.algebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 F)))))) (IntermediateField.inclusion.{u2, u1} K L _inst_1 _inst_2 _inst_4 E F hEF) e)) (Subtype.val.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (Set.{u1} L) (Set.instMembershipSet.{u1} L) x (SetLike.coe.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) E)) e)
 Case conversion may be inaccurate. Consider using '#align intermediate_field.coe_inclusion IntermediateField.coe_inclusionₓ'. -/
 @[simp]
 theorem coe_inclusion {E F : IntermediateField K L} (hEF : E ≤ F) (e : E) :

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

@@ -47,12 +47,14 @@ open BigOperators Polynomial
 
 variable (K L L' : Type _) [Field K] [Field L] [Field L'] [Algebra K L] [Algebra K L']
 
+#print IntermediateField /-
 /-- `S : intermediate_field K L` is a subset of `L` such that there is a field
 tower `L / S / K`. -/
 structure IntermediateField extends Subalgebra K L where
   neg_mem' : ∀ x ∈ carrier, -x ∈ carrier
   inv_mem' : ∀ x ∈ carrier, x⁻¹ ∈ carrier
 #align intermediate_field IntermediateField
+-/
 
 /-- Reinterpret an `intermediate_field` as a `subalgebra`. -/
 add_decl_doc IntermediateField.toSubalgebra
@@ -61,10 +63,12 @@ variable {K L L'} (S : IntermediateField K L)
 
 namespace IntermediateField
 
+#print IntermediateField.toSubfield /-
 /-- Reinterpret an `intermediate_field` as a `subfield`. -/
 def toSubfield : Subfield L :=
   { S.toSubalgebra, S with }
 #align intermediate_field.to_subfield IntermediateField.toSubfield
+-/
 
 instance : SetLike (IntermediateField K L) L :=
   ⟨fun S => S.toSubalgebra.carrier, by
@@ -80,22 +84,46 @@ instance : SubfieldClass (IntermediateField K L) L
   one_mem s := s.one_mem'
   inv_mem := inv_mem'
 
+/- warning: intermediate_field.mem_carrier -> IntermediateField.mem_carrier is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] {s : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4} {x : L}, Iff (Membership.Mem.{u2, u2} L (Set.{u2} L) (Set.hasMem.{u2} L) x (Subalgebra.carrier.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 s))) (Membership.Mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.hasMem.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x s)
+but is expected to have type
+  forall {K : Type.{u2}} {L : Type.{u1}} [_inst_1 : Field.{u2} K] [_inst_2 : Field.{u1} L] [_inst_4 : Algebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))] {s : IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4} {x : L}, Iff (Membership.mem.{u1, u1} L (Set.{u1} L) (Set.instMembershipSet.{u1} L) x (Subsemigroup.carrier.{u1} L (MulOneClass.toMul.{u1} L (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))))))) (Submonoid.toSubsemigroup.{u1} L (MulZeroOneClass.toMulOneClass.{u1} L (NonAssocSemiring.toMulZeroOneClass.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))) (Subsemiring.toSubmonoid.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))) (Subalgebra.toSubsemiring.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 s)))))) (Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x s)
+Case conversion may be inaccurate. Consider using '#align intermediate_field.mem_carrier IntermediateField.mem_carrierₓ'. -/
 @[simp]
 theorem mem_carrier {s : IntermediateField K L} {x : L} : x ∈ s.carrier ↔ x ∈ s :=
   Iff.rfl
 #align intermediate_field.mem_carrier IntermediateField.mem_carrier
 
+/- warning: intermediate_field.ext -> IntermediateField.ext is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] {S : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4} {T : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4}, (forall (x : L), Iff (Membership.Mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.hasMem.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S) (Membership.Mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.hasMem.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x T)) -> (Eq.{succ u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) S T)
+but is expected to have type
+  forall {K : Type.{u2}} {L : Type.{u1}} [_inst_1 : Field.{u2} K] [_inst_2 : Field.{u1} L] [_inst_4 : Algebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))] {S : IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4} {T : IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4}, (forall (x : L), Iff (Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x S) (Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x T)) -> (Eq.{succ u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) S T)
+Case conversion may be inaccurate. Consider using '#align intermediate_field.ext IntermediateField.extₓ'. -/
 /-- Two intermediate fields are equal if they have the same elements. -/
 @[ext]
 theorem ext {S T : IntermediateField K L} (h : ∀ x, x ∈ S ↔ x ∈ T) : S = T :=
   SetLike.ext h
 #align intermediate_field.ext IntermediateField.ext
 
+/- warning: intermediate_field.coe_to_subalgebra -> IntermediateField.coe_toSubalgebra is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] (S : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4), Eq.{succ u2} (Set.{u2} L) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_4) (Set.{u2} L) (HasLiftT.mk.{succ u2, succ u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_4) (Set.{u2} L) (CoeTCₓ.coe.{succ u2, succ u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_4) (Set.{u2} L) (SetLike.Set.hasCoeT.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_4) L (Subalgebra.setLike.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_4)))) (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S)) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (Set.{u2} L) (HasLiftT.mk.{succ u2, succ u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (Set.{u2} L) (CoeTCₓ.coe.{succ u2, succ u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (Set.{u2} L) (SetLike.Set.hasCoeT.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)))) S)
+but is expected to have type
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))] (S : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4), Eq.{succ u2} (Set.{u2} L) (SetLike.coe.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4) (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S)) (SetLike.coe.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) S)
+Case conversion may be inaccurate. Consider using '#align intermediate_field.coe_to_subalgebra IntermediateField.coe_toSubalgebraₓ'. -/
 @[simp]
 theorem coe_toSubalgebra : (S.toSubalgebra : Set L) = S :=
   rfl
 #align intermediate_field.coe_to_subalgebra IntermediateField.coe_toSubalgebra
 
+/- warning: intermediate_field.coe_to_subfield -> IntermediateField.coe_toSubfield is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] (S : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4), Eq.{succ u2} (Set.{u2} L) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Subfield.{u2} L _inst_2) (Set.{u2} L) (HasLiftT.mk.{succ u2, succ u2} (Subfield.{u2} L _inst_2) (Set.{u2} L) (CoeTCₓ.coe.{succ u2, succ u2} (Subfield.{u2} L _inst_2) (Set.{u2} L) (SetLike.Set.hasCoeT.{u2, u2} (Subfield.{u2} L _inst_2) L (Subfield.setLike.{u2} L _inst_2)))) (IntermediateField.toSubfield.{u1, u2} K L _inst_1 _inst_2 _inst_4 S)) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (Set.{u2} L) (HasLiftT.mk.{succ u2, succ u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (Set.{u2} L) (CoeTCₓ.coe.{succ u2, succ u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (Set.{u2} L) (SetLike.Set.hasCoeT.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)))) S)
+but is expected to have type
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))] (S : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4), Eq.{succ u2} (Set.{u2} L) (SetLike.coe.{u2, u2} (Subfield.{u2} L _inst_2) L (Subfield.instSetLikeSubfield.{u2} L _inst_2) (IntermediateField.toSubfield.{u1, u2} K L _inst_1 _inst_2 _inst_4 S)) (SetLike.coe.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) S)
+Case conversion may be inaccurate. Consider using '#align intermediate_field.coe_to_subfield IntermediateField.coe_toSubfieldₓ'. -/
 @[simp]
 theorem coe_toSubfield : (S.toSubfield : Set L) = S :=
   rfl
@@ -105,18 +133,36 @@ theorem coe_toSubfield : (S.toSubfield : Set L) = S :=
 theorem mem_mk (s : Set L) (hK : ∀ x, algebraMap K L x ∈ s) (ho hm hz ha hn hi) (x : L) :
     x ∈ IntermediateField.mk (Subalgebra.mk s ho hm hz ha hK) hn hi ↔ x ∈ s :=
   Iff.rfl
-#align intermediate_field.mem_mk IntermediateField.mem_mk
-
+#align intermediate_field.mem_mk IntermediateField.mem_mkₓ
+
+/- warning: intermediate_field.mem_to_subalgebra -> IntermediateField.mem_toSubalgebra is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] (s : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (x : L), Iff (Membership.Mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_4) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_4) L (Subalgebra.setLike.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_4)) x (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 s)) (Membership.Mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.hasMem.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x s)
+but is expected to have type
+  forall {K : Type.{u2}} {L : Type.{u1}} [_inst_1 : Field.{u2} K] [_inst_2 : Field.{u1} L] [_inst_4 : Algebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))] (s : IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (x : L), Iff (Membership.mem.{u1, u1} L (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) L (Subalgebra.instSetLikeSubalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4)) x (IntermediateField.toSubalgebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 s)) (Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x s)
+Case conversion may be inaccurate. Consider using '#align intermediate_field.mem_to_subalgebra IntermediateField.mem_toSubalgebraₓ'. -/
 @[simp]
 theorem mem_toSubalgebra (s : IntermediateField K L) (x : L) : x ∈ s.toSubalgebra ↔ x ∈ s :=
   Iff.rfl
 #align intermediate_field.mem_to_subalgebra IntermediateField.mem_toSubalgebra
 
+/- warning: intermediate_field.mem_to_subfield -> IntermediateField.mem_toSubfield is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] (s : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (x : L), Iff (Membership.Mem.{u2, u2} L (Subfield.{u2} L _inst_2) (SetLike.hasMem.{u2, u2} (Subfield.{u2} L _inst_2) L (Subfield.setLike.{u2} L _inst_2)) x (IntermediateField.toSubfield.{u1, u2} K L _inst_1 _inst_2 _inst_4 s)) (Membership.Mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.hasMem.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x s)
+but is expected to have type
+  forall {K : Type.{u2}} {L : Type.{u1}} [_inst_1 : Field.{u2} K] [_inst_2 : Field.{u1} L] [_inst_4 : Algebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))] (s : IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (x : L), Iff (Membership.mem.{u1, u1} L (Subfield.{u1} L _inst_2) (SetLike.instMembership.{u1, u1} (Subfield.{u1} L _inst_2) L (Subfield.instSetLikeSubfield.{u1} L _inst_2)) x (IntermediateField.toSubfield.{u2, u1} K L _inst_1 _inst_2 _inst_4 s)) (Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x s)
+Case conversion may be inaccurate. Consider using '#align intermediate_field.mem_to_subfield IntermediateField.mem_toSubfieldₓ'. -/
 @[simp]
 theorem mem_toSubfield (s : IntermediateField K L) (x : L) : x ∈ s.toSubfield ↔ x ∈ s :=
   Iff.rfl
 #align intermediate_field.mem_to_subfield IntermediateField.mem_toSubfield
 
+/- warning: intermediate_field.copy -> IntermediateField.copy is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] (S : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (s : Set.{u2} L), (Eq.{succ u2} (Set.{u2} L) s ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (Set.{u2} L) (HasLiftT.mk.{succ u2, succ u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (Set.{u2} L) (CoeTCₓ.coe.{succ u2, succ u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (Set.{u2} L) (SetLike.Set.hasCoeT.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)))) S)) -> (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)
+but is expected to have type
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))] (S : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (s : Set.{u2} L), (Eq.{succ u2} (Set.{u2} L) s (SetLike.coe.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) S)) -> (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)
+Case conversion may be inaccurate. Consider using '#align intermediate_field.copy IntermediateField.copyₓ'. -/
 /-- Copy of an intermediate field with a new `carrier` equal to the old one. Useful to fix
 definitional equalities. -/
 protected def copy (S : IntermediateField K L) (s : Set L) (hs : s = ↑S) : IntermediateField K L
@@ -130,12 +176,24 @@ protected def copy (S : IntermediateField K L) (s : Set L) (hs : s = ↑S) : Int
     hs'.symm ▸ S.inv_mem'
 #align intermediate_field.copy IntermediateField.copy
 
+/- warning: intermediate_field.coe_copy -> IntermediateField.coe_copy is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] (S : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (s : Set.{u2} L) (hs : Eq.{succ u2} (Set.{u2} L) s ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (Set.{u2} L) (HasLiftT.mk.{succ u2, succ u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (Set.{u2} L) (CoeTCₓ.coe.{succ u2, succ u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (Set.{u2} L) (SetLike.Set.hasCoeT.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)))) S)), Eq.{succ u2} (Set.{u2} L) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (Set.{u2} L) (HasLiftT.mk.{succ u2, succ u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (Set.{u2} L) (CoeTCₓ.coe.{succ u2, succ u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (Set.{u2} L) (SetLike.Set.hasCoeT.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)))) (IntermediateField.copy.{u1, u2} K L _inst_1 _inst_2 _inst_4 S s hs)) s
+but is expected to have type
+  forall {K : Type.{u2}} {L : Type.{u1}} [_inst_1 : Field.{u2} K] [_inst_2 : Field.{u1} L] [_inst_4 : Algebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))] (S : IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (s : Set.{u1} L) (hs : Eq.{succ u1} (Set.{u1} L) s (SetLike.coe.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) S)), Eq.{succ u1} (Set.{u1} L) (SetLike.coe.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (IntermediateField.copy.{u2, u1} K L _inst_1 _inst_2 _inst_4 S s hs)) s
+Case conversion may be inaccurate. Consider using '#align intermediate_field.coe_copy IntermediateField.coe_copyₓ'. -/
 @[simp]
 theorem coe_copy (S : IntermediateField K L) (s : Set L) (hs : s = ↑S) :
     (S.copy s hs : Set L) = s :=
   rfl
 #align intermediate_field.coe_copy IntermediateField.coe_copy
 
+/- warning: intermediate_field.copy_eq -> IntermediateField.copy_eq is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] (S : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (s : Set.{u2} L) (hs : Eq.{succ u2} (Set.{u2} L) s ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (Set.{u2} L) (HasLiftT.mk.{succ u2, succ u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (Set.{u2} L) (CoeTCₓ.coe.{succ u2, succ u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (Set.{u2} L) (SetLike.Set.hasCoeT.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)))) S)), Eq.{succ u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (IntermediateField.copy.{u1, u2} K L _inst_1 _inst_2 _inst_4 S s hs) S
+but is expected to have type
+  forall {K : Type.{u2}} {L : Type.{u1}} [_inst_1 : Field.{u2} K] [_inst_2 : Field.{u1} L] [_inst_4 : Algebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))] (S : IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (s : Set.{u1} L) (hs : Eq.{succ u1} (Set.{u1} L) s (SetLike.coe.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) S)), Eq.{succ u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (IntermediateField.copy.{u2, u1} K L _inst_1 _inst_2 _inst_4 S s hs) S
+Case conversion may be inaccurate. Consider using '#align intermediate_field.copy_eq IntermediateField.copy_eqₓ'. -/
 theorem copy_eq (S : IntermediateField K L) (s : Set L) (hs : s = ↑S) : S.copy s hs = S :=
   SetLike.coe_injective hs
 #align intermediate_field.copy_eq IntermediateField.copy_eq
@@ -150,76 +208,166 @@ subobject class.
 -/
 
 
+/- warning: intermediate_field.algebra_map_mem -> IntermediateField.algebraMap_mem is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] (S : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (x : K), Membership.Mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.hasMem.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) (fun (_x : RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) => K -> L) (RingHom.hasCoeToFun.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) (algebraMap.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_4) x) S
+but is expected to have type
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))] (S : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (x : K), Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) x) (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))))) (algebraMap.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4) x) S
+Case conversion may be inaccurate. Consider using '#align intermediate_field.algebra_map_mem IntermediateField.algebraMap_memₓ'. -/
 /-- An intermediate field contains the image of the smaller field. -/
 theorem algebraMap_mem (x : K) : algebraMap K L x ∈ S :=
   S.algebraMap_mem' x
 #align intermediate_field.algebra_map_mem IntermediateField.algebraMap_mem
 
+/- warning: intermediate_field.smul_mem -> IntermediateField.smul_mem is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] (S : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) {y : L}, (Membership.Mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.hasMem.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) y S) -> (forall {x : K}, Membership.Mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.hasMem.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) (SMul.smul.{u1, u2} K L (SMulZeroClass.toHasSmul.{u1, u2} K L (AddZeroClass.toHasZero.{u2} L (AddMonoid.toAddZeroClass.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} K L (MulZeroClass.toHasZero.{u1} K (MulZeroOneClass.toMulZeroClass.{u1} K (MonoidWithZero.toMulZeroOneClass.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (AddZeroClass.toHasZero.{u2} L (AddMonoid.toAddZeroClass.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} K L (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (AddZeroClass.toHasZero.{u2} L (AddMonoid.toAddZeroClass.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))))) (Module.toMulActionWithZero.{u1, u2} K L (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) (Algebra.toModule.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_4))))) x y) S)
+but is expected to have type
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))] (S : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) {y : L}, (Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) y S) -> (forall {x : K}, Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) (HSMul.hSMul.{u1, u2, u2} K L L (instHSMul.{u1, u2} K L (Algebra.toSMul.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4)) x y) S)
+Case conversion may be inaccurate. Consider using '#align intermediate_field.smul_mem IntermediateField.smul_memₓ'. -/
 /-- An intermediate field is closed under scalar multiplication. -/
 theorem smul_mem {y : L} : y ∈ S → ∀ {x : K}, x • y ∈ S :=
   S.toSubalgebra.smul_mem
 #align intermediate_field.smul_mem IntermediateField.smul_mem
 
+/- warning: intermediate_field.one_mem -> IntermediateField.one_mem is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] (S : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4), Membership.Mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.hasMem.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) (OfNat.ofNat.{u2} L 1 (OfNat.mk.{u2} L 1 (One.one.{u2} L (AddMonoidWithOne.toOne.{u2} L (AddGroupWithOne.toAddMonoidWithOne.{u2} L (AddCommGroupWithOne.toAddGroupWithOne.{u2} L (Ring.toAddCommGroupWithOne.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))))) S
+but is expected to have type
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))] (S : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4), Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) (OfNat.ofNat.{u2} L 1 (One.toOfNat1.{u2} L (Semiring.toOne.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) S
+Case conversion may be inaccurate. Consider using '#align intermediate_field.one_mem IntermediateField.one_memₓ'. -/
 /-- An intermediate field contains the ring's 1. -/
 protected theorem one_mem : (1 : L) ∈ S :=
   one_mem S
 #align intermediate_field.one_mem IntermediateField.one_mem
 
+/- warning: intermediate_field.zero_mem -> IntermediateField.zero_mem is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] (S : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4), Membership.Mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.hasMem.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) (OfNat.ofNat.{u2} L 0 (OfNat.mk.{u2} L 0 (Zero.zero.{u2} L (MulZeroClass.toHasZero.{u2} L (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} L (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} L (NonAssocRing.toNonUnitalNonAssocRing.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))))))) S
+but is expected to have type
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))] (S : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4), Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) (OfNat.ofNat.{u2} L 0 (Zero.toOfNat0.{u2} L (CommMonoidWithZero.toZero.{u2} L (CommGroupWithZero.toCommMonoidWithZero.{u2} L (Semifield.toCommGroupWithZero.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) S
+Case conversion may be inaccurate. Consider using '#align intermediate_field.zero_mem IntermediateField.zero_memₓ'. -/
 /-- An intermediate field contains the ring's 0. -/
 protected theorem zero_mem : (0 : L) ∈ S :=
   zero_mem S
 #align intermediate_field.zero_mem IntermediateField.zero_mem
 
+/- warning: intermediate_field.mul_mem -> IntermediateField.mul_mem is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] (S : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) {x : L} {y : L}, (Membership.Mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.hasMem.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S) -> (Membership.Mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.hasMem.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) y S) -> (Membership.Mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.hasMem.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) (HMul.hMul.{u2, u2, u2} L L L (instHMul.{u2} L (Distrib.toHasMul.{u2} L (Ring.toDistrib.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) x y) S)
+but is expected to have type
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))] (S : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) {x : L} {y : L}, (Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S) -> (Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) y S) -> (Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) (HMul.hMul.{u2, u2, u2} L L L (instHMul.{u2} L (NonUnitalNonAssocRing.toMul.{u2} L (NonAssocRing.toNonUnitalNonAssocRing.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) x y) S)
+Case conversion may be inaccurate. Consider using '#align intermediate_field.mul_mem IntermediateField.mul_memₓ'. -/
 /-- An intermediate field is closed under multiplication. -/
 protected theorem mul_mem {x y : L} : x ∈ S → y ∈ S → x * y ∈ S :=
   mul_mem
 #align intermediate_field.mul_mem IntermediateField.mul_mem
 
+/- warning: intermediate_field.add_mem -> IntermediateField.add_mem is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))] (S : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) {x : L} {y : L}, (Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S) -> (Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) y S) -> (Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) (HAdd.hAdd.{u2, u2, u2} L L L (instHAdd.{u2} L (Distrib.toAdd.{u2} L (NonUnitalNonAssocSemiring.toDistrib.{u2} L (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} L (NonAssocRing.toNonUnitalNonAssocRing.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))))) x y) S)
+Case conversion may be inaccurate. Consider using '#align intermediate_field.add_mem IntermediateField.add_memₓ'. -/
 /-- An intermediate field is closed under addition. -/
 protected theorem add_mem {x y : L} : x ∈ S → y ∈ S → x + y ∈ S :=
   add_mem
 #align intermediate_field.add_mem IntermediateField.add_mem
 
+/- warning: intermediate_field.sub_mem -> IntermediateField.sub_mem is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] (S : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) {x : L} {y : L}, (Membership.Mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.hasMem.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S) -> (Membership.Mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.hasMem.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) y S) -> (Membership.Mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.hasMem.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) (HSub.hSub.{u2, u2, u2} L L L (instHSub.{u2} L (SubNegMonoid.toHasSub.{u2} L (AddGroup.toSubNegMonoid.{u2} L (AddGroupWithOne.toAddGroup.{u2} L (AddCommGroupWithOne.toAddGroupWithOne.{u2} L (Ring.toAddCommGroupWithOne.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))))) x y) S)
+but is expected to have type
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))] (S : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) {x : L} {y : L}, (Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S) -> (Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) y S) -> (Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) (HSub.hSub.{u2, u2, u2} L L L (instHSub.{u2} L (Ring.toSub.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) x y) S)
+Case conversion may be inaccurate. Consider using '#align intermediate_field.sub_mem IntermediateField.sub_memₓ'. -/
 /-- An intermediate field is closed under subtraction -/
 protected theorem sub_mem {x y : L} : x ∈ S → y ∈ S → x - y ∈ S :=
   sub_mem
 #align intermediate_field.sub_mem IntermediateField.sub_mem
 
+/- warning: intermediate_field.neg_mem -> IntermediateField.neg_mem is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] (S : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) {x : L}, (Membership.Mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.hasMem.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S) -> (Membership.Mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.hasMem.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) (Neg.neg.{u2} L (SubNegMonoid.toHasNeg.{u2} L (AddGroup.toSubNegMonoid.{u2} L (AddGroupWithOne.toAddGroup.{u2} L (AddCommGroupWithOne.toAddGroupWithOne.{u2} L (Ring.toAddCommGroupWithOne.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))) x) S)
+but is expected to have type
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))] (S : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) {x : L}, (Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S) -> (Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) (Neg.neg.{u2} L (Ring.toNeg.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) x) S)
+Case conversion may be inaccurate. Consider using '#align intermediate_field.neg_mem IntermediateField.neg_memₓ'. -/
 /-- An intermediate field is closed under negation. -/
 protected theorem neg_mem {x : L} : x ∈ S → -x ∈ S :=
   neg_mem
 #align intermediate_field.neg_mem IntermediateField.neg_mem
 
+/- warning: intermediate_field.inv_mem -> IntermediateField.inv_mem is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] (S : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) {x : L}, (Membership.Mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.hasMem.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S) -> (Membership.Mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.hasMem.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) (Inv.inv.{u2} L (DivInvMonoid.toHasInv.{u2} L (DivisionRing.toDivInvMonoid.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) x) S)
+but is expected to have type
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))] (S : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) {x : L}, (Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S) -> (Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) (Inv.inv.{u2} L (Field.toInv.{u2} L _inst_2) x) S)
+Case conversion may be inaccurate. Consider using '#align intermediate_field.inv_mem IntermediateField.inv_memₓ'. -/
 /-- An intermediate field is closed under inverses. -/
 protected theorem inv_mem {x : L} : x ∈ S → x⁻¹ ∈ S :=
   inv_mem
 #align intermediate_field.inv_mem IntermediateField.inv_mem
 
+/- warning: intermediate_field.div_mem -> IntermediateField.div_mem is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] (S : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) {x : L} {y : L}, (Membership.Mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.hasMem.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S) -> (Membership.Mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.hasMem.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) y S) -> (Membership.Mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.hasMem.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) (HDiv.hDiv.{u2, u2, u2} L L L (instHDiv.{u2} L (DivInvMonoid.toHasDiv.{u2} L (DivisionRing.toDivInvMonoid.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) x y) S)
+but is expected to have type
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))] (S : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) {x : L} {y : L}, (Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S) -> (Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) y S) -> (Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) (HDiv.hDiv.{u2, u2, u2} L L L (instHDiv.{u2} L (Field.toDiv.{u2} L _inst_2)) x y) S)
+Case conversion may be inaccurate. Consider using '#align intermediate_field.div_mem IntermediateField.div_memₓ'. -/
 /-- An intermediate field is closed under division. -/
 protected theorem div_mem {x y : L} : x ∈ S → y ∈ S → x / y ∈ S :=
   div_mem
 #align intermediate_field.div_mem IntermediateField.div_mem
 
+/- warning: intermediate_field.list_prod_mem -> IntermediateField.list_prod_mem is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] (S : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) {l : List.{u2} L}, (forall (x : L), (Membership.Mem.{u2, u2} L (List.{u2} L) (List.hasMem.{u2} L) x l) -> (Membership.Mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.hasMem.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) -> (Membership.Mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.hasMem.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) (List.prod.{u2} L (Distrib.toHasMul.{u2} L (Ring.toDistrib.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (AddMonoidWithOne.toOne.{u2} L (AddGroupWithOne.toAddMonoidWithOne.{u2} L (AddCommGroupWithOne.toAddGroupWithOne.{u2} L (Ring.toAddCommGroupWithOne.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) l) S)
+but is expected to have type
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))] (S : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) {l : List.{u2} L}, (forall (x : L), (Membership.mem.{u2, u2} L (List.{u2} L) (List.instMembershipList.{u2} L) x l) -> (Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) -> (Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) (List.prod.{u2} L (NonUnitalNonAssocRing.toMul.{u2} L (NonAssocRing.toNonUnitalNonAssocRing.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) (Semiring.toOne.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) l) S)
+Case conversion may be inaccurate. Consider using '#align intermediate_field.list_prod_mem IntermediateField.list_prod_memₓ'. -/
 /-- Product of a list of elements in an intermediate_field is in the intermediate_field. -/
 protected theorem list_prod_mem {l : List L} : (∀ x ∈ l, x ∈ S) → l.Prod ∈ S :=
   list_prod_mem
 #align intermediate_field.list_prod_mem IntermediateField.list_prod_mem
 
+/- warning: intermediate_field.list_sum_mem -> IntermediateField.list_sum_mem is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] (S : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) {l : List.{u2} L}, (forall (x : L), (Membership.Mem.{u2, u2} L (List.{u2} L) (List.hasMem.{u2} L) x l) -> (Membership.Mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.hasMem.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) -> (Membership.Mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.hasMem.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) (List.sum.{u2} L (Distrib.toHasAdd.{u2} L (Ring.toDistrib.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (MulZeroClass.toHasZero.{u2} L (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} L (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} L (NonAssocRing.toNonUnitalNonAssocRing.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))) l) S)
+but is expected to have type
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))] (S : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) {l : List.{u2} L}, (forall (x : L), (Membership.mem.{u2, u2} L (List.{u2} L) (List.instMembershipList.{u2} L) x l) -> (Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) -> (Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) (List.sum.{u2} L (Distrib.toAdd.{u2} L (NonUnitalNonAssocSemiring.toDistrib.{u2} L (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} L (NonAssocRing.toNonUnitalNonAssocRing.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))) (CommMonoidWithZero.toZero.{u2} L (CommGroupWithZero.toCommMonoidWithZero.{u2} L (Semifield.toCommGroupWithZero.{u2} L (Field.toSemifield.{u2} L _inst_2)))) l) S)
+Case conversion may be inaccurate. Consider using '#align intermediate_field.list_sum_mem IntermediateField.list_sum_memₓ'. -/
 /-- Sum of a list of elements in an intermediate field is in the intermediate_field. -/
 protected theorem list_sum_mem {l : List L} : (∀ x ∈ l, x ∈ S) → l.Sum ∈ S :=
   list_sum_mem
 #align intermediate_field.list_sum_mem IntermediateField.list_sum_mem
 
+/- warning: intermediate_field.multiset_prod_mem -> IntermediateField.multiset_prod_mem is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] (S : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (m : Multiset.{u2} L), (forall (a : L), (Membership.Mem.{u2, u2} L (Multiset.{u2} L) (Multiset.hasMem.{u2} L) a m) -> (Membership.Mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.hasMem.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) a S)) -> (Membership.Mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.hasMem.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) (Multiset.prod.{u2} L (CommRing.toCommMonoid.{u2} L (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2))) m) S)
+but is expected to have type
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))] (S : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (m : Multiset.{u2} L), (forall (a : L), (Membership.mem.{u2, u2} L (Multiset.{u2} L) (Multiset.instMembershipMultiset.{u2} L) a m) -> (Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) a S)) -> (Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) (Multiset.prod.{u2} L (CommRing.toCommMonoid.{u2} L (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2))) m) S)
+Case conversion may be inaccurate. Consider using '#align intermediate_field.multiset_prod_mem IntermediateField.multiset_prod_memₓ'. -/
 /-- Product of a multiset of elements in an intermediate field is in the intermediate_field. -/
 protected theorem multiset_prod_mem (m : Multiset L) : (∀ a ∈ m, a ∈ S) → m.Prod ∈ S :=
   multiset_prod_mem m
 #align intermediate_field.multiset_prod_mem IntermediateField.multiset_prod_mem
 
+/- warning: intermediate_field.multiset_sum_mem -> IntermediateField.multiset_sum_mem is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] (S : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (m : Multiset.{u2} L), (forall (a : L), (Membership.Mem.{u2, u2} L (Multiset.{u2} L) (Multiset.hasMem.{u2} L) a m) -> (Membership.Mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.hasMem.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) a S)) -> (Membership.Mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.hasMem.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) (Multiset.sum.{u2} L (AddCommGroup.toAddCommMonoid.{u2} L (NonUnitalNonAssocRing.toAddCommGroup.{u2} L (NonAssocRing.toNonUnitalNonAssocRing.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) m) S)
+but is expected to have type
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))] (S : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (m : Multiset.{u2} L), (forall (a : L), (Membership.mem.{u2, u2} L (Multiset.{u2} L) (Multiset.instMembershipMultiset.{u2} L) a m) -> (Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) a S)) -> (Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) (Multiset.sum.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} L (NonAssocRing.toNonUnitalNonAssocRing.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) m) S)
+Case conversion may be inaccurate. Consider using '#align intermediate_field.multiset_sum_mem IntermediateField.multiset_sum_memₓ'. -/
 /-- Sum of a multiset of elements in a `intermediate_field` is in the `intermediate_field`. -/
 protected theorem multiset_sum_mem (m : Multiset L) : (∀ a ∈ m, a ∈ S) → m.Sum ∈ S :=
   multiset_sum_mem m
 #align intermediate_field.multiset_sum_mem IntermediateField.multiset_sum_mem
 
+/- warning: intermediate_field.prod_mem -> IntermediateField.prod_mem is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] (S : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) {ι : Type.{u3}} {t : Finset.{u3} ι} {f : ι -> L}, (forall (c : ι), (Membership.Mem.{u3, u3} ι (Finset.{u3} ι) (Finset.hasMem.{u3} ι) c t) -> (Membership.Mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.hasMem.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) (f c) S)) -> (Membership.Mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.hasMem.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) (Finset.prod.{u2, u3} L ι (CommRing.toCommMonoid.{u2} L (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2))) t (fun (i : ι) => f i)) S)
+but is expected to have type
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))] (S : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) {ι : Type.{u3}} {t : Finset.{u3} ι} {f : ι -> L}, (forall (c : ι), (Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) c t) -> (Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) (f c) S)) -> (Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) (Finset.prod.{u2, u3} L ι (CommRing.toCommMonoid.{u2} L (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2))) t (fun (i : ι) => f i)) S)
+Case conversion may be inaccurate. Consider using '#align intermediate_field.prod_mem IntermediateField.prod_memₓ'. -/
 /-- Product of elements of an intermediate field indexed by a `finset` is in the intermediate_field.
 -/
 protected theorem prod_mem {ι : Type _} {t : Finset ι} {f : ι → L} (h : ∀ c ∈ t, f c ∈ S) :
@@ -227,6 +375,12 @@ protected theorem prod_mem {ι : Type _} {t : Finset ι} {f : ι → L} (h : ∀
   prod_mem h
 #align intermediate_field.prod_mem IntermediateField.prod_mem
 
+/- warning: intermediate_field.sum_mem -> IntermediateField.sum_mem is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align intermediate_field.sum_mem IntermediateField.sum_memₓ'. -/
 /-- Sum of elements in a `intermediate_field` indexed by a `finset` is in the `intermediate_field`.
 -/
 protected theorem sum_mem {ι : Type _} {t : Finset ι} {f : ι → L} (h : ∀ c ∈ t, f c ∈ S) :
@@ -234,53 +388,125 @@ protected theorem sum_mem {ι : Type _} {t : Finset ι} {f : ι → L} (h : ∀
   sum_mem h
 #align intermediate_field.sum_mem IntermediateField.sum_mem
 
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+Case conversion may be inaccurate. Consider using '#align intermediate_field.pow_mem IntermediateField.pow_memₓ'. -/
 protected theorem pow_mem {x : L} (hx : x ∈ S) (n : ℤ) : x ^ n ∈ S :=
   zpow_mem hx n
 #align intermediate_field.pow_mem IntermediateField.pow_mem
 
+/- warning: intermediate_field.zsmul_mem -> IntermediateField.zsmul_mem is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align intermediate_field.zsmul_mem IntermediateField.zsmul_memₓ'. -/
 protected theorem zsmul_mem {x : L} (hx : x ∈ S) (n : ℤ) : n • x ∈ S :=
   zsmul_mem hx n
 #align intermediate_field.zsmul_mem IntermediateField.zsmul_mem
 
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 protected theorem coe_int_mem (n : ℤ) : (n : L) ∈ S :=
   coe_int_mem S n
 #align intermediate_field.coe_int_mem IntermediateField.coe_int_mem
 
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+Case conversion may be inaccurate. Consider using '#align intermediate_field.coe_add IntermediateField.coe_addₓ'. -/
 protected theorem coe_add (x y : S) : (↑(x + y) : L) = ↑x + ↑y :=
   rfl
 #align intermediate_field.coe_add IntermediateField.coe_add
 
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 protected theorem coe_neg (x : S) : (↑(-x) : L) = -↑x :=
   rfl
 #align intermediate_field.coe_neg IntermediateField.coe_neg
 
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+Case conversion may be inaccurate. Consider using '#align intermediate_field.coe_mul IntermediateField.coe_mulₓ'. -/
 protected theorem coe_mul (x y : S) : (↑(x * y) : L) = ↑x * ↑y :=
   rfl
 #align intermediate_field.coe_mul IntermediateField.coe_mul
 
+/- warning: intermediate_field.coe_inv -> IntermediateField.coe_inv is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align intermediate_field.coe_inv IntermediateField.coe_invₓ'. -/
 protected theorem coe_inv (x : S) : (↑x⁻¹ : L) = (↑x)⁻¹ :=
   rfl
 #align intermediate_field.coe_inv IntermediateField.coe_inv
 
+/- warning: intermediate_field.coe_zero -> IntermediateField.coe_zero 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 intermediate_field.coe_zero IntermediateField.coe_zeroₓ'. -/
 protected theorem coe_zero : ((0 : S) : L) = 0 :=
   rfl
 #align intermediate_field.coe_zero IntermediateField.coe_zero
 
+/- warning: intermediate_field.coe_one -> IntermediateField.coe_one is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align intermediate_field.coe_one IntermediateField.coe_oneₓ'. -/
 protected theorem coe_one : ((1 : S) : L) = 1 :=
   rfl
 #align intermediate_field.coe_one IntermediateField.coe_one
 
+/- warning: intermediate_field.coe_pow -> IntermediateField.coe_pow is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align intermediate_field.coe_pow IntermediateField.coe_powₓ'. -/
 protected theorem coe_pow (x : S) (n : ℕ) : (↑(x ^ n) : L) = ↑x ^ n :=
   SubmonoidClass.coe_pow x n
 #align intermediate_field.coe_pow IntermediateField.coe_pow
 
 end InheritedLemmas
 
+/- warning: intermediate_field.coe_nat_mem -> IntermediateField.coe_nat_mem is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] (S : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (n : Nat), Membership.Mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.hasMem.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) ((fun (a : Type) (b : Type.{u2}) [self : HasLiftT.{1, succ u2} a b] => self.0) Nat L (HasLiftT.mk.{1, succ u2} Nat L (CoeTCₓ.coe.{1, succ u2} Nat L (Nat.castCoe.{u2} L (AddMonoidWithOne.toNatCast.{u2} L (AddGroupWithOne.toAddMonoidWithOne.{u2} L (AddCommGroupWithOne.toAddGroupWithOne.{u2} L (Ring.toAddCommGroupWithOne.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))))) n) S
+but is expected to have type
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))] (S : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (n : Nat), Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) (Nat.cast.{u2} L (Semiring.toNatCast.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) n) S
+Case conversion may be inaccurate. Consider using '#align intermediate_field.coe_nat_mem IntermediateField.coe_nat_memₓ'. -/
 theorem coe_nat_mem (n : ℕ) : (n : L) ∈ S := by simpa using coe_int_mem S n
 #align intermediate_field.coe_nat_mem IntermediateField.coe_nat_mem
 
 end IntermediateField
 
+/- warning: subalgebra.to_intermediate_field -> Subalgebra.toIntermediateField is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] (S : Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_4), (forall (x : L), (Membership.Mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_4) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_4) L (Subalgebra.setLike.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_4)) x S) -> (Membership.Mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_4) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_4) L (Subalgebra.setLike.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_4)) (Inv.inv.{u2} L (DivInvMonoid.toHasInv.{u2} L (DivisionRing.toDivInvMonoid.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) x) S)) -> (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)
+but is expected to have type
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))] (S : Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4), (forall (x : L), (Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4)) x S) -> (Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4)) (Inv.inv.{u2} L (Field.toInv.{u2} L _inst_2) x) S)) -> (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)
+Case conversion may be inaccurate. Consider using '#align subalgebra.to_intermediate_field Subalgebra.toIntermediateFieldₓ'. -/
 /-- Turn a subalgebra closed under inverses into an intermediate field -/
 def Subalgebra.toIntermediateField (S : Subalgebra K L) (inv_mem : ∀ x ∈ S, x⁻¹ ∈ S) :
     IntermediateField K L :=
@@ -289,6 +515,12 @@ def Subalgebra.toIntermediateField (S : Subalgebra K L) (inv_mem : ∀ x ∈ S,
     inv_mem' := inv_mem }
 #align subalgebra.to_intermediate_field Subalgebra.toIntermediateField
 
+/- warning: to_subalgebra_to_intermediate_field -> toSubalgebra_toIntermediateField is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] (S : Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_4) (inv_mem : forall (x : L), (Membership.Mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_4) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_4) L (Subalgebra.setLike.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_4)) x S) -> (Membership.Mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_4) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_4) L (Subalgebra.setLike.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_4)) (Inv.inv.{u2} L (DivInvMonoid.toHasInv.{u2} L (DivisionRing.toDivInvMonoid.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) x) S)), Eq.{succ u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_4) (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 (Subalgebra.toIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4 S inv_mem)) S
+but is expected to have type
+  forall {K : Type.{u2}} {L : Type.{u1}} [_inst_1 : Field.{u2} K] [_inst_2 : Field.{u1} L] [_inst_4 : Algebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))] (S : Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (inv_mem : forall (x : L), (Membership.mem.{u1, u1} L (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) L (Subalgebra.instSetLikeSubalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4)) x S) -> (Membership.mem.{u1, u1} L (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) L (Subalgebra.instSetLikeSubalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4)) (Inv.inv.{u1} L (Field.toInv.{u1} L _inst_2) x) S)), Eq.{succ u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (IntermediateField.toSubalgebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 (Subalgebra.toIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4 S inv_mem)) S
+Case conversion may be inaccurate. Consider using '#align to_subalgebra_to_intermediate_field toSubalgebra_toIntermediateFieldₓ'. -/
 @[simp]
 theorem toSubalgebra_toIntermediateField (S : Subalgebra K L) (inv_mem : ∀ x ∈ S, x⁻¹ ∈ S) :
     (S.toIntermediateField inv_mem).toSubalgebra = S :=
@@ -297,6 +529,12 @@ theorem toSubalgebra_toIntermediateField (S : Subalgebra K L) (inv_mem : ∀ x 
   rfl
 #align to_subalgebra_to_intermediate_field toSubalgebra_toIntermediateField
 
+/- warning: to_intermediate_field_to_subalgebra -> toIntermediateField_toSubalgebra is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] (S : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4), Eq.{succ u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (Subalgebra.toIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4 (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S) (fun (x : L) => IntermediateField.inv_mem.{u1, u2} K L _inst_1 _inst_2 _inst_4 S x)) S
+but is expected to have type
+  forall {K : Type.{u2}} {L : Type.{u1}} [_inst_1 : Field.{u2} K] [_inst_2 : Field.{u1} L] [_inst_4 : Algebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))] (S : IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4), Eq.{succ u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (Subalgebra.toIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4 (IntermediateField.toSubalgebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 S) (fun (x : L) => IntermediateField.inv_mem.{u2, u1} K L _inst_1 _inst_2 _inst_4 S x)) S
+Case conversion may be inaccurate. Consider using '#align to_intermediate_field_to_subalgebra toIntermediateField_toSubalgebraₓ'. -/
 @[simp]
 theorem toIntermediateField_toSubalgebra (S : IntermediateField K L) :
     (S.toSubalgebra.toIntermediateField fun x => S.inv_mem) = S :=
@@ -305,6 +543,12 @@ theorem toIntermediateField_toSubalgebra (S : IntermediateField K L) :
   rfl
 #align to_intermediate_field_to_subalgebra toIntermediateField_toSubalgebra
 
+/- warning: subalgebra.to_intermediate_field' -> Subalgebra.toIntermediateField' is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))] (S : Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4), (IsField.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4) L (Subalgebra.instSetLikeSubalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4)) x S)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 S)) -> (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)
+Case conversion may be inaccurate. Consider using '#align subalgebra.to_intermediate_field' Subalgebra.toIntermediateField'ₓ'. -/
 /-- Turn a subalgebra satisfying `is_field` into an intermediate_field -/
 def Subalgebra.toIntermediateField' (S : Subalgebra K L) (hS : IsField S) : IntermediateField K L :=
   S.toIntermediateField fun x hx => by
@@ -317,6 +561,12 @@ def Subalgebra.toIntermediateField' (S : Subalgebra K L) (hS : IsField S) : Inte
     exact hy.symm ▸ y.2
 #align subalgebra.to_intermediate_field' Subalgebra.toIntermediateField'
 
+/- warning: to_subalgebra_to_intermediate_field' -> toSubalgebra_toIntermediateField' 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 to_subalgebra_to_intermediate_field' toSubalgebra_toIntermediateField'ₓ'. -/
 @[simp]
 theorem toSubalgebra_toIntermediateField' (S : Subalgebra K L) (hS : IsField S) :
     (S.toIntermediateField' hS).toSubalgebra = S :=
@@ -325,6 +575,12 @@ theorem toSubalgebra_toIntermediateField' (S : Subalgebra K L) (hS : IsField S)
   rfl
 #align to_subalgebra_to_intermediate_field' toSubalgebra_toIntermediateField'
 
+/- warning: to_intermediate_field'_to_subalgebra -> toIntermediateField'_toSubalgebra is a dubious translation:
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+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] (S : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4), Eq.{succ u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (Subalgebra.toIntermediateField'.{u1, u2} K L _inst_1 _inst_2 _inst_4 (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S) (Field.toIsField.{u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) S) (SubfieldClass.toField.{u2, u2} L _inst_2 (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4) (IntermediateField.subfieldClass.{u1, u2} K L _inst_1 _inst_2 _inst_4) S))) S
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align to_intermediate_field'_to_subalgebra toIntermediateField'_toSubalgebraₓ'. -/
 @[simp]
 theorem toIntermediateField'_toSubalgebra (S : IntermediateField K L) :
     S.toSubalgebra.toIntermediateField' (Field.toIsField S) = S :=
@@ -333,6 +589,12 @@ theorem toIntermediateField'_toSubalgebra (S : IntermediateField K L) :
   rfl
 #align to_intermediate_field'_to_subalgebra toIntermediateField'_toSubalgebra
 
+/- warning: subfield.to_intermediate_field -> Subfield.toIntermediateField is a dubious translation:
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+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] (S : Subfield.{u2} L _inst_2), (forall (x : K), Membership.Mem.{u2, u2} L (Subfield.{u2} L _inst_2) (SetLike.hasMem.{u2, u2} (Subfield.{u2} L _inst_2) L (Subfield.setLike.{u2} L _inst_2)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) (fun (_x : RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) => K -> L) (RingHom.hasCoeToFun.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) (algebraMap.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_4) x) S) -> (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align subfield.to_intermediate_field Subfield.toIntermediateFieldₓ'. -/
 /-- Turn a subfield of `L` containing the image of `K` into an intermediate field -/
 def Subfield.toIntermediateField (S : Subfield L) (algebra_map_mem : ∀ x, algebraMap K L x ∈ S) :
     IntermediateField K L :=
@@ -341,11 +603,23 @@ def Subfield.toIntermediateField (S : Subfield L) (algebra_map_mem : ∀ x, alge
 
 namespace IntermediateField
 
+/- warning: intermediate_field.to_field -> IntermediateField.toField 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 intermediate_field.to_field IntermediateField.toFieldₓ'. -/
 /-- An intermediate field inherits a field structure -/
 instance toField : Field S :=
   S.toSubfield.toField
 #align intermediate_field.to_field IntermediateField.toField
 
+/- warning: intermediate_field.coe_sum -> IntermediateField.coe_sum is a dubious translation:
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+but is expected to have type
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))] (S : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) {ι : Type.{u3}} [_inst_6 : Fintype.{u3} ι] (f : ι -> (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S))), Eq.{succ u2} L (Subtype.val.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Set.{u2} L) (Set.instMembershipSet.{u2} L) x (SetLike.coe.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) S)) (Finset.sum.{u2, u3} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (Ring.toNonAssocRing.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (DivisionRing.toRing.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (Field.toDivisionRing.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (IntermediateField.toField.{u1, u2} K L _inst_1 _inst_2 _inst_4 S))))))) (Finset.univ.{u3} ι _inst_6) (fun (i : ι) => f i))) (Finset.sum.{u2, u3} L ι (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} L (NonAssocRing.toNonUnitalNonAssocRing.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) (Finset.univ.{u3} ι _inst_6) (fun (i : ι) => Subtype.val.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Set.{u2} L) (Set.instMembershipSet.{u2} L) x (SetLike.coe.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) S)) (f i)))
+Case conversion may be inaccurate. Consider using '#align intermediate_field.coe_sum IntermediateField.coe_sumₓ'. -/
 @[simp, norm_cast]
 theorem coe_sum {ι : Type _} [Fintype ι] (f : ι → S) : (↑(∑ i, f i) : L) = ∑ i, (f i : L) := by
   classical
@@ -354,6 +628,12 @@ theorem coe_sum {ι : Type _} [Fintype ι] (f : ι → S) : (↑(∑ i, f i) : L
     · rw [Finset.sum_insert hi, AddMemClass.coe_add, H, Finset.sum_insert hi]
 #align intermediate_field.coe_sum IntermediateField.coe_sum
 
+/- warning: intermediate_field.coe_prod -> IntermediateField.coe_prod is a dubious translation:
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_inst_2 _inst_4) (SetLike.hasMem.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S))))) (f i)))
+but is expected to have type
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))] (S : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) {ι : Type.{u3}} [_inst_6 : Fintype.{u3} ι] (f : ι -> (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S))), Eq.{succ u2} L (Subtype.val.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Set.{u2} L) (Set.instMembershipSet.{u2} L) x (SetLike.coe.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) S)) (Finset.prod.{u2, u3} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) ι (Submonoid.toCommMonoid.{u2} L (CommRing.toCommMonoid.{u2} L (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2))) (Subsemiring.toSubmonoid.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Subalgebra.toSubsemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S)))) (Finset.univ.{u3} ι _inst_6) (fun (i : ι) => f i))) (Finset.prod.{u2, u3} L ι (CommRing.toCommMonoid.{u2} L (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_2))) (Finset.univ.{u3} ι _inst_6) (fun (i : ι) => Subtype.val.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Set.{u2} L) (Set.instMembershipSet.{u2} L) x (SetLike.coe.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) S)) (f i)))
+Case conversion may be inaccurate. Consider using '#align intermediate_field.coe_prod IntermediateField.coe_prodₓ'. -/
 @[simp, norm_cast]
 theorem coe_prod {ι : Type _} [Fintype ι] (f : ι → S) : (↑(∏ i, f i) : L) = ∏ i, (f i : L) := by
   classical
@@ -365,52 +645,113 @@ theorem coe_prod {ι : Type _} [Fintype ι] (f : ι → S) : (↑(∏ i, f i) :
 /-! `intermediate_field`s inherit structure from their `subalgebra` coercions. -/
 
 
+/- warning: intermediate_field.module' -> IntermediateField.module' is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] (S : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) {R : Type.{u3}} [_inst_6 : Semiring.{u3} R] [_inst_7 : SMul.{u3, u1} R K] [_inst_8 : Module.{u3, u2} R L _inst_6 (AddCommGroup.toAddCommMonoid.{u2} L (NonUnitalNonAssocRing.toAddCommGroup.{u2} L (NonAssocRing.toNonUnitalNonAssocRing.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))] [_inst_9 : IsScalarTower.{u3, u1, u2} R K L _inst_7 (SMulZeroClass.toHasSmul.{u1, u2} K L (AddZeroClass.toHasZero.{u2} L (AddMonoid.toAddZeroClass.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} K L (MulZeroClass.toHasZero.{u1} K (MulZeroOneClass.toMulZeroClass.{u1} K (MonoidWithZero.toMulZeroOneClass.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (AddZeroClass.toHasZero.{u2} L (AddMonoid.toAddZeroClass.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} K L (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (AddZeroClass.toHasZero.{u2} L (AddMonoid.toAddZeroClass.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))))) (Module.toMulActionWithZero.{u1, u2} K L (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) (Algebra.toModule.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_4))))) (SMulZeroClass.toHasSmul.{u3, u2} R L (AddZeroClass.toHasZero.{u2} L (AddMonoid.toAddZeroClass.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (AddCommGroup.toAddCommMonoid.{u2} L (NonUnitalNonAssocRing.toAddCommGroup.{u2} L (NonAssocRing.toNonUnitalNonAssocRing.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))))) (SMulWithZero.toSmulZeroClass.{u3, u2} R L (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_6)))) (AddZeroClass.toHasZero.{u2} L (AddMonoid.toAddZeroClass.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (AddCommGroup.toAddCommMonoid.{u2} L (NonUnitalNonAssocRing.toAddCommGroup.{u2} L (NonAssocRing.toNonUnitalNonAssocRing.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))))) (MulActionWithZero.toSMulWithZero.{u3, u2} R L (Semiring.toMonoidWithZero.{u3} R _inst_6) (AddZeroClass.toHasZero.{u2} L (AddMonoid.toAddZeroClass.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (AddCommGroup.toAddCommMonoid.{u2} L (NonUnitalNonAssocRing.toAddCommGroup.{u2} L (NonAssocRing.toNonUnitalNonAssocRing.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))))) (Module.toMulActionWithZero.{u3, u2} R L _inst_6 (AddCommGroup.toAddCommMonoid.{u2} L (NonUnitalNonAssocRing.toAddCommGroup.{u2} L (NonAssocRing.toNonUnitalNonAssocRing.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) _inst_8))))], Module.{u3, u2} R (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) S) _inst_6 (AddCommGroup.toAddCommMonoid.{u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) S) (NonUnitalNonAssocRing.toAddCommGroup.{u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) S) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) S) (Ring.toNonAssocRing.{u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) S) (DivisionRing.toRing.{u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) S) (Field.toDivisionRing.{u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) S) (IntermediateField.toField.{u1, u2} K L _inst_1 _inst_2 _inst_4 S)))))))
+but is expected to have type
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))] (S : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) {R : Type.{u3}} [_inst_6 : Semiring.{u3} R] [_inst_7 : SMul.{u3, u1} R K] [_inst_8 : Module.{u3, u2} R L _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} L (NonAssocRing.toNonUnitalNonAssocRing.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))] [_inst_9 : IsScalarTower.{u3, u1, u2} R K L _inst_7 (Algebra.toSMul.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4) (SMulZeroClass.toSMul.{u3, u2} R L (CommMonoidWithZero.toZero.{u2} L (CommGroupWithZero.toCommMonoidWithZero.{u2} L (Semifield.toCommGroupWithZero.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (SMulWithZero.toSMulZeroClass.{u3, u2} R L (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_6)) (CommMonoidWithZero.toZero.{u2} L (CommGroupWithZero.toCommMonoidWithZero.{u2} L (Semifield.toCommGroupWithZero.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (MulActionWithZero.toSMulWithZero.{u3, u2} R L (Semiring.toMonoidWithZero.{u3} R _inst_6) (CommMonoidWithZero.toZero.{u2} L (CommGroupWithZero.toCommMonoidWithZero.{u2} L (Semifield.toCommGroupWithZero.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Module.toMulActionWithZero.{u3, u2} R L _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} L (NonAssocRing.toNonUnitalNonAssocRing.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) _inst_8))))], Module.{u3, u2} R (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (Ring.toNonAssocRing.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (DivisionRing.toRing.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (Field.toDivisionRing.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (IntermediateField.toField.{u1, u2} K L _inst_1 _inst_2 _inst_4 S)))))))
+Case conversion may be inaccurate. Consider using '#align intermediate_field.module' IntermediateField.module'ₓ'. -/
 instance module' {R} [Semiring R] [SMul R K] [Module R L] [IsScalarTower R K L] : Module R S :=
   S.toSubalgebra.module'
 #align intermediate_field.module' IntermediateField.module'
 
+/- warning: intermediate_field.module -> IntermediateField.module is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] (S : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4), Module.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) S) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) S) (NonUnitalNonAssocRing.toAddCommGroup.{u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) S) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) S) (Ring.toNonAssocRing.{u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) S) (DivisionRing.toRing.{u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) S) (Field.toDivisionRing.{u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) S) (IntermediateField.toField.{u1, u2} K L _inst_1 _inst_2 _inst_4 S)))))))
+but is expected to have type
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))] (S : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4), Module.{u1, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (Ring.toNonAssocRing.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (DivisionRing.toRing.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (Field.toDivisionRing.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (IntermediateField.toField.{u1, u2} K L _inst_1 _inst_2 _inst_4 S)))))))
+Case conversion may be inaccurate. Consider using '#align intermediate_field.module IntermediateField.moduleₓ'. -/
 instance module : Module K S :=
   S.toSubalgebra.Module
 #align intermediate_field.module IntermediateField.module
 
+/- warning: intermediate_field.is_scalar_tower -> IntermediateField.isScalarTower is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] (S : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) {R : Type.{u3}} [_inst_6 : Semiring.{u3} R] [_inst_7 : SMul.{u3, u1} R K] [_inst_8 : Module.{u3, u2} R L _inst_6 (AddCommGroup.toAddCommMonoid.{u2} L (NonUnitalNonAssocRing.toAddCommGroup.{u2} L (NonAssocRing.toNonUnitalNonAssocRing.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))] [_inst_9 : IsScalarTower.{u3, u1, u2} R K L _inst_7 (SMulZeroClass.toHasSmul.{u1, u2} K L (AddZeroClass.toHasZero.{u2} L (AddMonoid.toAddZeroClass.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} K L (MulZeroClass.toHasZero.{u1} K (MulZeroOneClass.toMulZeroClass.{u1} K (MonoidWithZero.toMulZeroOneClass.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (AddZeroClass.toHasZero.{u2} L (AddMonoid.toAddZeroClass.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} K L (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (AddZeroClass.toHasZero.{u2} L (AddMonoid.toAddZeroClass.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))))) (Module.toMulActionWithZero.{u1, u2} K L (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) (Algebra.toModule.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_4))))) (SMulZeroClass.toHasSmul.{u3, u2} R L (AddZeroClass.toHasZero.{u2} L (AddMonoid.toAddZeroClass.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (AddCommGroup.toAddCommMonoid.{u2} L (NonUnitalNonAssocRing.toAddCommGroup.{u2} L (NonAssocRing.toNonUnitalNonAssocRing.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))))) (SMulWithZero.toSmulZeroClass.{u3, u2} R L (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_6)))) (AddZeroClass.toHasZero.{u2} L (AddMonoid.toAddZeroClass.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (AddCommGroup.toAddCommMonoid.{u2} L (NonUnitalNonAssocRing.toAddCommGroup.{u2} L (NonAssocRing.toNonUnitalNonAssocRing.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))))) (MulActionWithZero.toSMulWithZero.{u3, u2} R L (Semiring.toMonoidWithZero.{u3} R _inst_6) (AddZeroClass.toHasZero.{u2} L (AddMonoid.toAddZeroClass.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (AddCommGroup.toAddCommMonoid.{u2} L (NonUnitalNonAssocRing.toAddCommGroup.{u2} L (NonAssocRing.toNonUnitalNonAssocRing.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))))) (Module.toMulActionWithZero.{u3, u2} R L _inst_6 (AddCommGroup.toAddCommMonoid.{u2} L (NonUnitalNonAssocRing.toAddCommGroup.{u2} L (NonAssocRing.toNonUnitalNonAssocRing.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) _inst_8))))], IsScalarTower.{u3, u1, u2} R K (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) S) _inst_7 (SMulZeroClass.toHasSmul.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} 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(coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) S) _inst_6 (AddCommGroup.toAddCommMonoid.{u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) S) (NonUnitalNonAssocRing.toAddCommGroup.{u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) S) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) S) (Ring.toNonAssocRing.{u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) S) (DivisionRing.toRing.{u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) S) (Field.toDivisionRing.{u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) S) (IntermediateField.toField.{u1, u2} K L _inst_1 _inst_2 _inst_4 S))))))) (IntermediateField.module'.{u1, u2, u3} K L _inst_1 _inst_2 _inst_4 S R _inst_6 _inst_7 _inst_8 _inst_9)))))
+but is expected to have type
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))] (S : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) {R : Type.{u3}} [_inst_6 : Semiring.{u3} R] [_inst_7 : SMul.{u3, u1} R K] [_inst_8 : Module.{u3, u2} R L _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} L (NonAssocRing.toNonUnitalNonAssocRing.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))] [_inst_9 : IsScalarTower.{u3, u1, u2} R K L _inst_7 (Algebra.toSMul.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4) (SMulZeroClass.toSMul.{u3, u2} R L (CommMonoidWithZero.toZero.{u2} L (CommGroupWithZero.toCommMonoidWithZero.{u2} L (Semifield.toCommGroupWithZero.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (SMulWithZero.toSMulZeroClass.{u3, u2} R L (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_6)) (CommMonoidWithZero.toZero.{u2} L (CommGroupWithZero.toCommMonoidWithZero.{u2} L (Semifield.toCommGroupWithZero.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (MulActionWithZero.toSMulWithZero.{u3, u2} R L (Semiring.toMonoidWithZero.{u3} R _inst_6) (CommMonoidWithZero.toZero.{u2} L (CommGroupWithZero.toCommMonoidWithZero.{u2} L (Semifield.toCommGroupWithZero.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (Module.toMulActionWithZero.{u3, u2} R L _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} L (NonAssocRing.toNonUnitalNonAssocRing.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) _inst_8))))], IsScalarTower.{u3, u1, u2} R K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) _inst_7 (Algebra.toSMul.{u1, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S)) (Subalgebra.algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S))) (SMulZeroClass.toSMul.{u3, u2} R (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (ZeroMemClass.zero.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (CommMonoidWithZero.toZero.{u2} L (CommGroupWithZero.toCommMonoidWithZero.{u2} L (Semifield.toCommGroupWithZero.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (AddSubmonoidClass.toZeroMemClass.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (AddMonoid.toAddZeroClass.{u2} L (AddMonoidWithOne.toAddMonoid.{u2} L (AddGroupWithOne.toAddMonoidWithOne.{u2} L (Ring.toAddGroupWithOne.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SubsemiringClass.toAddSubmonoidClass.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SubringClass.toSubsemiringClass.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)) (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SubfieldClass.toSubringClass.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L _inst_2 (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (IntermediateField.instSubfieldClassIntermediateFieldInstSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4))))) S) (SMulWithZero.toSMulZeroClass.{u3, u2} R (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_6)) (ZeroMemClass.zero.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (CommMonoidWithZero.toZero.{u2} L (CommGroupWithZero.toCommMonoidWithZero.{u2} L (Semifield.toCommGroupWithZero.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (AddSubmonoidClass.toZeroMemClass.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (AddMonoid.toAddZeroClass.{u2} L (AddMonoidWithOne.toAddMonoid.{u2} L (AddGroupWithOne.toAddMonoidWithOne.{u2} L (Ring.toAddGroupWithOne.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SubsemiringClass.toAddSubmonoidClass.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SubringClass.toSubsemiringClass.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)) (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SubfieldClass.toSubringClass.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L _inst_2 (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (IntermediateField.instSubfieldClassIntermediateFieldInstSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4))))) S) (MulActionWithZero.toSMulWithZero.{u3, u2} R (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (Semiring.toMonoidWithZero.{u3} R _inst_6) (ZeroMemClass.zero.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (CommMonoidWithZero.toZero.{u2} L (CommGroupWithZero.toCommMonoidWithZero.{u2} L (Semifield.toCommGroupWithZero.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (AddSubmonoidClass.toZeroMemClass.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (AddMonoid.toAddZeroClass.{u2} L (AddMonoidWithOne.toAddMonoid.{u2} L (AddGroupWithOne.toAddMonoidWithOne.{u2} L (Ring.toAddGroupWithOne.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SubsemiringClass.toAddSubmonoidClass.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SubringClass.toSubsemiringClass.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)) (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SubfieldClass.toSubringClass.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L _inst_2 (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (IntermediateField.instSubfieldClassIntermediateFieldInstSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4))))) S) (Module.toMulActionWithZero.{u3, u2} R (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (Ring.toNonAssocRing.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (DivisionRing.toRing.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (Field.toDivisionRing.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (IntermediateField.toField.{u1, u2} K L _inst_1 _inst_2 _inst_4 S))))))) (IntermediateField.module'.{u1, u2, u3} K L _inst_1 _inst_2 _inst_4 S R _inst_6 _inst_7 _inst_8 _inst_9)))))
+Case conversion may be inaccurate. Consider using '#align intermediate_field.is_scalar_tower IntermediateField.isScalarTowerₓ'. -/
 instance isScalarTower {R} [Semiring R] [SMul R K] [Module R L] [IsScalarTower R K L] :
     IsScalarTower R K S :=
   S.toSubalgebra.IsScalarTower
 #align intermediate_field.is_scalar_tower IntermediateField.isScalarTower
 
+/- warning: intermediate_field.coe_smul -> IntermediateField.coe_smul is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] (S : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) {R : Type.{u3}} [_inst_6 : Semiring.{u3} R] [_inst_7 : SMul.{u3, u1} R K] [_inst_8 : Module.{u3, u2} R L _inst_6 (AddCommGroup.toAddCommMonoid.{u2} L (NonUnitalNonAssocRing.toAddCommGroup.{u2} L (NonAssocRing.toNonUnitalNonAssocRing.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))] [_inst_9 : IsScalarTower.{u3, u1, u2} R K L _inst_7 (SMulZeroClass.toHasSmul.{u1, u2} K L (AddZeroClass.toHasZero.{u2} L (AddMonoid.toAddZeroClass.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} K L (MulZeroClass.toHasZero.{u1} K (MulZeroOneClass.toMulZeroClass.{u1} K (MonoidWithZero.toMulZeroOneClass.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (AddZeroClass.toHasZero.{u2} L (AddMonoid.toAddZeroClass.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} K L (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (AddZeroClass.toHasZero.{u2} L (AddMonoid.toAddZeroClass.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))))) (Module.toMulActionWithZero.{u1, u2} K L (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) (Algebra.toModule.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_4))))) (SMulZeroClass.toHasSmul.{u3, u2} R L (AddZeroClass.toHasZero.{u2} L (AddMonoid.toAddZeroClass.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (AddCommGroup.toAddCommMonoid.{u2} L (NonUnitalNonAssocRing.toAddCommGroup.{u2} L (NonAssocRing.toNonUnitalNonAssocRing.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))))) (SMulWithZero.toSmulZeroClass.{u3, u2} R L (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_6)))) (AddZeroClass.toHasZero.{u2} L (AddMonoid.toAddZeroClass.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (AddCommGroup.toAddCommMonoid.{u2} L (NonUnitalNonAssocRing.toAddCommGroup.{u2} L (NonAssocRing.toNonUnitalNonAssocRing.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))))) (MulActionWithZero.toSMulWithZero.{u3, u2} R L (Semiring.toMonoidWithZero.{u3} R _inst_6) (AddZeroClass.toHasZero.{u2} L (AddMonoid.toAddZeroClass.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (AddCommGroup.toAddCommMonoid.{u2} L (NonUnitalNonAssocRing.toAddCommGroup.{u2} L (NonAssocRing.toNonUnitalNonAssocRing.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))))) (Module.toMulActionWithZero.{u3, u2} R L _inst_6 (AddCommGroup.toAddCommMonoid.{u2} L (NonUnitalNonAssocRing.toAddCommGroup.{u2} L (NonAssocRing.toNonUnitalNonAssocRing.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) _inst_8))))] (r : R) (x : coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) S), Eq.{succ u2} L ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} 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+but is expected to have type
+  forall {K : Type.{u2}} {L : Type.{u1}} [_inst_1 : Field.{u2} K] [_inst_2 : Field.{u1} L] [_inst_4 : Algebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))] (S : IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) {R : Type.{u3}} [_inst_6 : Semiring.{u3} R] [_inst_7 : SMul.{u3, u2} R K] [_inst_8 : Module.{u3, u1} R L _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} L (NonAssocRing.toNonUnitalNonAssocRing.{u1} L (Ring.toNonAssocRing.{u1} L (DivisionRing.toRing.{u1} L (Field.toDivisionRing.{u1} L _inst_2))))))] [_inst_9 : IsScalarTower.{u3, u2, u1} R K L _inst_7 (Algebra.toSMul.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) 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_inst_2)))))) _inst_8))))] (r : R) (x : Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x S)), Eq.{succ u1} L (Subtype.val.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (Set.{u1} L) (Set.instMembershipSet.{u1} L) x (SetLike.coe.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) S)) (HSMul.hSMul.{u3, u1, u1} R (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x S)) (Subtype.{succ u1} L 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(Semiring.toMonoidWithZero.{u3} R _inst_6) (CommMonoidWithZero.toZero.{u1} L (CommGroupWithZero.toCommMonoidWithZero.{u1} L (Semifield.toCommGroupWithZero.{u1} L (Field.toSemifield.{u1} L _inst_2)))) (Module.toMulActionWithZero.{u3, u1} R L _inst_6 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} L (NonAssocRing.toNonUnitalNonAssocRing.{u1} L (Ring.toNonAssocRing.{u1} L (DivisionRing.toRing.{u1} L (Field.toDivisionRing.{u1} L _inst_2)))))) _inst_8))))) r (Subtype.val.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (Set.{u1} L) (Set.instMembershipSet.{u1} L) x (SetLike.coe.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) S)) x))
+Case conversion may be inaccurate. Consider using '#align intermediate_field.coe_smul IntermediateField.coe_smulₓ'. -/
 @[simp]
 theorem coe_smul {R} [Semiring R] [SMul R K] [Module R L] [IsScalarTower R K L] (r : R) (x : S) :
     ↑(r • x) = (r • x : L) :=
   rfl
 #align intermediate_field.coe_smul IntermediateField.coe_smul
 
+/- warning: intermediate_field.algebra' -> IntermediateField.algebra' 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 intermediate_field.algebra' IntermediateField.algebra'ₓ'. -/
 instance algebra' {K'} [CommSemiring K'] [SMul K' K] [Algebra K' L] [IsScalarTower K' K L] :
     Algebra K' S :=
   S.toSubalgebra.algebra'
 #align intermediate_field.algebra' IntermediateField.algebra'
 
+/- warning: intermediate_field.algebra -> IntermediateField.algebra 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 intermediate_field.algebra IntermediateField.algebraₓ'. -/
 instance algebra : Algebra K S :=
   S.toSubalgebra.Algebra
 #align intermediate_field.algebra IntermediateField.algebra
 
+/- warning: intermediate_field.to_algebra -> IntermediateField.toAlgebra is a dubious translation:
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+but is expected to have type
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))] (S : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) {R : Type.{u3}} [_inst_6 : Semiring.{u3} R] [_inst_7 : Algebra.{u2, u3} L R (Semifield.toCommSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)) _inst_6], Algebra.{u2, u3} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) R (Subalgebra.toCommSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Semifield.toCommSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)) _inst_4 (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S)) _inst_6
+Case conversion may be inaccurate. Consider using '#align intermediate_field.to_algebra IntermediateField.toAlgebraₓ'. -/
 instance toAlgebra {R : Type _} [Semiring R] [Algebra L R] : Algebra S R :=
   S.toSubalgebra.toAlgebra
 #align intermediate_field.to_algebra IntermediateField.toAlgebra
 
+/- warning: intermediate_field.is_scalar_tower_bot -> IntermediateField.isScalarTower_bot is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] (S : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) {R : Type.{u3}} [_inst_6 : Semiring.{u3} R] [_inst_7 : Algebra.{u2, u3} L R (Semifield.toCommSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)) _inst_6], IsScalarTower.{u2, u2, u3} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) S) L R (SMulZeroClass.toHasSmul.{u2, u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 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(succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) S) (SubsemiringClass.toCommSemiring.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) S L (Semifield.toCommSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)) (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4) (IntermediateField.toAlgebra._proof_1.{u1, u2} K L _inst_1 _inst_2 _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_6))) (Algebra.toModule.{u2, u3} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) S) R (SubsemiringClass.toCommSemiring.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) S L (Semifield.toCommSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)) (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4) (IntermediateField.toAlgebra._proof_1.{u1, u2} K L _inst_1 _inst_2 _inst_4)) _inst_6 (IntermediateField.toAlgebra.{u1, u2, u3} K L _inst_1 _inst_2 _inst_4 S R _inst_6 _inst_7))))))
+but is expected to have type
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))] (S : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) {R : Type.{u3}} [_inst_6 : Semiring.{u3} R] [_inst_7 : Algebra.{u2, u3} L R (Semifield.toCommSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)) _inst_6], IsScalarTower.{u2, u2, u3} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) L R (Subalgebra.instSMulSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebra.{u1, u2, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 L (Algebra.toSMul.{u2, u2} L L (Semifield.toCommSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (Algebra.id.{u2} L (Semifield.toCommSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S)) (Algebra.toSMul.{u2, u3} L R (Semifield.toCommSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)) _inst_6 _inst_7) (Subalgebra.instSMulSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebra.{u1, u2, u3} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 R (Algebra.toSMul.{u2, u3} L R (Semifield.toCommSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)) _inst_6 _inst_7) (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S))
+Case conversion may be inaccurate. Consider using '#align intermediate_field.is_scalar_tower_bot IntermediateField.isScalarTower_botₓ'. -/
 instance isScalarTower_bot {R : Type _} [Semiring R] [Algebra L R] : IsScalarTower S L R :=
   IsScalarTower.subalgebra _ _ _ S.toSubalgebra
 #align intermediate_field.is_scalar_tower_bot IntermediateField.isScalarTower_bot
 
+/- warning: intermediate_field.is_scalar_tower_mid -> IntermediateField.isScalarTower_mid is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] (S : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) {R : Type.{u3}} [_inst_6 : Semiring.{u3} R] [_inst_7 : Algebra.{u2, u3} L R (Semifield.toCommSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)) _inst_6] [_inst_8 : Algebra.{u1, u3} K R (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) _inst_6] [_inst_9 : IsScalarTower.{u1, u2, u3} K L R (SMulZeroClass.toHasSmul.{u1, u2} K L (AddZeroClass.toHasZero.{u2} L (AddMonoid.toAddZeroClass.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L 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(MonoidWithZero.toMulZeroOneClass.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_6)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} K R (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (AddZeroClass.toHasZero.{u3} R (AddMonoid.toAddZeroClass.{u3} R (AddCommMonoid.toAddMonoid.{u3} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_6)))))) (Module.toMulActionWithZero.{u1, u3} K R (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K 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_inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_6))) (Algebra.toModule.{u1, u3} K R (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) _inst_6 _inst_8)))))
+but is expected to have type
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))] (S : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) {R : Type.{u3}} [_inst_6 : Semiring.{u3} R] [_inst_7 : Algebra.{u2, u3} L R (Semifield.toCommSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)) _inst_6] [_inst_8 : Algebra.{u1, u3} K R (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) _inst_6] [_inst_9 : IsScalarTower.{u1, u2, u3} K L R (Algebra.toSMul.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4) (Algebra.toSMul.{u2, u3} L R (Semifield.toCommSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)) _inst_6 _inst_7) (Algebra.toSMul.{u1, u3} K R (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) _inst_6 _inst_8)], IsScalarTower.{u1, u2, u3} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) R (Algebra.toSMul.{u1, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S)) (IntermediateField.algebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S)) (Subalgebra.instSMulSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebra.{u1, u2, u3} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 R (Algebra.toSMul.{u2, u3} L R (Semifield.toCommSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)) _inst_6 _inst_7) (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S)) (Algebra.toSMul.{u1, u3} K R (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) _inst_6 _inst_8)
+Case conversion may be inaccurate. Consider using '#align intermediate_field.is_scalar_tower_mid IntermediateField.isScalarTower_midₓ'. -/
 instance isScalarTower_mid {R : Type _} [Semiring R] [Algebra L R] [Algebra K R]
     [IsScalarTower K L R] : IsScalarTower K S R :=
   IsScalarTower.subalgebra' _ _ _ S.toSubalgebra
 #align intermediate_field.is_scalar_tower_mid IntermediateField.isScalarTower_mid
 
+/- warning: intermediate_field.is_scalar_tower_mid' -> IntermediateField.isScalarTower_mid' is a dubious translation:
+lean 3 declaration is
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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) (Algebra.toModule.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_4)))))
+but is expected to have type
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))] (S : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4), IsScalarTower.{u1, u2, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) L (Algebra.toSMul.{u1, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S)) (IntermediateField.algebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S)) (Subalgebra.instSMulSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebra.{u1, u2, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 L (Algebra.toSMul.{u2, u2} L L (Semifield.toCommSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (Algebra.id.{u2} L (Semifield.toCommSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S)) (Algebra.toSMul.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4)
+Case conversion may be inaccurate. Consider using '#align intermediate_field.is_scalar_tower_mid' IntermediateField.isScalarTower_mid'ₓ'. -/
 /-- Specialize `is_scalar_tower_mid` to the common case where the top field is `L` -/
 instance isScalarTower_mid' : IsScalarTower K S L :=
   S.isScalarTower_mid
 #align intermediate_field.is_scalar_tower_mid' IntermediateField.isScalarTower_mid'
 
+#print IntermediateField.map /-
 /-- If `f : L →+* L'` fixes `K`, `S.map f` is the intermediate field between `L'` and `K`
 such that `x ∈ S ↔ f x ∈ S.map f`. -/
 def map (f : L →ₐ[K] L') (S : IntermediateField K L) : IntermediateField K L' :=
@@ -422,18 +763,37 @@ def map (f : L →ₐ[K] L') (S : IntermediateField K L) : IntermediateField K L
       exact ⟨x⁻¹, S.inv_mem hx, map_inv₀ f x⟩
     neg_mem' := fun x hx => (S.toSubalgebra.map f).neg_mem hx }
 #align intermediate_field.map IntermediateField.map
+-/
 
+/- warning: intermediate_field.coe_map -> IntermediateField.coe_map is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {L : Type.{u2}} {L' : Type.{u3}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_3 : Field.{u3} L'] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] [_inst_5 : Algebra.{u1, u3} K L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3)))] (S : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (f : AlgHom.{u1, u2, u3} K L L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3))) _inst_4 _inst_5), Eq.{succ u3} (Set.{u3} L') ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (IntermediateField.{u1, u3} K L' _inst_1 _inst_3 _inst_5) (Set.{u3} L') (HasLiftT.mk.{succ u3, succ u3} (IntermediateField.{u1, u3} K L' _inst_1 _inst_3 _inst_5) (Set.{u3} L') (CoeTCₓ.coe.{succ u3, succ u3} (IntermediateField.{u1, u3} K L' _inst_1 _inst_3 _inst_5) (Set.{u3} L') (SetLike.Set.hasCoeT.{u3, u3} (IntermediateField.{u1, u3} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.setLike.{u1, u3} K L' _inst_1 _inst_3 _inst_5)))) (IntermediateField.map.{u1, u2, u3} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 f S)) (Set.image.{u2, u3} L L' (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} K L L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3))) _inst_4 _inst_5) (fun (_x : AlgHom.{u1, u2, u3} K L L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3))) _inst_4 _inst_5) => L -> L') ([anonymous].{u1, u2, u3} K L L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3))) _inst_4 _inst_5) f) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (Set.{u2} L) (HasLiftT.mk.{succ u2, succ u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (Set.{u2} L) (CoeTCₓ.coe.{succ u2, succ u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (Set.{u2} L) (SetLike.Set.hasCoeT.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)))) S))
+but is expected to have type
+  forall {K : Type.{u3}} {L : Type.{u2}} {L' : Type.{u1}} [_inst_1 : Field.{u3} K] [_inst_2 : Field.{u2} L] [_inst_3 : Field.{u1} L'] [_inst_4 : Algebra.{u3, u2} K L (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))] [_inst_5 : Algebra.{u3, u1} K L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3)))] (S : IntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) (f : AlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5), Eq.{succ u1} (Set.{u1} L') (SetLike.coe.{u1, u1} (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.instSetLikeIntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 f S)) (Set.image.{u2, u1} L L' (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5) L (fun (_x : L) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : L) => L') _x) (SMulHomClass.toFunLike.{max u2 u1, u3, u2, u1} (AlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5) K L L' (SMulZeroClass.toSMul.{u3, u2} K L (AddMonoid.toZero.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))))) (DistribSMul.toSMulZeroClass.{u3, u2} K L (AddMonoid.toAddZeroClass.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))))) (DistribMulAction.toDistribSMul.{u3, u2} K L (MonoidWithZero.toMonoid.{u3} K (Semiring.toMonoidWithZero.{u3} K (CommSemiring.toSemiring.{u3} K (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))))) (Module.toDistribMulAction.{u3, u2} K L (CommSemiring.toSemiring.{u3} K (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (Algebra.toModule.{u3, u2} K L (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4))))) (SMulZeroClass.toSMul.{u3, u1} K L' (AddMonoid.toZero.{u1} L' (AddCommMonoid.toAddMonoid.{u1} L' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L' (Semiring.toNonAssocSemiring.{u1} L' (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3)))))))) (DistribSMul.toSMulZeroClass.{u3, u1} K L' (AddMonoid.toAddZeroClass.{u1} L' (AddCommMonoid.toAddMonoid.{u1} L' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L' (Semiring.toNonAssocSemiring.{u1} L' (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3)))))))) (DistribMulAction.toDistribSMul.{u3, u1} K L' (MonoidWithZero.toMonoid.{u3} K (Semiring.toMonoidWithZero.{u3} K (CommSemiring.toSemiring.{u3} K (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} L' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L' (Semiring.toNonAssocSemiring.{u1} L' (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))))))) (Module.toDistribMulAction.{u3, u1} K L' (CommSemiring.toSemiring.{u3} K (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L' (Semiring.toNonAssocSemiring.{u1} L' (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3)))))) (Algebra.toModule.{u3, u1} K L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u3, u2, u1} (AlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5) K L L' (MonoidWithZero.toMonoid.{u3} K (Semiring.toMonoidWithZero.{u3} K (CommSemiring.toSemiring.{u3} K (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))))) (AddCommMonoid.toAddMonoid.{u1} L' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L' (Semiring.toNonAssocSemiring.{u1} L' (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))))))) (Module.toDistribMulAction.{u3, u2} K L (CommSemiring.toSemiring.{u3} K (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (Algebra.toModule.{u3, u2} K L (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4)) (Module.toDistribMulAction.{u3, u1} K L' (CommSemiring.toSemiring.{u3} K (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L' (Semiring.toNonAssocSemiring.{u1} L' (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3)))))) (Algebra.toModule.{u3, u1} K L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_5)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u3, u2, u1} (AlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5) K L L' (MonoidWithZero.toMonoid.{u3} K (Semiring.toMonoidWithZero.{u3} K (CommSemiring.toSemiring.{u3} K (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L' (Semiring.toNonAssocSemiring.{u1} L' (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))))) (Module.toDistribMulAction.{u3, u2} K L (CommSemiring.toSemiring.{u3} K (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (Algebra.toModule.{u3, u2} K L (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4)) (Module.toDistribMulAction.{u3, u1} K L' (CommSemiring.toSemiring.{u3} K (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L' (Semiring.toNonAssocSemiring.{u1} L' (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3)))))) (Algebra.toModule.{u3, u1} K L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, u2, u1, max u2 u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 (AlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5) (AlgHom.algHomClass.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5))))) f) (SetLike.coe.{u2, u2} (IntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) S))
+Case conversion may be inaccurate. Consider using '#align intermediate_field.coe_map IntermediateField.coe_mapₓ'. -/
 @[simp]
 theorem coe_map (f : L →ₐ[K] L') : (S.map f : Set L') = f '' S :=
   rfl
 #align intermediate_field.coe_map IntermediateField.coe_map
 
+/- warning: intermediate_field.map_map -> IntermediateField.map_map is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {L₁ : Type.{u2}} {L₂ : Type.{u3}} {L₃ : Type.{u4}} [_inst_6 : Field.{u1} K] [_inst_7 : Field.{u2} L₁] [_inst_8 : Algebra.{u1, u2} K L₁ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_6)) (Ring.toSemiring.{u2} L₁ (DivisionRing.toRing.{u2} L₁ (Field.toDivisionRing.{u2} L₁ _inst_7)))] [_inst_9 : Field.{u3} L₂] [_inst_10 : Algebra.{u1, u3} K L₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_6)) (Ring.toSemiring.{u3} L₂ (DivisionRing.toRing.{u3} L₂ (Field.toDivisionRing.{u3} L₂ _inst_9)))] [_inst_11 : Field.{u4} L₃] [_inst_12 : Algebra.{u1, u4} K L₃ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_6)) (Ring.toSemiring.{u4} L₃ (DivisionRing.toRing.{u4} L₃ (Field.toDivisionRing.{u4} L₃ _inst_11)))] (E : IntermediateField.{u1, u2} K L₁ _inst_6 _inst_7 _inst_8) (f : AlgHom.{u1, u2, u3} K L₁ L₂ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_6)) (Ring.toSemiring.{u2} L₁ (DivisionRing.toRing.{u2} L₁ (Field.toDivisionRing.{u2} L₁ _inst_7))) (Ring.toSemiring.{u3} L₂ (DivisionRing.toRing.{u3} L₂ (Field.toDivisionRing.{u3} L₂ _inst_9))) _inst_8 _inst_10) (g : AlgHom.{u1, u3, u4} K L₂ L₃ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_6)) (Ring.toSemiring.{u3} L₂ (DivisionRing.toRing.{u3} L₂ (Field.toDivisionRing.{u3} L₂ _inst_9))) (Ring.toSemiring.{u4} L₃ (DivisionRing.toRing.{u4} L₃ (Field.toDivisionRing.{u4} L₃ _inst_11))) _inst_10 _inst_12), Eq.{succ u4} (IntermediateField.{u1, u4} K L₃ _inst_6 _inst_11 _inst_12) (IntermediateField.map.{u1, u3, u4} K L₂ L₃ _inst_6 _inst_9 _inst_11 _inst_10 _inst_12 g (IntermediateField.map.{u1, u2, u3} K L₁ L₂ _inst_6 _inst_7 _inst_9 _inst_8 _inst_10 f E)) (IntermediateField.map.{u1, u2, u4} K L₁ L₃ _inst_6 _inst_7 _inst_11 _inst_8 _inst_12 (AlgHom.comp.{u1, u2, u3, u4} K L₁ L₂ L₃ (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_6)) (Ring.toSemiring.{u2} L₁ (DivisionRing.toRing.{u2} L₁ (Field.toDivisionRing.{u2} L₁ _inst_7))) (Ring.toSemiring.{u3} L₂ (DivisionRing.toRing.{u3} L₂ (Field.toDivisionRing.{u3} L₂ _inst_9))) (Ring.toSemiring.{u4} L₃ (DivisionRing.toRing.{u4} L₃ (Field.toDivisionRing.{u4} L₃ _inst_11))) _inst_8 _inst_10 _inst_12 g f) E)
+but is expected to have type
+  forall {K : Type.{u4}} {L₁ : Type.{u3}} {L₂ : Type.{u2}} {L₃ : Type.{u1}} [_inst_6 : Field.{u4} K] [_inst_7 : Field.{u3} L₁] [_inst_8 : Algebra.{u4, u3} K L₁ (Semifield.toCommSemiring.{u4} K (Field.toSemifield.{u4} K _inst_6)) (DivisionSemiring.toSemiring.{u3} L₁ (Semifield.toDivisionSemiring.{u3} L₁ (Field.toSemifield.{u3} L₁ _inst_7)))] [_inst_9 : Field.{u2} L₂] [_inst_10 : Algebra.{u4, u2} K L₂ (Semifield.toCommSemiring.{u4} K (Field.toSemifield.{u4} K _inst_6)) (DivisionSemiring.toSemiring.{u2} L₂ (Semifield.toDivisionSemiring.{u2} L₂ (Field.toSemifield.{u2} L₂ _inst_9)))] [_inst_11 : Field.{u1} L₃] [_inst_12 : Algebra.{u4, u1} K L₃ (Semifield.toCommSemiring.{u4} K (Field.toSemifield.{u4} K _inst_6)) (DivisionSemiring.toSemiring.{u1} L₃ (Semifield.toDivisionSemiring.{u1} L₃ (Field.toSemifield.{u1} L₃ _inst_11)))] (E : IntermediateField.{u4, u3} K L₁ _inst_6 _inst_7 _inst_8) (f : AlgHom.{u4, u3, u2} K L₁ L₂ (Semifield.toCommSemiring.{u4} K (Field.toSemifield.{u4} K _inst_6)) (DivisionSemiring.toSemiring.{u3} L₁ (Semifield.toDivisionSemiring.{u3} L₁ (Field.toSemifield.{u3} L₁ _inst_7))) (DivisionSemiring.toSemiring.{u2} L₂ (Semifield.toDivisionSemiring.{u2} L₂ (Field.toSemifield.{u2} L₂ _inst_9))) _inst_8 _inst_10) (g : AlgHom.{u4, u2, u1} K L₂ L₃ (Semifield.toCommSemiring.{u4} K (Field.toSemifield.{u4} K _inst_6)) (DivisionSemiring.toSemiring.{u2} L₂ (Semifield.toDivisionSemiring.{u2} L₂ (Field.toSemifield.{u2} L₂ _inst_9))) (DivisionSemiring.toSemiring.{u1} L₃ (Semifield.toDivisionSemiring.{u1} L₃ (Field.toSemifield.{u1} L₃ _inst_11))) _inst_10 _inst_12), Eq.{succ u1} (IntermediateField.{u4, u1} K L₃ _inst_6 _inst_11 _inst_12) (IntermediateField.map.{u4, u2, u1} K L₂ L₃ _inst_6 _inst_9 _inst_11 _inst_10 _inst_12 g (IntermediateField.map.{u4, u3, u2} K L₁ L₂ _inst_6 _inst_7 _inst_9 _inst_8 _inst_10 f E)) (IntermediateField.map.{u4, u3, u1} K L₁ L₃ _inst_6 _inst_7 _inst_11 _inst_8 _inst_12 (AlgHom.comp.{u4, u3, u2, u1} K L₁ L₂ L₃ (Semifield.toCommSemiring.{u4} K (Field.toSemifield.{u4} K _inst_6)) (DivisionSemiring.toSemiring.{u3} L₁ (Semifield.toDivisionSemiring.{u3} L₁ (Field.toSemifield.{u3} L₁ _inst_7))) (DivisionSemiring.toSemiring.{u2} L₂ (Semifield.toDivisionSemiring.{u2} L₂ (Field.toSemifield.{u2} L₂ _inst_9))) (DivisionSemiring.toSemiring.{u1} L₃ (Semifield.toDivisionSemiring.{u1} L₃ (Field.toSemifield.{u1} L₃ _inst_11))) _inst_8 _inst_10 _inst_12 g f) E)
+Case conversion may be inaccurate. Consider using '#align intermediate_field.map_map IntermediateField.map_mapₓ'. -/
 theorem map_map {K L₁ L₂ L₃ : Type _} [Field K] [Field L₁] [Algebra K L₁] [Field L₂] [Algebra K L₂]
     [Field L₃] [Algebra K L₃] (E : IntermediateField K L₁) (f : L₁ →ₐ[K] L₂) (g : L₂ →ₐ[K] L₃) :
     (E.map f).map g = E.map (g.comp f) :=
   SetLike.coe_injective <| Set.image_image _ _ _
 #align intermediate_field.map_map IntermediateField.map_map
 
+/- warning: intermediate_field.intermediate_field_map -> IntermediateField.intermediateFieldMap is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {L : Type.{u2}} {L' : Type.{u3}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_3 : Field.{u3} L'] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] [_inst_5 : Algebra.{u1, u3} K L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3)))] (e : AlgEquiv.{u1, u2, u3} K L L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3))) _inst_4 _inst_5) (E : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4), AlgEquiv.{u1, u2, u3} K (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) E) (coeSort.{succ u3, succ (succ u3)} (IntermediateField.{u1, u3} K L' _inst_1 _inst_3 _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (IntermediateField.{u1, u3} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.setLike.{u1, u3} K L' _inst_1 _inst_3 _inst_5)) (IntermediateField.map.{u1, u2, u3} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u1, u2, u3} K L L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3))) _inst_4 _inst_5 e) E)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) E) (DivisionRing.toRing.{u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) E) (Field.toDivisionRing.{u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) E) (IntermediateField.toField.{u1, u2} K L _inst_1 _inst_2 _inst_4 E)))) (Ring.toSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (IntermediateField.{u1, u3} K L' _inst_1 _inst_3 _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (IntermediateField.{u1, u3} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.setLike.{u1, u3} K L' _inst_1 _inst_3 _inst_5)) (IntermediateField.map.{u1, u2, u3} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u1, u2, u3} K L L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3))) _inst_4 _inst_5 e) E)) (DivisionRing.toRing.{u3} (coeSort.{succ u3, succ (succ u3)} (IntermediateField.{u1, u3} K L' _inst_1 _inst_3 _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (IntermediateField.{u1, u3} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.setLike.{u1, u3} K L' _inst_1 _inst_3 _inst_5)) (IntermediateField.map.{u1, u2, u3} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u1, u2, u3} K L L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3))) _inst_4 _inst_5 e) E)) (Field.toDivisionRing.{u3} (coeSort.{succ u3, succ (succ u3)} (IntermediateField.{u1, u3} K L' _inst_1 _inst_3 _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (IntermediateField.{u1, u3} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.setLike.{u1, u3} K L' _inst_1 _inst_3 _inst_5)) (IntermediateField.map.{u1, u2, u3} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u1, u2, u3} K L L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3))) _inst_4 _inst_5 e) E)) (IntermediateField.toField.{u1, u3} K L' _inst_1 _inst_3 _inst_5 (IntermediateField.map.{u1, u2, u3} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u1, u2, u3} K L L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3))) _inst_4 _inst_5 e) E))))) (IntermediateField.algebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 E) (IntermediateField.algebra.{u1, u3} K L' _inst_1 _inst_3 _inst_5 (IntermediateField.map.{u1, u2, u3} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u1, u2, u3} K L L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3))) _inst_4 _inst_5 e) E))
+but is expected to have type
+  forall {K : Type.{u1}} {L : Type.{u2}} {L' : Type.{u3}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_3 : Field.{u3} L'] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))] [_inst_5 : Algebra.{u1, u3} K L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3)))] (e : AlgEquiv.{u1, u2, u3} K L L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))) _inst_4 _inst_5) (E : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4), AlgEquiv.{u1, u2, u3} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x E)) (Subtype.{succ u3} L' (fun (x : L') => Membership.mem.{u3, u3} L' (IntermediateField.{u1, u3} K L' _inst_1 _inst_3 _inst_5) (SetLike.instMembership.{u3, u3} (IntermediateField.{u1, u3} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.instSetLikeIntermediateField.{u1, u3} K L' _inst_1 _inst_3 _inst_5)) x (IntermediateField.map.{u1, u2, u3} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u1, u2, u3} K L L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))) _inst_4 _inst_5 e) E))) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 E)) (Subalgebra.toSemiring.{u1, u3} K L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))) _inst_5 (IntermediateField.toSubalgebra.{u1, u3} K L' _inst_1 _inst_3 _inst_5 (IntermediateField.map.{u1, u2, u3} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u1, u2, u3} K L L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))) _inst_4 _inst_5 e) E))) (IntermediateField.algebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 E) (IntermediateField.algebra.{u1, u3} K L' _inst_1 _inst_3 _inst_5 (IntermediateField.map.{u1, u2, u3} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u1, u2, u3} K L L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))) _inst_4 _inst_5 e) E))
+Case conversion may be inaccurate. Consider using '#align intermediate_field.intermediate_field_map IntermediateField.intermediateFieldMapₓ'. -/
 /-- Given an equivalence `e : L ≃ₐ[K] L'` of `K`-field extensions and an intermediate
 field `E` of `L/K`, `intermediate_field_equiv_map e E` is the induced equivalence
 between `E` and `E.map e` -/
@@ -441,6 +801,12 @@ def intermediateFieldMap (e : L ≃ₐ[K] L') (E : IntermediateField K L) : E 
   e.subalgebraMap E.toSubalgebra
 #align intermediate_field.intermediate_field_map IntermediateField.intermediateFieldMap
 
+/- warning: intermediate_field.intermediate_field_map_apply_coe -> IntermediateField.intermediateFieldMap_apply_coe is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {L : Type.{u2}} {L' : Type.{u3}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_3 : Field.{u3} L'] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] [_inst_5 : Algebra.{u1, u3} K L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3)))] (e : AlgEquiv.{u1, u2, u3} K L L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3))) _inst_4 _inst_5) (E : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (a : coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) E), Eq.{succ u3} L' ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (coeSort.{succ u3, succ (succ u3)} (IntermediateField.{u1, u3} K L' _inst_1 _inst_3 _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (IntermediateField.{u1, u3} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.setLike.{u1, u3} K L' _inst_1 _inst_3 _inst_5)) (IntermediateField.map.{u1, u2, u3} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u1, u2, u3} K L L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3))) _inst_4 _inst_5 e) E)) L' (HasLiftT.mk.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (IntermediateField.{u1, u3} K L' _inst_1 _inst_3 _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (IntermediateField.{u1, u3} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.setLike.{u1, u3} K L' _inst_1 _inst_3 _inst_5)) (IntermediateField.map.{u1, u2, u3} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u1, u2, u3} K L L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3))) _inst_4 _inst_5 e) E)) L' (CoeTCₓ.coe.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (IntermediateField.{u1, u3} K L' _inst_1 _inst_3 _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (IntermediateField.{u1, u3} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.setLike.{u1, u3} K L' _inst_1 _inst_3 _inst_5)) (IntermediateField.map.{u1, u2, u3} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u1, u2, u3} K L L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3))) _inst_4 _inst_5 e) E)) L' (coeBase.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (IntermediateField.{u1, u3} K L' _inst_1 _inst_3 _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (IntermediateField.{u1, u3} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.setLike.{u1, u3} K L' _inst_1 _inst_3 _inst_5)) (IntermediateField.map.{u1, u2, u3} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u1, u2, u3} K L L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3))) _inst_4 _inst_5 e) E)) L' (coeSubtype.{succ u3} L' (fun (x : L') => Membership.Mem.{u3, u3} L' (IntermediateField.{u1, u3} K L' _inst_1 _inst_3 _inst_5) (SetLike.hasMem.{u3, u3} (IntermediateField.{u1, u3} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.setLike.{u1, u3} K L' _inst_1 _inst_3 _inst_5)) x (IntermediateField.map.{u1, u2, u3} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u1, u2, u3} K L L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3))) _inst_4 _inst_5 e) E)))))) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgEquiv.{u1, u2, u3} K (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) E) (coeSort.{succ u3, succ (succ u3)} (IntermediateField.{u1, u3} K L' _inst_1 _inst_3 _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (IntermediateField.{u1, u3} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.setLike.{u1, u3} K L' _inst_1 _inst_3 _inst_5)) (IntermediateField.map.{u1, u2, u3} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u1, u2, u3} K L L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3))) _inst_4 _inst_5 e) E)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) E) (DivisionRing.toRing.{u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) E) (Field.toDivisionRing.{u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) E) (IntermediateField.toField.{u1, u2} K L _inst_1 _inst_2 _inst_4 E)))) (Ring.toSemiring.{u3} (coeSort.{succ u3, succ (succ u3)} (IntermediateField.{u1, u3} K L' _inst_1 _inst_3 _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (IntermediateField.{u1, u3} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.setLike.{u1, u3} K L' _inst_1 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+but is expected to have type
+  forall {K : Type.{u3}} {L : Type.{u2}} {L' : Type.{u1}} [_inst_1 : Field.{u3} K] [_inst_2 : Field.{u2} L] [_inst_3 : Field.{u1} L'] [_inst_4 : Algebra.{u3, u2} K L (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))] [_inst_5 : Algebra.{u3, u1} K L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3)))] (e : AlgEquiv.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5) (E : IntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) (a : Subtype.{succ u2} L (fun (x 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_inst_5 e) E))) (AddCommMonoid.toAddMonoid.{u1} (Subtype.{succ u1} L' (fun (x : L') => Membership.mem.{u1, u1} L' (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) (SetLike.instMembership.{u1, u1} (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.instSetLikeIntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5)) x (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Subtype.{succ u1} L' (fun (x : L') => Membership.mem.{u1, u1} L' (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) (SetLike.instMembership.{u1, u1} 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_inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} L' (fun (x : L') => Membership.mem.{u1, u1} L' (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) (SetLike.instMembership.{u1, u1} (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.instSetLikeIntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5)) x (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))) (Subalgebra.toSemiring.{u3, u1} K L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_5 (IntermediateField.toSubalgebra.{u3, u1} K L' _inst_1 _inst_3 _inst_5 (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E)))))))) (DistribSMul.toSMulZeroClass.{u3, u1} K (Subtype.{succ u1} L' (fun (x : L') => 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(Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Subtype.{succ u1} L' (fun (x : L') => Membership.mem.{u1, u1} L' (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) (SetLike.instMembership.{u1, u1} (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.instSetLikeIntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5)) x (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Subtype.{succ u1} L' (fun (x : L') => Membership.mem.{u1, u1} L' (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) (SetLike.instMembership.{u1, u1} (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.instSetLikeIntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5)) x (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} L' (fun (x : L') => Membership.mem.{u1, u1} L' (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) (SetLike.instMembership.{u1, u1} (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.instSetLikeIntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5)) x (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))) (Subalgebra.toSemiring.{u3, u1} K L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_5 (IntermediateField.toSubalgebra.{u3, u1} K L' _inst_1 _inst_3 _inst_5 (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E)))))))) (DistribMulAction.toDistribSMul.{u3, u1} K (Subtype.{succ u1} L' (fun (x : L') => Membership.mem.{u1, u1} L' (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) (SetLike.instMembership.{u1, u1} (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.instSetLikeIntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5)) x (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))) (MonoidWithZero.toMonoid.{u3} K (Semiring.toMonoidWithZero.{u3} K (CommSemiring.toSemiring.{u3} K (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} (Subtype.{succ u1} L' (fun (x : L') => Membership.mem.{u1, u1} L' (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) (SetLike.instMembership.{u1, u1} (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.instSetLikeIntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5)) x (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Subtype.{succ u1} L' (fun (x : L') => Membership.mem.{u1, u1} L' (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) (SetLike.instMembership.{u1, u1} (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.instSetLikeIntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5)) x (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Subtype.{succ u1} L' (fun (x : L') => Membership.mem.{u1, u1} L' (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) (SetLike.instMembership.{u1, u1} (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.instSetLikeIntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5)) x (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} L' (fun (x : L') => Membership.mem.{u1, u1} L' (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) (SetLike.instMembership.{u1, u1} 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_inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))) (IntermediateField.algebra.{u3, u1} K L' _inst_1 _inst_3 _inst_5 (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E)))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u3, u2, u1} (AlgEquiv.{u3, u2, u1} K (Subtype.{succ u2} L (fun (x : L) 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_inst_5 e) E))) (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (Subalgebra.toSemiring.{u3, u2} K L (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u3, u2} K L _inst_1 _inst_2 _inst_4 E)) (Subalgebra.toSemiring.{u3, u1} K L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_5 (IntermediateField.toSubalgebra.{u3, u1} K L' _inst_1 _inst_3 _inst_5 (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))) (IntermediateField.algebra.{u3, u2} K L _inst_1 _inst_2 _inst_4 E) (IntermediateField.algebra.{u3, u1} K L' _inst_1 _inst_3 _inst_5 (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))) K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4)) x E)) (Subtype.{succ u1} L' (fun (x : L') => Membership.mem.{u1, u1} L' (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) (SetLike.instMembership.{u1, u1} (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.instSetLikeIntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5)) x (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))) (MonoidWithZero.toMonoid.{u3} K (Semiring.toMonoidWithZero.{u3} K (CommSemiring.toSemiring.{u3} K (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ 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(DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))))))) (Module.toDistribMulAction.{u3, u2} K L (CommSemiring.toSemiring.{u3} K (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (Algebra.toModule.{u3, u2} K L (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4)) (Module.toDistribMulAction.{u3, u1} K L' (CommSemiring.toSemiring.{u3} K (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L' (Semiring.toNonAssocSemiring.{u1} L' (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3)))))) (Algebra.toModule.{u3, u1} K L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_5)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u3, u2, u1} (AlgEquiv.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5) K L L' (MonoidWithZero.toMonoid.{u3} K (Semiring.toMonoidWithZero.{u3} K (CommSemiring.toSemiring.{u3} K (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L' (Semiring.toNonAssocSemiring.{u1} L' (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))))) (Module.toDistribMulAction.{u3, u2} K L (CommSemiring.toSemiring.{u3} K (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (Algebra.toModule.{u3, u2} K L (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4)) (Module.toDistribMulAction.{u3, u1} K L' (CommSemiring.toSemiring.{u3} K (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L' (Semiring.toNonAssocSemiring.{u1} L' (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3)))))) (Algebra.toModule.{u3, u1} K L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, u2, u1, max u2 u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 (AlgEquiv.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5) (AlgEquivClass.toAlgHomClass.{max u2 u1, u3, u2, u1} (AlgEquiv.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5) K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 (AlgEquiv.instAlgEquivClassAlgEquiv.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5)))))) e (Subtype.val.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (Set.{u2} L) (Set.instMembershipSet.{u2} L) x (SetLike.coe.{u2, u2} (IntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) E)) a))
+Case conversion may be inaccurate. Consider using '#align intermediate_field.intermediate_field_map_apply_coe IntermediateField.intermediateFieldMap_apply_coeₓ'. -/
 /- We manually add these two simp lemmas because `@[simps]` before `intermediate_field_map`
   led to a timeout. -/
 @[simp]
@@ -449,6 +815,12 @@ theorem intermediateFieldMap_apply_coe (e : L ≃ₐ[K] L') (E : IntermediateFie
   rfl
 #align intermediate_field.intermediate_field_map_apply_coe IntermediateField.intermediateFieldMap_apply_coe
 
+/- warning: intermediate_field.intermediate_field_map_symm_apply_coe -> IntermediateField.intermediateFieldMap_symm_apply_coe is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {L : Type.{u2}} {L' : Type.{u3}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_3 : Field.{u3} L'] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] [_inst_5 : Algebra.{u1, u3} K L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3)))] (e : AlgEquiv.{u1, u2, u3} K L L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3))) _inst_4 _inst_5) (E : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (a : coeSort.{succ u3, succ (succ u3)} (IntermediateField.{u1, u3} K L' _inst_1 _inst_3 _inst_5) 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(Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_5 _inst_4) => L' -> L) (AlgEquiv.hasCoeToFun.{u1, u3, u2} K L' L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3))) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_5 _inst_4) (AlgEquiv.symm.{u1, u2, u3} K L L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3))) _inst_4 _inst_5 e) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (coeSort.{succ u3, succ (succ u3)} (IntermediateField.{u1, u3} K L' _inst_1 _inst_3 _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (IntermediateField.{u1, u3} K 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+but is expected to have type
+  forall {K : Type.{u3}} {L : Type.{u2}} {L' : Type.{u1}} [_inst_1 : Field.{u3} K] [_inst_2 : Field.{u2} L] [_inst_3 : Field.{u1} L'] [_inst_4 : Algebra.{u3, u2} K L (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))] [_inst_5 : Algebra.{u3, u1} K L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3)))] (e : AlgEquiv.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5) (E : IntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) (a : Subtype.{succ u1} L' (fun (x : L') => Membership.mem.{u1, u1} L' (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) (SetLike.instMembership.{u1, u1} (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.instSetLikeIntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5)) x (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : L') => L) (Subtype.val.{succ u1} L' (fun (x : L') => Membership.mem.{u1, u1} L' (Set.{u1} L') (Set.instMembershipSet.{u1} L') x (SetLike.coe.{u1, u1} (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) L' 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_inst_4 _inst_5 e) E))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Subtype.{succ u1} L' (fun (x : L') => Membership.mem.{u1, u1} L' (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) (SetLike.instMembership.{u1, u1} (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.instSetLikeIntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5)) x (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Subtype.{succ u1} L' (fun (x : L') => Membership.mem.{u1, u1} L' (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) 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_inst_5 e) E)) (IntermediateField.algebra.{u3, u2} K L _inst_1 _inst_2 _inst_4 E)) K (Subtype.{succ u1} L' (fun (x : L') => Membership.mem.{u1, u1} L' (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) (SetLike.instMembership.{u1, u1} (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.instSetLikeIntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5)) x (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))) (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u3, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} 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L' (Field.toSemifield.{u1} L' _inst_3)))))))) (DistribMulAction.toDistribSMul.{u3, u1} K L' (MonoidWithZero.toMonoid.{u3} K (Semiring.toMonoidWithZero.{u3} K (CommSemiring.toSemiring.{u3} K (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} L' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L' (Semiring.toNonAssocSemiring.{u1} L' (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))))))) (Module.toDistribMulAction.{u3, u1} K L' (CommSemiring.toSemiring.{u3} K (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L' (Semiring.toNonAssocSemiring.{u1} L' (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3)))))) (Algebra.toModule.{u3, u1} K L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_5))))) (SMulZeroClass.toSMul.{u3, u2} K L (AddMonoid.toZero.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))))) (DistribSMul.toSMulZeroClass.{u3, u2} K L (AddMonoid.toAddZeroClass.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))))) (DistribMulAction.toDistribSMul.{u3, u2} K L (MonoidWithZero.toMonoid.{u3} K (Semiring.toMonoidWithZero.{u3} K (CommSemiring.toSemiring.{u3} K (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))))) (Module.toDistribMulAction.{u3, u2} K L (CommSemiring.toSemiring.{u3} K (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (Algebra.toModule.{u3, u2} K L (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u3, u1, u2} (AlgEquiv.{u3, u1, u2} K L' L (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_5 _inst_4) K L' L (MonoidWithZero.toMonoid.{u3} K (Semiring.toMonoidWithZero.{u3} K (CommSemiring.toSemiring.{u3} K (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} L' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L' (Semiring.toNonAssocSemiring.{u1} L' (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))))))) (AddCommMonoid.toAddMonoid.{u2} L 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(Field.toSemifield.{u3} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (Algebra.toModule.{u3, u2} K L (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u3, u1, u2} (AlgEquiv.{u3, u1, u2} K L' L (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_5 _inst_4) K L' L (MonoidWithZero.toMonoid.{u3} K (Semiring.toMonoidWithZero.{u3} K (CommSemiring.toSemiring.{u3} K (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L' (Semiring.toNonAssocSemiring.{u1} L' (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (Module.toDistribMulAction.{u3, u1} K L' (CommSemiring.toSemiring.{u3} K (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L' (Semiring.toNonAssocSemiring.{u1} L' (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3)))))) (Algebra.toModule.{u3, u1} K L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} 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max u2 u1} K L' L (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_5 _inst_4 (AlgEquiv.{u3, u1, u2} K L' L (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_5 _inst_4) (AlgEquivClass.toAlgHomClass.{max u2 u1, u3, u1, u2} (AlgEquiv.{u3, u1, u2} K L' L (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_5 _inst_4) K L' L (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_5 _inst_4 (AlgEquiv.instAlgEquivClassAlgEquiv.{u3, u1, u2} K L' L (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_5 _inst_4)))))) (AlgEquiv.symm.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) (Subtype.val.{succ u1} L' (fun (x : L') => Membership.mem.{u1, u1} L' (Set.{u1} L') (Set.instMembershipSet.{u1} L') x (SetLike.coe.{u1, u1} (IntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.instSetLikeIntermediateField.{u3, u1} K L' _inst_1 _inst_3 _inst_5) (IntermediateField.map.{u3, u2, u1} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (AlgEquiv.toAlgHom.{u3, u2, u1} K L L' (Semifield.toCommSemiring.{u3} K (Field.toSemifield.{u3} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (DivisionSemiring.toSemiring.{u1} L' (Semifield.toDivisionSemiring.{u1} L' (Field.toSemifield.{u1} L' _inst_3))) _inst_4 _inst_5 e) E))) a))
+Case conversion may be inaccurate. Consider using '#align intermediate_field.intermediate_field_map_symm_apply_coe IntermediateField.intermediateFieldMap_symm_apply_coeₓ'. -/
 @[simp]
 theorem intermediateFieldMap_symm_apply_coe (e : L ≃ₐ[K] L') (E : IntermediateField K L)
     (a : E.map e.toAlgHom) : ↑((intermediateFieldMap e E).symm a) = e.symm a :=
@@ -461,17 +833,31 @@ namespace AlgHom
 
 variable (f : L →ₐ[K] L')
 
+#print AlgHom.fieldRange /-
 /-- The range of an algebra homomorphism, as an intermediate field. -/
 @[simps toSubalgebra]
 def fieldRange : IntermediateField K L' :=
   { f.range, (f : L →+* L').fieldRange with }
 #align alg_hom.field_range AlgHom.fieldRange
+-/
 
+/- warning: alg_hom.coe_field_range -> AlgHom.coe_fieldRange is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {L : Type.{u2}} {L' : Type.{u3}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_3 : Field.{u3} L'] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] [_inst_5 : Algebra.{u1, u3} K L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3)))] (f : AlgHom.{u1, u2, u3} K L L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3))) _inst_4 _inst_5), Eq.{succ u3} (Set.{u3} L') ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (IntermediateField.{u1, u3} K L' _inst_1 _inst_3 _inst_5) (Set.{u3} L') (HasLiftT.mk.{succ u3, succ u3} (IntermediateField.{u1, u3} K L' _inst_1 _inst_3 _inst_5) (Set.{u3} L') (CoeTCₓ.coe.{succ u3, succ u3} (IntermediateField.{u1, u3} K L' _inst_1 _inst_3 _inst_5) (Set.{u3} L') (SetLike.Set.hasCoeT.{u3, u3} (IntermediateField.{u1, u3} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.setLike.{u1, u3} K L' _inst_1 _inst_3 _inst_5)))) (AlgHom.fieldRange.{u1, u2, u3} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 f)) (Set.range.{u3, succ u2} L' L (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} K L L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3))) _inst_4 _inst_5) (fun (_x : AlgHom.{u1, u2, u3} K L L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3))) _inst_4 _inst_5) => L -> L') ([anonymous].{u1, u2, u3} K L L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3))) _inst_4 _inst_5) f))
+but is expected to have type
+  forall {K : Type.{u2}} {L : Type.{u1}} {L' : Type.{u3}} [_inst_1 : Field.{u2} K] [_inst_2 : Field.{u1} L] [_inst_3 : Field.{u3} L'] [_inst_4 : Algebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))] [_inst_5 : Algebra.{u2, u3} K L' (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3)))] (f : AlgHom.{u2, u1, u3} K L L' (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))) _inst_4 _inst_5), Eq.{succ u3} (Set.{u3} L') (SetLike.coe.{u3, u3} (IntermediateField.{u2, u3} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.instSetLikeIntermediateField.{u2, u3} K L' _inst_1 _inst_3 _inst_5) (AlgHom.fieldRange.{u2, u1, u3} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 f)) (Set.range.{u3, succ u1} L' L (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (AlgHom.{u2, u1, u3} K L L' (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))) _inst_4 _inst_5) L (fun (_x : L) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : L) => L') _x) (SMulHomClass.toFunLike.{max u1 u3, u2, u1, u3} (AlgHom.{u2, u1, u3} K L L' (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))) _inst_4 _inst_5) K L L' (SMulZeroClass.toSMul.{u2, u1} K L (AddMonoid.toZero.{u1} L (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))))) (DistribSMul.toSMulZeroClass.{u2, u1} K L (AddMonoid.toAddZeroClass.{u1} L (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))))) (DistribMulAction.toDistribSMul.{u2, u1} K L (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))))))) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4))))) (SMulZeroClass.toSMul.{u2, u3} K L' (AddMonoid.toZero.{u3} L' (AddCommMonoid.toAddMonoid.{u3} L' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} L' (Semiring.toNonAssocSemiring.{u3} L' (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3)))))))) (DistribSMul.toSMulZeroClass.{u2, u3} K L' (AddMonoid.toAddZeroClass.{u3} L' (AddCommMonoid.toAddMonoid.{u3} L' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} L' (Semiring.toNonAssocSemiring.{u3} L' (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3)))))))) (DistribMulAction.toDistribSMul.{u2, u3} K L' (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u3} L' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} L' (Semiring.toNonAssocSemiring.{u3} L' (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))))))) (Module.toDistribMulAction.{u2, u3} K L' (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} L' (Semiring.toNonAssocSemiring.{u3} L' (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3)))))) (Algebra.toModule.{u2, u3} K L' (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))) _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u3, u2, u1, u3} (AlgHom.{u2, u1, u3} K L L' (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))) _inst_4 _inst_5) K L L' (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))))))) (AddCommMonoid.toAddMonoid.{u3} L' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} L' (Semiring.toNonAssocSemiring.{u3} L' (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))))))) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4)) (Module.toDistribMulAction.{u2, u3} K L' (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} L' (Semiring.toNonAssocSemiring.{u3} L' (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3)))))) (Algebra.toModule.{u2, u3} K L' (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))) _inst_5)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u3, u2, u1, u3} (AlgHom.{u2, u1, u3} K L L' (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))) _inst_4 _inst_5) K L L' (MonoidWithZero.toMonoid.{u2} K (Semiring.toMonoidWithZero.{u2} K (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} L' (Semiring.toNonAssocSemiring.{u3} L' (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))))) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4)) (Module.toDistribMulAction.{u2, u3} K L' (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} L' (Semiring.toNonAssocSemiring.{u3} L' (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3)))))) (Algebra.toModule.{u2, u3} K L' (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))) _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u1, u3, max u1 u3} K L L' (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))) _inst_4 _inst_5 (AlgHom.{u2, u1, u3} K L L' (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))) _inst_4 _inst_5) (AlgHom.algHomClass.{u2, u1, u3} K L L' (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))) _inst_4 _inst_5))))) f))
+Case conversion may be inaccurate. Consider using '#align alg_hom.coe_field_range AlgHom.coe_fieldRangeₓ'. -/
 @[simp]
 theorem coe_fieldRange : ↑f.fieldRange = Set.range f :=
   rfl
 #align alg_hom.coe_field_range AlgHom.coe_fieldRange
 
+/- warning: alg_hom.field_range_to_subfield -> AlgHom.fieldRange_toSubfield is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {L : Type.{u2}} {L' : Type.{u3}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_3 : Field.{u3} L'] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] [_inst_5 : Algebra.{u1, u3} K L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3)))] (f : AlgHom.{u1, u2, u3} K L L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3))) _inst_4 _inst_5), Eq.{succ u3} (Subfield.{u3} L' _inst_3) (IntermediateField.toSubfield.{u1, u3} K L' _inst_1 _inst_3 _inst_5 (AlgHom.fieldRange.{u1, u2, u3} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 f)) (RingHom.fieldRange.{u2, u3} L L' _inst_2 _inst_3 ((fun (a : Sort.{max (succ u2) (succ u3)}) (b : Sort.{max (succ u2) (succ u3)}) [self : HasLiftT.{max (succ u2) (succ u3), max (succ u2) (succ u3)} a b] => self.0) (AlgHom.{u1, u2, u3} K L L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3))) _inst_4 _inst_5) (RingHom.{u2, u3} L L' (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (NonAssocRing.toNonAssocSemiring.{u3} L' (Ring.toNonAssocRing.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3))))) (HasLiftT.mk.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} K L L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3))) _inst_4 _inst_5) (RingHom.{u2, u3} L L' (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (NonAssocRing.toNonAssocSemiring.{u3} L' (Ring.toNonAssocRing.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3))))) (CoeTCₓ.coe.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} K L L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3))) _inst_4 _inst_5) (RingHom.{u2, u3} L L' (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (NonAssocRing.toNonAssocSemiring.{u3} L' (Ring.toNonAssocRing.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3))))) (RingHom.hasCoeT.{max u2 u3, u2, u3} (AlgHom.{u1, u2, u3} K L L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3))) _inst_4 _inst_5) L L' (NonAssocRing.toNonAssocSemiring.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))) (NonAssocRing.toNonAssocSemiring.{u3} L' (Ring.toNonAssocRing.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3)))) (AlgHomClass.toRingHomClass.{max u2 u3, u1, u2, u3} (AlgHom.{u1, u2, u3} K L L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3))) _inst_4 _inst_5) K L L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3))) _inst_4 _inst_5 (AlgHom.algHomClass.{u1, u2, u3} K L L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3))) _inst_4 _inst_5))))) f))
+but is expected to have type
+  forall {K : Type.{u2}} {L : Type.{u1}} {L' : Type.{u3}} [_inst_1 : Field.{u2} K] [_inst_2 : Field.{u1} L] [_inst_3 : Field.{u3} L'] [_inst_4 : Algebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))] [_inst_5 : Algebra.{u2, u3} K L' (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3)))] (f : AlgHom.{u2, u1, u3} K L L' (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))) _inst_4 _inst_5), Eq.{succ u3} (Subfield.{u3} L' _inst_3) (IntermediateField.toSubfield.{u2, u3} K L' _inst_1 _inst_3 _inst_5 (AlgHom.fieldRange.{u2, u1, u3} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 f)) (RingHom.fieldRange.{u1, u3} L L' _inst_2 _inst_3 (RingHomClass.toRingHom.{max u1 u3, u1, u3} (AlgHom.{u2, u1, u3} K L L' (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))) _inst_4 _inst_5) L L' (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))) (Semiring.toNonAssocSemiring.{u3} L' (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3)))) (AlgHomClass.toRingHomClass.{max u1 u3, u2, u1, u3} (AlgHom.{u2, u1, u3} K L L' (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))) _inst_4 _inst_5) K L L' (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))) _inst_4 _inst_5 (AlgHom.algHomClass.{u2, u1, u3} K L L' (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))) _inst_4 _inst_5)) f))
+Case conversion may be inaccurate. Consider using '#align alg_hom.field_range_to_subfield AlgHom.fieldRange_toSubfieldₓ'. -/
 @[simp]
 theorem fieldRange_toSubfield : f.fieldRange.toSubfield = (f : L →+* L').fieldRange :=
   rfl
@@ -479,6 +865,12 @@ theorem fieldRange_toSubfield : f.fieldRange.toSubfield = (f : L →+* L').field
 
 variable {f}
 
+/- warning: alg_hom.mem_field_range -> AlgHom.mem_fieldRange is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {L : Type.{u2}} {L' : Type.{u3}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_3 : Field.{u3} L'] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] [_inst_5 : Algebra.{u1, u3} K L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3)))] {f : AlgHom.{u1, u2, u3} K L L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3))) _inst_4 _inst_5} {y : L'}, Iff (Membership.Mem.{u3, u3} L' (IntermediateField.{u1, u3} K L' _inst_1 _inst_3 _inst_5) (SetLike.hasMem.{u3, u3} (IntermediateField.{u1, u3} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.setLike.{u1, u3} K L' _inst_1 _inst_3 _inst_5)) y (AlgHom.fieldRange.{u1, u2, u3} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 f)) (Exists.{succ u2} L (fun (x : L) => Eq.{succ u3} L' (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} K L L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3))) _inst_4 _inst_5) (fun (_x : AlgHom.{u1, u2, u3} K L L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3))) _inst_4 _inst_5) => L -> L') ([anonymous].{u1, u2, u3} K L L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3))) _inst_4 _inst_5) f x) y))
+but is expected to have type
+  forall {K : Type.{u2}} {L : Type.{u1}} {L' : Type.{u3}} [_inst_1 : Field.{u2} K] [_inst_2 : Field.{u1} L] [_inst_3 : Field.{u3} L'] [_inst_4 : Algebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))] [_inst_5 : Algebra.{u2, u3} K L' (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3)))] {f : AlgHom.{u2, u1, u3} K L L' (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))) _inst_4 _inst_5} {y : L'}, Iff (Membership.mem.{u3, u3} L' (IntermediateField.{u2, u3} K L' _inst_1 _inst_3 _inst_5) (SetLike.instMembership.{u3, u3} (IntermediateField.{u2, u3} K L' _inst_1 _inst_3 _inst_5) L' (IntermediateField.instSetLikeIntermediateField.{u2, u3} K L' _inst_1 _inst_3 _inst_5)) y (AlgHom.fieldRange.{u2, u1, u3} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 f)) (Exists.{succ u1} L (fun (x : L) => Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : L) => L') x) (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (AlgHom.{u2, u1, u3} K L L' (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))) _inst_4 _inst_5) L (fun (_x : L) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : L) => L') _x) (SMulHomClass.toFunLike.{max u1 u3, u2, u1, u3} (AlgHom.{u2, u1, u3} K L L' (Semifield.toCommSemiring.{u2} K 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(Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} L' (Semiring.toNonAssocSemiring.{u3} L' (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))))) (Module.toDistribMulAction.{u2, u1} K L (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))) (Algebra.toModule.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4)) (Module.toDistribMulAction.{u2, u3} K L' (CommSemiring.toSemiring.{u2} K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} L' (Semiring.toNonAssocSemiring.{u3} L' (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3)))))) (Algebra.toModule.{u2, u3} K L' (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))) _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u1, u3, max u1 u3} K L L' (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))) _inst_4 _inst_5 (AlgHom.{u2, u1, u3} K L L' (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))) _inst_4 _inst_5) (AlgHom.algHomClass.{u2, u1, u3} K L L' (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))) _inst_4 _inst_5))))) f x) y))
+Case conversion may be inaccurate. Consider using '#align alg_hom.mem_field_range AlgHom.mem_fieldRangeₓ'. -/
 @[simp]
 theorem mem_fieldRange {y : L'} : y ∈ f.fieldRange ↔ ∃ x, f x = y :=
   Iff.rfl
@@ -488,34 +880,76 @@ end AlgHom
 
 namespace IntermediateField
 
+/- warning: intermediate_field.val -> IntermediateField.val is a dubious translation:
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+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] (S : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4), AlgHom.{u1, u2, u2} K (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) S) L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) S) (DivisionRing.toRing.{u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) S) (Field.toDivisionRing.{u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) S) (IntermediateField.toField.{u1, u2} K L _inst_1 _inst_2 _inst_4 S)))) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (IntermediateField.algebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S) _inst_4
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align intermediate_field.val IntermediateField.valₓ'. -/
 /-- The embedding from an intermediate field of `L / K` to `L`. -/
 def val : S →ₐ[K] L :=
   S.toSubalgebra.val
 #align intermediate_field.val IntermediateField.val
 
+/- warning: intermediate_field.coe_val -> IntermediateField.coe_val is a dubious translation:
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+but is expected to have type
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))] (S : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4), Eq.{succ u2} (forall (ᾰ : Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)), (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L 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(IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (IntermediateField.algebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S) _inst_4) K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) L (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (Algebra.toModule.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u2, u1, u2, u2} (AlgHom.{u1, u2, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (IntermediateField.algebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S) _inst_4) K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) L (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K 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(Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (Module.toDistribMulAction.{u1, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L 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+Case conversion may be inaccurate. Consider using '#align intermediate_field.coe_val IntermediateField.coe_valₓ'. -/
 @[simp]
 theorem coe_val : ⇑S.val = coe :=
   rfl
 #align intermediate_field.coe_val IntermediateField.coe_val
 
+/- warning: intermediate_field.val_mk -> IntermediateField.val_mk is a dubious translation:
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(IntermediateField.algebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S)))))) (SMulZeroClass.toSMul.{u1, u2} K L (AddMonoid.toZero.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))))) (DistribSMul.toSMulZeroClass.{u1, u2} K L (AddMonoid.toAddZeroClass.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))))) (DistribMulAction.toDistribSMul.{u1, u2} K L (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) 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_inst_4)) x S)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S)))))) (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))))) (Module.toDistribMulAction.{u1, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S))))) (Algebra.toModule.{u1, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S)) (IntermediateField.algebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S))) (Module.toDistribMulAction.{u1, u2} K L (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K 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+Case conversion may be inaccurate. Consider using '#align intermediate_field.val_mk IntermediateField.val_mkₓ'. -/
 @[simp]
 theorem val_mk {x : L} (hx : x ∈ S) : S.val ⟨x, hx⟩ = x :=
   rfl
 #align intermediate_field.val_mk IntermediateField.val_mk
 
+/- warning: intermediate_field.range_val -> IntermediateField.range_val is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align intermediate_field.range_val IntermediateField.range_valₓ'. -/
 theorem range_val : S.val.range = S.toSubalgebra :=
   S.toSubalgebra.range_val
 #align intermediate_field.range_val IntermediateField.range_val
 
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+Case conversion may be inaccurate. Consider using '#align intermediate_field.field_range_val IntermediateField.fieldRange_valₓ'. -/
 @[simp]
 theorem fieldRange_val : S.val.fieldRange = S :=
   SetLike.ext' Subtype.range_val
 #align intermediate_field.field_range_val IntermediateField.fieldRange_val
 
+/- warning: intermediate_field.alg_hom.inhabited -> IntermediateField.AlgHom.inhabited is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] (S : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4), Inhabited.{succ u2} (AlgHom.{u1, u2, u2} K (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) S) L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) S) (DivisionRing.toRing.{u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) S) (Field.toDivisionRing.{u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) S) (IntermediateField.toField.{u1, u2} K L _inst_1 _inst_2 _inst_4 S)))) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (IntermediateField.algebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S) _inst_4)
+but is expected to have type
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))] (S : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4), Inhabited.{succ u2} (AlgHom.{u1, u2, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)) L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) (IntermediateField.algebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S) _inst_4)
+Case conversion may be inaccurate. Consider using '#align intermediate_field.alg_hom.inhabited IntermediateField.AlgHom.inhabitedₓ'. -/
 instance AlgHom.inhabited : Inhabited (S →ₐ[K] L) :=
   ⟨S.val⟩
 #align intermediate_field.alg_hom.inhabited IntermediateField.AlgHom.inhabited
 
+/- warning: intermediate_field.aeval_coe -> IntermediateField.aeval_coe is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] (S : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) {R : Type.{u3}} [_inst_6 : CommRing.{u3} R] [_inst_7 : Algebra.{u3, u1} R K (CommRing.toCommSemiring.{u3} R _inst_6) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))] [_inst_8 : Algebra.{u3, u2} R L (CommRing.toCommSemiring.{u3} R _inst_6) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] [_inst_9 : IsScalarTower.{u3, u1, u2} R K L (SMulZeroClass.toHasSmul.{u3, u1} R K (AddZeroClass.toHasZero.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K 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+but is expected to have type
+  forall {K : Type.{u2}} {L : Type.{u1}} [_inst_1 : Field.{u2} K] [_inst_2 : Field.{u1} L] [_inst_4 : Algebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))] (S : IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) {R : Type.{u3}} [_inst_6 : CommRing.{u3} R] [_inst_7 : Algebra.{u3, u2} R K (CommRing.toCommSemiring.{u3} R _inst_6) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))] [_inst_8 : Algebra.{u3, u1} R L (CommRing.toCommSemiring.{u3} R _inst_6) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))] [_inst_9 : IsScalarTower.{u3, u2, u1} R K L (Algebra.toSMul.{u3, u2} R K (CommRing.toCommSemiring.{u3} R _inst_6) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) _inst_7) (Algebra.toSMul.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (Algebra.toSMul.{u3, u1} R L (CommRing.toCommSemiring.{u3} R _inst_6) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_8)] (x : Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x S)) (P : Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) => L) P) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (AlgHom.{u3, u3, u1} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) L (CommRing.toCommSemiring.{u3} R _inst_6) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (Polynomial.algebraOfAlgebra.{u3, u3} R R (CommRing.toCommSemiring.{u3} R _inst_6) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) _inst_8) (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (fun (_x : Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) => L) _x) (SMulHomClass.toFunLike.{max u1 u3, u3, u3, u1} (AlgHom.{u3, u3, u1} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) L (CommRing.toCommSemiring.{u3} R _inst_6) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (Polynomial.algebraOfAlgebra.{u3, u3} R R (CommRing.toCommSemiring.{u3} R _inst_6) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) _inst_8) R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) L (SMulZeroClass.toSMul.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (AddMonoid.toZero.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (AddCommMonoid.toAddMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6)))))))) (DistribSMul.toSMulZeroClass.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (AddCommMonoid.toAddMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6)))))))) (DistribMulAction.toDistribSMul.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6)))) (AddCommMonoid.toAddMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))))))) (Module.toDistribMulAction.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6)))))) (Algebra.toModule.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (CommRing.toCommSemiring.{u3} R _inst_6) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (Polynomial.algebraOfAlgebra.{u3, u3} R R (CommRing.toCommSemiring.{u3} R _inst_6) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6)))))))) (SMulZeroClass.toSMul.{u3, u1} R L (AddMonoid.toZero.{u1} L (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))))) (DistribSMul.toSMulZeroClass.{u3, u1} R L (AddMonoid.toAddZeroClass.{u1} L (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))))) (DistribMulAction.toDistribSMul.{u3, u1} R L (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6)))) (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))))))) (Module.toDistribMulAction.{u3, u1} R L (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))) (Algebra.toModule.{u3, u1} R L (CommRing.toCommSemiring.{u3} R _inst_6) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_8))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u3, u3, u3, u1} (AlgHom.{u3, u3, u1} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) L (CommRing.toCommSemiring.{u3} R _inst_6) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (Polynomial.algebraOfAlgebra.{u3, u3} R R (CommRing.toCommSemiring.{u3} R _inst_6) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) _inst_8) R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) L (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6)))) (AddCommMonoid.toAddMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))))))) (AddCommMonoid.toAddMonoid.{u1} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))))))) (Module.toDistribMulAction.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6)))))) (Algebra.toModule.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (CommRing.toCommSemiring.{u3} R _inst_6) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (Polynomial.algebraOfAlgebra.{u3, u3} R R (CommRing.toCommSemiring.{u3} R _inst_6) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))))) (Module.toDistribMulAction.{u3, u1} R L (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))))) (Algebra.toModule.{u3, u1} R L (CommRing.toCommSemiring.{u3} R _inst_6) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_8)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u3, u3, u3, u1} (AlgHom.{u3, u3, u1} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) L (CommRing.toCommSemiring.{u3} R _inst_6) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) (Polynomial.algebraOfAlgebra.{u3, u3} R R (CommRing.toCommSemiring.{u3} R _inst_6) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) _inst_8) R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) L (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} L (Semiring.toNonAssocSemiring.{u1} L (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))))) (Module.toDistribMulAction.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6)))))) (Algebra.toModule.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (CommRing.toCommSemiring.{u3} R _inst_6) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (Polynomial.algebraOfAlgebra.{u3, u3} R R (CommRing.toCommSemiring.{u3} R _inst_6) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))))) (Module.toDistribMulAction.{u3, u1} R L (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6)) 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K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 S)))))) (Module.toDistribMulAction.{u3, u1} R (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x S)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x S)) 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_inst_6)))) (AddCommMonoid.toAddMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))))))) (AddCommMonoid.toAddMonoid.{u1} (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x S)) 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(IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x S)) (Subalgebra.toSemiring.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 S)))))) (Module.toDistribMulAction.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} 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(IntermediateField.toSubalgebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 S)) (IntermediateField.algebra'.{u2, u1, u3} K L _inst_1 _inst_2 _inst_4 S R (CommRing.toCommSemiring.{u3} R _inst_6) (Algebra.toSMul.{u3, u2} R K (CommRing.toCommSemiring.{u3} R _inst_6) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) _inst_7) _inst_8 _inst_9))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u3, u3, u3, u1} (AlgHom.{u3, u3, u1} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x S)) (CommRing.toCommSemiring.{u3} R _inst_6) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R 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_inst_6))))) (Module.toDistribMulAction.{u3, u1} R (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x S)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x S)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} 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(AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, u3, u1, max u1 u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x S)) (CommRing.toCommSemiring.{u3} R _inst_6) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (Subalgebra.toSemiring.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L 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(Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) _inst_7) _inst_8 _inst_9)) (AlgHom.algHomClass.{u3, u3, u1} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x S)) (CommRing.toCommSemiring.{u3} R _inst_6) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (Subalgebra.toSemiring.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 S)) 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(Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 S)) (IntermediateField.algebra'.{u2, u1, u3} K L _inst_1 _inst_2 _inst_4 S R (CommRing.toCommSemiring.{u3} R _inst_6) (Algebra.toSMul.{u3, u2} R K (CommRing.toCommSemiring.{u3} R _inst_6) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) _inst_7) _inst_8 _inst_9) x) P))
+Case conversion may be inaccurate. Consider using '#align intermediate_field.aeval_coe IntermediateField.aeval_coeₓ'. -/
 theorem aeval_coe {R : Type _} [CommRing R] [Algebra R K] [Algebra R L] [IsScalarTower R K L]
     (x : S) (P : R[X]) : aeval (x : L) P = aeval x P :=
   by
@@ -526,6 +960,12 @@ theorem aeval_coe {R : Type _} [CommRing R] [Algebra R K] [Algebra R L] [IsScala
     rfl
 #align intermediate_field.aeval_coe IntermediateField.aeval_coe
 
+/- warning: intermediate_field.coe_is_integral_iff -> IntermediateField.coe_isIntegral_iff is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] (S : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) {R : Type.{u3}} [_inst_6 : CommRing.{u3} R] [_inst_7 : Algebra.{u3, u1} R K (CommRing.toCommSemiring.{u3} R _inst_6) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))] [_inst_8 : Algebra.{u3, u2} R L (CommRing.toCommSemiring.{u3} R _inst_6) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] [_inst_9 : IsScalarTower.{u3, u1, u2} R K L (SMulZeroClass.toHasSmul.{u3, u1} R K (AddZeroClass.toHasZero.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))))) (SMulWithZero.toSmulZeroClass.{u3, u1} R K (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6)))))) (AddZeroClass.toHasZero.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))))) (MulActionWithZero.toSMulWithZero.{u3, u1} R K (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (AddZeroClass.toHasZero.{u1} K 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(MulActionWithZero.toSMulWithZero.{u3, u2} R L (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (AddZeroClass.toHasZero.{u2} L (AddMonoid.toAddZeroClass.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))))) (Module.toMulActionWithZero.{u3, u2} R L (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) (Algebra.toModule.{u3, u2} R L (CommRing.toCommSemiring.{u3} R _inst_6) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_8)))))] {x : coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) S}, Iff (IsIntegral.{u3, u2} R L _inst_6 (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)) _inst_8 ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) S) L (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L 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(SMulZeroClass.toHasSmul.{u3, u1} R K (AddZeroClass.toHasZero.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))))) (SMulWithZero.toSmulZeroClass.{u3, u1} R K (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6)))))) (AddZeroClass.toHasZero.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))))) (MulActionWithZero.toSMulWithZero.{u3, u1} R K (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6))) (AddZeroClass.toHasZero.{u1} K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))))) (Module.toMulActionWithZero.{u3, u1} R K (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_6)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Algebra.toModule.{u3, u1} R K (CommRing.toCommSemiring.{u3} R _inst_6) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) _inst_7))))) _inst_8 _inst_9) x)
+but is expected to have type
+  forall {K : Type.{u2}} {L : Type.{u1}} [_inst_1 : Field.{u2} K] [_inst_2 : Field.{u1} L] [_inst_4 : Algebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))] (S : IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) {R : Type.{u3}} [_inst_6 : CommRing.{u3} R] [_inst_7 : Algebra.{u3, u2} R K (CommRing.toCommSemiring.{u3} R _inst_6) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))] [_inst_8 : Algebra.{u3, u1} R L (CommRing.toCommSemiring.{u3} R _inst_6) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))] [_inst_9 : IsScalarTower.{u3, u2, u1} R K L (Algebra.toSMul.{u3, u2} R K (CommRing.toCommSemiring.{u3} R _inst_6) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) _inst_7) (Algebra.toSMul.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (Algebra.toSMul.{u3, u1} R L (CommRing.toCommSemiring.{u3} R _inst_6) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_8)] {x : Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x S)}, Iff (IsIntegral.{u3, u1} R L _inst_6 (DivisionRing.toRing.{u1} L (Field.toDivisionRing.{u1} L _inst_2)) _inst_8 (Subtype.val.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (Set.{u1} L) (Set.instMembershipSet.{u1} L) x (SetLike.coe.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) S)) x)) (IsIntegral.{u3, u1} R (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x S)) _inst_6 (Subalgebra.toRing.{u2, u1} K L (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)) (DivisionRing.toRing.{u1} L (Field.toDivisionRing.{u1} L _inst_2)) _inst_4 (IntermediateField.toSubalgebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 S)) (IntermediateField.algebra'.{u2, u1, u3} K L _inst_1 _inst_2 _inst_4 S R (CommRing.toCommSemiring.{u3} R _inst_6) (Algebra.toSMul.{u3, u2} R K (CommRing.toCommSemiring.{u3} R _inst_6) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) _inst_7) _inst_8 _inst_9) x)
+Case conversion may be inaccurate. Consider using '#align intermediate_field.coe_is_integral_iff IntermediateField.coe_isIntegral_iffₓ'. -/
 theorem coe_isIntegral_iff {R : Type _} [CommRing R] [Algebra R K] [Algebra R L]
     [IsScalarTower R K L] {x : S} : IsIntegral R (x : L) ↔ IsIntegral R x :=
   by
@@ -540,6 +980,12 @@ theorem coe_isIntegral_iff {R : Type _} [CommRing R] [Algebra R K] [Algebra R L]
     rw [← aeval_def, aeval_coe, aeval_def, hProot, ZeroMemClass.coe_zero]
 #align intermediate_field.coe_is_integral_iff IntermediateField.coe_isIntegral_iff
 
+/- warning: intermediate_field.inclusion -> IntermediateField.inclusion is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] {E : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4} {F : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4}, (LE.le.{u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (Preorder.toHasLe.{u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (PartialOrder.toPreorder.{u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.partialOrder.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)))) E F) -> (AlgHom.{u1, u2, u2} K (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) E) (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) F) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) E) (DivisionRing.toRing.{u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) E) (Field.toDivisionRing.{u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) E) (IntermediateField.toField.{u1, u2} K L _inst_1 _inst_2 _inst_4 E)))) (Ring.toSemiring.{u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) F) (DivisionRing.toRing.{u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) F) (Field.toDivisionRing.{u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) F) (IntermediateField.toField.{u1, u2} K L _inst_1 _inst_2 _inst_4 F)))) (IntermediateField.algebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 E) (IntermediateField.algebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 F))
+but is expected to have type
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))] {E : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4} {F : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4}, (LE.le.{u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (Preorder.toLE.{u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (PartialOrder.toPreorder.{u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instPartialOrder.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)))) E F) -> (AlgHom.{u1, u2, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x E)) (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x F)) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 E)) (Subalgebra.toSemiring.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 F)) (IntermediateField.algebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 E) (IntermediateField.algebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 F))
+Case conversion may be inaccurate. Consider using '#align intermediate_field.inclusion IntermediateField.inclusionₓ'. -/
 /-- The map `E → F` when `E` is an intermediate field contained in the intermediate field `F`.
 
 This is the intermediate field version of `subalgebra.inclusion`. -/
@@ -547,22 +993,46 @@ def inclusion {E F : IntermediateField K L} (hEF : E ≤ F) : E →ₐ[K] F :=
   Subalgebra.inclusion hEF
 #align intermediate_field.inclusion IntermediateField.inclusion
 
+/- warning: intermediate_field.inclusion_injective -> IntermediateField.inclusion_injective is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] {E : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4} {F : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4} (hEF : LE.le.{u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (Preorder.toHasLe.{u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (PartialOrder.toPreorder.{u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.partialOrder.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)))) E F), Function.Injective.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} 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_inst_1 _inst_2 _inst_4 F)) (fun (_x : AlgHom.{u1, u2, u2} K (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) E) (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) F) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) E) (DivisionRing.toRing.{u2} (coeSort.{succ u2, succ (succ u2)} 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+but is expected to have type
+  forall {K : Type.{u2}} {L : Type.{u1}} [_inst_1 : Field.{u2} K] [_inst_2 : Field.{u1} L] [_inst_4 : Algebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))] {E : IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4} {F : IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4} (hEF : LE.le.{u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (Preorder.toLE.{u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (PartialOrder.toPreorder.{u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instPartialOrder.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)))) E F), Function.Injective.{succ u1, succ u1} (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 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+Case conversion may be inaccurate. Consider using '#align intermediate_field.inclusion_injective IntermediateField.inclusion_injectiveₓ'. -/
 theorem inclusion_injective {E F : IntermediateField K L} (hEF : E ≤ F) :
     Function.Injective (inclusion hEF) :=
   Subalgebra.inclusion_injective hEF
 #align intermediate_field.inclusion_injective IntermediateField.inclusion_injective
 
+/- warning: intermediate_field.inclusion_self -> IntermediateField.inclusion_self is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] {E : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4}, Eq.{succ u2} (AlgHom.{u1, u2, u2} K (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) E) (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) E) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) E) (DivisionRing.toRing.{u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) E) (Field.toDivisionRing.{u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) E) (IntermediateField.toField.{u1, u2} K L _inst_1 _inst_2 _inst_4 E)))) (Ring.toSemiring.{u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) E) (DivisionRing.toRing.{u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) E) (Field.toDivisionRing.{u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) E) (IntermediateField.toField.{u1, u2} K L _inst_1 _inst_2 _inst_4 E)))) (IntermediateField.algebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 E) (IntermediateField.algebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 E)) (IntermediateField.inclusion.{u1, u2} K L _inst_1 _inst_2 _inst_4 E E (le_refl.{u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (PartialOrder.toPreorder.{u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.partialOrder.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4))) E)) (AlgHom.id.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) E) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) E) (DivisionRing.toRing.{u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) E) (Field.toDivisionRing.{u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) E) (IntermediateField.toField.{u1, u2} K L _inst_1 _inst_2 _inst_4 E)))) (IntermediateField.algebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 E))
+but is expected to have type
+  forall {K : Type.{u2}} {L : Type.{u1}} [_inst_1 : Field.{u2} K] [_inst_2 : Field.{u1} L] [_inst_4 : Algebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))] {E : IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4}, Eq.{succ u1} (AlgHom.{u2, u1, u1} K (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x E)) (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x E)) (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (Subalgebra.toSemiring.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 E)) (Subalgebra.toSemiring.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 E)) (IntermediateField.algebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 E) (IntermediateField.algebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 E)) (IntermediateField.inclusion.{u2, u1} K L _inst_1 _inst_2 _inst_4 E E (le_refl.{u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (PartialOrder.toPreorder.{u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instPartialOrder.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4))) E)) (AlgHom.id.{u2, u1} K (Subtype.{succ u1} L (fun (x : L) => Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x E)) (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (Subalgebra.toSemiring.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4 (IntermediateField.toSubalgebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 E)) (IntermediateField.algebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 E))
+Case conversion may be inaccurate. Consider using '#align intermediate_field.inclusion_self IntermediateField.inclusion_selfₓ'. -/
 @[simp]
 theorem inclusion_self {E : IntermediateField K L} : inclusion (le_refl E) = AlgHom.id K E :=
   Subalgebra.inclusion_self
 #align intermediate_field.inclusion_self IntermediateField.inclusion_self
 
+/- warning: intermediate_field.inclusion_inclusion -> IntermediateField.inclusion_inclusion is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {K : Type.{u2}} {L : Type.{u1}} [_inst_1 : Field.{u2} K] [_inst_2 : Field.{u1} L] [_inst_4 : Algebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))] {E : IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4} {F : IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4} {G : IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4} (hEF : LE.le.{u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (Preorder.toLE.{u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (PartialOrder.toPreorder.{u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instPartialOrder.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)))) E F) (hFG : LE.le.{u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) 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(IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (PartialOrder.toPreorder.{u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instPartialOrder.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4))) E F G hEF hFG)) x)
+Case conversion may be inaccurate. Consider using '#align intermediate_field.inclusion_inclusion IntermediateField.inclusion_inclusionₓ'. -/
 @[simp]
 theorem inclusion_inclusion {E F G : IntermediateField K L} (hEF : E ≤ F) (hFG : F ≤ G) (x : E) :
     inclusion hFG (inclusion hEF x) = inclusion (le_trans hEF hFG) x :=
   Subalgebra.inclusion_inclusion hEF hFG x
 #align intermediate_field.inclusion_inclusion IntermediateField.inclusion_inclusion
 
+/- warning: intermediate_field.coe_inclusion -> IntermediateField.coe_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 intermediate_field.coe_inclusion IntermediateField.coe_inclusionₓ'. -/
 @[simp]
 theorem coe_inclusion {E F : IntermediateField K L} (hEF : E ≤ F) (e : E) :
     (inclusion hEF e : L) = e :=
@@ -571,6 +1041,12 @@ theorem coe_inclusion {E F : IntermediateField K L} (hEF : E ≤ F) (e : E) :
 
 variable {S}
 
+/- warning: intermediate_field.to_subalgebra_injective -> IntermediateField.toSubalgebra_injective is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] {S : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4} {S' : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4}, (Eq.{succ u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_4) (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S) (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S')) -> (Eq.{succ u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) S S')
+but is expected to have type
+  forall {K : Type.{u2}} {L : Type.{u1}} [_inst_1 : Field.{u2} K] [_inst_2 : Field.{u1} L] [_inst_4 : Algebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))] {S : IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4} {S' : IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4}, (Eq.{succ u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (IntermediateField.toSubalgebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 S) (IntermediateField.toSubalgebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 S')) -> (Eq.{succ u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) S S')
+Case conversion may be inaccurate. Consider using '#align intermediate_field.to_subalgebra_injective IntermediateField.toSubalgebra_injectiveₓ'. -/
 theorem toSubalgebra_injective {S S' : IntermediateField K L}
     (h : S.toSubalgebra = S'.toSubalgebra) : S = S' :=
   by
@@ -580,20 +1056,44 @@ theorem toSubalgebra_injective {S S' : IntermediateField K L}
 
 variable (S)
 
+/- warning: intermediate_field.set_range_subset -> IntermediateField.set_range_subset is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] (S : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4), HasSubset.Subset.{u2} (Set.{u2} L) (Set.hasSubset.{u2} L) (Set.range.{u2, succ u1} L K (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) (fun (_x : RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) => K -> L) (RingHom.hasCoeToFun.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) (algebraMap.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_4))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (Set.{u2} L) (HasLiftT.mk.{succ u2, succ u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (Set.{u2} L) (CoeTCₓ.coe.{succ u2, succ u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (Set.{u2} L) (SetLike.Set.hasCoeT.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)))) S)
+but is expected to have type
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))] (S : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4), HasSubset.Subset.{u2} (Set.{u2} L) (Set.instHasSubsetSet.{u2} L) (Set.range.{u2, succ u1} L K (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => L) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))))) K L (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u2} K L (Semiring.toNonAssocSemiring.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Semiring.toNonAssocSemiring.{u2} L (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))))))) (algebraMap.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4))) (SetLike.coe.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) S)
+Case conversion may be inaccurate. Consider using '#align intermediate_field.set_range_subset IntermediateField.set_range_subsetₓ'. -/
 theorem set_range_subset : Set.range (algebraMap K L) ⊆ S :=
   S.toSubalgebra.range_subset
 #align intermediate_field.set_range_subset IntermediateField.set_range_subset
 
+/- warning: intermediate_field.field_range_le -> IntermediateField.fieldRange_le is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] (S : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4), LE.le.{u2} (Subfield.{u2} L _inst_2) (Preorder.toHasLe.{u2} (Subfield.{u2} L _inst_2) (PartialOrder.toPreorder.{u2} (Subfield.{u2} L _inst_2) (SetLike.partialOrder.{u2, u2} (Subfield.{u2} L _inst_2) L (Subfield.setLike.{u2} L _inst_2)))) (RingHom.fieldRange.{u1, u2} K L _inst_1 _inst_2 (algebraMap.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_4)) (IntermediateField.toSubfield.{u1, u2} K L _inst_1 _inst_2 _inst_4 S)
+but is expected to have type
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))] (S : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4), LE.le.{u2} (Subfield.{u2} L _inst_2) (Preorder.toLE.{u2} (Subfield.{u2} L _inst_2) (PartialOrder.toPreorder.{u2} (Subfield.{u2} L _inst_2) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Subfield.{u2} L _inst_2) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Subfield.{u2} L _inst_2) (Subfield.instCompleteLatticeSubfield.{u2} L _inst_2))))) (RingHom.fieldRange.{u1, u2} K L _inst_1 _inst_2 (algebraMap.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4)) (IntermediateField.toSubfield.{u1, u2} K L _inst_1 _inst_2 _inst_4 S)
+Case conversion may be inaccurate. Consider using '#align intermediate_field.field_range_le IntermediateField.fieldRange_leₓ'. -/
 theorem fieldRange_le : (algebraMap K L).fieldRange ≤ S.toSubfield := fun x hx =>
   S.toSubalgebra.range_subset (by rwa [Set.mem_range, ← RingHom.mem_fieldRange])
 #align intermediate_field.field_range_le IntermediateField.fieldRange_le
 
+/- warning: intermediate_field.to_subalgebra_le_to_subalgebra -> IntermediateField.toSubalgebra_le_toSubalgebra is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] {S : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4} {S' : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4}, Iff (LE.le.{u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_4) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_4) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_4) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_4) L (Subalgebra.setLike.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_4)))) (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S) (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S')) (LE.le.{u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (Preorder.toHasLe.{u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (PartialOrder.toPreorder.{u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.partialOrder.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)))) S S')
+but is expected to have type
+  forall {K : Type.{u2}} {L : Type.{u1}} [_inst_1 : Field.{u2} K] [_inst_2 : Field.{u1} L] [_inst_4 : Algebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))] {S : IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4} {S' : IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4}, Iff (LE.le.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (Algebra.instCompleteLatticeSubalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4))))) (IntermediateField.toSubalgebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 S) (IntermediateField.toSubalgebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 S')) (LE.le.{u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (Preorder.toLE.{u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (PartialOrder.toPreorder.{u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instPartialOrder.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)))) S S')
+Case conversion may be inaccurate. Consider using '#align intermediate_field.to_subalgebra_le_to_subalgebra IntermediateField.toSubalgebra_le_toSubalgebraₓ'. -/
 @[simp]
 theorem toSubalgebra_le_toSubalgebra {S S' : IntermediateField K L} :
     S.toSubalgebra ≤ S'.toSubalgebra ↔ S ≤ S' :=
   Iff.rfl
 #align intermediate_field.to_subalgebra_le_to_subalgebra IntermediateField.toSubalgebra_le_toSubalgebra
 
+/- warning: intermediate_field.to_subalgebra_lt_to_subalgebra -> IntermediateField.toSubalgebra_lt_toSubalgebra is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] {S : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4} {S' : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4}, Iff (LT.lt.{u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_4) (Preorder.toHasLt.{u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_4) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_4) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_4) L (Subalgebra.setLike.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_4)))) (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S) (IntermediateField.toSubalgebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 S')) (LT.lt.{u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (Preorder.toHasLt.{u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (PartialOrder.toPreorder.{u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.partialOrder.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)))) S S')
+but is expected to have type
+  forall {K : Type.{u2}} {L : Type.{u1}} [_inst_1 : Field.{u2} K] [_inst_2 : Field.{u1} L] [_inst_4 : Algebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))] {S : IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4} {S' : IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4}, Iff (LT.lt.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (Preorder.toLT.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (Algebra.instCompleteLatticeSubalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4))))) (IntermediateField.toSubalgebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 S) (IntermediateField.toSubalgebra.{u2, u1} K L _inst_1 _inst_2 _inst_4 S')) (LT.lt.{u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (Preorder.toLT.{u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (PartialOrder.toPreorder.{u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instPartialOrder.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)))) S S')
+Case conversion may be inaccurate. Consider using '#align intermediate_field.to_subalgebra_lt_to_subalgebra IntermediateField.toSubalgebra_lt_toSubalgebraₓ'. -/
 @[simp]
 theorem toSubalgebra_lt_toSubalgebra {S S' : IntermediateField K L} :
     S.toSubalgebra < S'.toSubalgebra ↔ S < S' :=
@@ -604,11 +1104,23 @@ variable {S}
 
 section Tower
 
+/- warning: intermediate_field.lift -> IntermediateField.lift is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] {F : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4}, (IntermediateField.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) F) _inst_1 (IntermediateField.toField.{u1, u2} K L _inst_1 _inst_2 _inst_4 F) (IntermediateField.algebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 F)) -> (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)
+but is expected to have type
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))] {F : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4}, (IntermediateField.{u1, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x F)) _inst_1 (IntermediateField.toField.{u1, u2} K L _inst_1 _inst_2 _inst_4 F) (IntermediateField.algebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 F)) -> (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)
+Case conversion may be inaccurate. Consider using '#align intermediate_field.lift IntermediateField.liftₓ'. -/
 /-- Lift an intermediate_field of an intermediate_field -/
 def lift {F : IntermediateField K L} (E : IntermediateField K F) : IntermediateField K L :=
   E.map (val F)
 #align intermediate_field.lift IntermediateField.lift
 
+/- warning: intermediate_field.has_lift -> IntermediateField.hasLift is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] {F : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4}, HasLiftT.{succ u2, succ u2} (IntermediateField.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) F) _inst_1 (IntermediateField.toField.{u1, u2} K L _inst_1 _inst_2 _inst_4 F) (IntermediateField.algebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 F)) (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)
+but is expected to have type
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))] {F : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4}, CoeOut.{succ u2, succ u2} (IntermediateField.{u1, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x F)) _inst_1 (IntermediateField.toField.{u1, u2} K L _inst_1 _inst_2 _inst_4 F) (IntermediateField.algebra.{u1, u2} K L _inst_1 _inst_2 _inst_4 F)) (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)
+Case conversion may be inaccurate. Consider using '#align intermediate_field.has_lift IntermediateField.hasLiftₓ'. -/
 instance hasLift {F : IntermediateField K L} :
     HasLiftT (IntermediateField K F) (IntermediateField K L) :=
   ⟨lift⟩
@@ -618,36 +1130,60 @@ section RestrictScalars
 
 variable (K) [Algebra L' L] [IsScalarTower K L' L]
 
+#print IntermediateField.restrictScalars /-
 /-- Given a tower `L / ↥E / L' / K` of field extensions, where `E` is an `L'`-intermediate field of
 `L`, reinterpret `E` as a `K`-intermediate field of `L`. -/
 def restrictScalars (E : IntermediateField L' L) : IntermediateField K L :=
   { E.toSubfield, E.toSubalgebra.restrictScalars K with carrier := E.carrier }
 #align intermediate_field.restrict_scalars IntermediateField.restrictScalars
+-/
 
+/- warning: intermediate_field.coe_restrict_scalars -> IntermediateField.coe_restrictScalars is a dubious translation:
+lean 3 declaration is
+  forall (K : Type.{u1}) {L : Type.{u2}} {L' : Type.{u3}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_3 : Field.{u3} L'] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] [_inst_5 : Algebra.{u1, u3} K L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3)))] [_inst_6 : Algebra.{u3, u2} L' L (Semifield.toCommSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] [_inst_7 : IsScalarTower.{u1, u3, u2} K L' L (SMulZeroClass.toHasSmul.{u1, u3} K L' (AddZeroClass.toHasZero.{u3} L' (AddMonoid.toAddZeroClass.{u3} L' (AddCommMonoid.toAddMonoid.{u3} L' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} L' 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(Field.toSemifield.{u1} K _inst_1)))) (AddZeroClass.toHasZero.{u3} L' (AddMonoid.toAddZeroClass.{u3} L' (AddCommMonoid.toAddMonoid.{u3} L' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} L' (Semiring.toNonAssocSemiring.{u3} L' (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3))))))))) (Module.toMulActionWithZero.{u1, u3} K L' (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} L' (Semiring.toNonAssocSemiring.{u3} L' (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3)))))) (Algebra.toModule.{u1, u3} K L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3))) _inst_5))))) 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_inst_2))))))))) (MulActionWithZero.toSMulWithZero.{u3, u2} L' L (Semiring.toMonoidWithZero.{u3} L' (CommSemiring.toSemiring.{u3} L' (Semifield.toCommSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3)))) (AddZeroClass.toHasZero.{u2} L (AddMonoid.toAddZeroClass.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))))) (Module.toMulActionWithZero.{u3, u2} L' L (CommSemiring.toSemiring.{u3} L' (Semifield.toCommSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) (Algebra.toModule.{u3, u2} L' L (Semifield.toCommSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_6))))) (SMulZeroClass.toHasSmul.{u1, u2} K L (AddZeroClass.toHasZero.{u2} L (AddMonoid.toAddZeroClass.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} K L (MulZeroClass.toHasZero.{u1} K (MulZeroOneClass.toMulZeroClass.{u1} K (MonoidWithZero.toMulZeroOneClass.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (AddZeroClass.toHasZero.{u2} L (AddMonoid.toAddZeroClass.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} K L (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (AddZeroClass.toHasZero.{u2} L (AddMonoid.toAddZeroClass.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))))) (Module.toMulActionWithZero.{u1, u2} K L (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) (Algebra.toModule.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_4)))))] {E : IntermediateField.{u3, u2} L' L _inst_3 _inst_2 _inst_6}, Eq.{succ u2} (Set.{u2} L) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (Set.{u2} L) (HasLiftT.mk.{succ u2, succ u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (Set.{u2} L) (CoeTCₓ.coe.{succ u2, succ u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (Set.{u2} L) (SetLike.Set.hasCoeT.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)))) (IntermediateField.restrictScalars.{u1, u2, u3} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 E)) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (IntermediateField.{u3, u2} L' L _inst_3 _inst_2 _inst_6) (Set.{u2} L) (HasLiftT.mk.{succ u2, succ u2} (IntermediateField.{u3, u2} L' L _inst_3 _inst_2 _inst_6) (Set.{u2} L) (CoeTCₓ.coe.{succ u2, succ u2} (IntermediateField.{u3, u2} L' L _inst_3 _inst_2 _inst_6) (Set.{u2} L) (SetLike.Set.hasCoeT.{u2, u2} (IntermediateField.{u3, u2} L' L _inst_3 _inst_2 _inst_6) L (IntermediateField.setLike.{u3, u2} L' L _inst_3 _inst_2 _inst_6)))) E)
+but is expected to have type
+  forall (K : Type.{u1}) {L : Type.{u2}} {L' : Type.{u3}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_3 : Field.{u3} L'] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))] [_inst_5 : Algebra.{u1, u3} K L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3)))] [_inst_6 : Algebra.{u3, u2} L' L (Semifield.toCommSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))] [_inst_7 : IsScalarTower.{u1, u3, u2} K L' L (Algebra.toSMul.{u1, u3} K L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))) _inst_5) (Algebra.toSMul.{u3, u2} L' L (Semifield.toCommSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_6) (Algebra.toSMul.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4)] {E : IntermediateField.{u3, u2} L' L _inst_3 _inst_2 _inst_6}, Eq.{succ u2} (Set.{u2} L) (SetLike.coe.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (IntermediateField.restrictScalars.{u1, u2, u3} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 E)) (SetLike.coe.{u2, u2} (IntermediateField.{u3, u2} L' L _inst_3 _inst_2 _inst_6) L (IntermediateField.instSetLikeIntermediateField.{u3, u2} L' L _inst_3 _inst_2 _inst_6) E)
+Case conversion may be inaccurate. Consider using '#align intermediate_field.coe_restrict_scalars IntermediateField.coe_restrictScalarsₓ'. -/
 @[simp]
 theorem coe_restrictScalars {E : IntermediateField L' L} :
     (restrictScalars K E : Set L) = (E : Set L) :=
   rfl
 #align intermediate_field.coe_restrict_scalars IntermediateField.coe_restrictScalars
 
+#print IntermediateField.restrictScalars_toSubalgebra /-
 @[simp]
 theorem restrictScalars_toSubalgebra {E : IntermediateField L' L} :
     (E.restrictScalars K).toSubalgebra = E.toSubalgebra.restrictScalars K :=
   SetLike.coe_injective rfl
 #align intermediate_field.restrict_scalars_to_subalgebra IntermediateField.restrictScalars_toSubalgebra
+-/
 
+#print IntermediateField.restrictScalars_toSubfield /-
 @[simp]
 theorem restrictScalars_toSubfield {E : IntermediateField L' L} :
     (E.restrictScalars K).toSubfield = E.toSubfield :=
   SetLike.coe_injective rfl
 #align intermediate_field.restrict_scalars_to_subfield IntermediateField.restrictScalars_toSubfield
+-/
 
+/- warning: intermediate_field.mem_restrict_scalars -> IntermediateField.mem_restrictScalars is a dubious translation:
+lean 3 declaration is
+  forall (K : Type.{u1}) {L : Type.{u2}} {L' : Type.{u3}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_3 : Field.{u3} L'] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] [_inst_5 : Algebra.{u1, u3} K L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3)))] [_inst_6 : Algebra.{u3, u2} L' L (Semifield.toCommSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] [_inst_7 : IsScalarTower.{u1, u3, u2} K L' L (SMulZeroClass.toHasSmul.{u1, u3} K L' (AddZeroClass.toHasZero.{u3} L' (AddMonoid.toAddZeroClass.{u3} L' (AddCommMonoid.toAddMonoid.{u3} L' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} L' (Semiring.toNonAssocSemiring.{u3} L' (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3))))))))) (SMulWithZero.toSmulZeroClass.{u1, u3} K L' (MulZeroClass.toHasZero.{u1} K (MulZeroOneClass.toMulZeroClass.{u1} K (MonoidWithZero.toMulZeroOneClass.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (AddZeroClass.toHasZero.{u3} L' (AddMonoid.toAddZeroClass.{u3} L' (AddCommMonoid.toAddMonoid.{u3} L' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} L' (Semiring.toNonAssocSemiring.{u3} L' (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3))))))))) (MulActionWithZero.toSMulWithZero.{u1, u3} K L' (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (AddZeroClass.toHasZero.{u3} L' (AddMonoid.toAddZeroClass.{u3} L' (AddCommMonoid.toAddMonoid.{u3} L' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} L' (Semiring.toNonAssocSemiring.{u3} L' (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3))))))))) (Module.toMulActionWithZero.{u1, u3} K L' (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} L' (Semiring.toNonAssocSemiring.{u3} L' (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3)))))) (Algebra.toModule.{u1, u3} K L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3))) _inst_5))))) (SMulZeroClass.toHasSmul.{u3, u2} L' L (AddZeroClass.toHasZero.{u2} L (AddMonoid.toAddZeroClass.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))))) (SMulWithZero.toSmulZeroClass.{u3, u2} L' L (MulZeroClass.toHasZero.{u3} L' (MulZeroOneClass.toMulZeroClass.{u3} L' (MonoidWithZero.toMulZeroOneClass.{u3} L' (Semiring.toMonoidWithZero.{u3} L' (CommSemiring.toSemiring.{u3} L' (Semifield.toCommSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))))))) (AddZeroClass.toHasZero.{u2} L (AddMonoid.toAddZeroClass.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))))) (MulActionWithZero.toSMulWithZero.{u3, u2} L' L (Semiring.toMonoidWithZero.{u3} L' (CommSemiring.toSemiring.{u3} L' (Semifield.toCommSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3)))) (AddZeroClass.toHasZero.{u2} L (AddMonoid.toAddZeroClass.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))))) (Module.toMulActionWithZero.{u3, u2} L' L (CommSemiring.toSemiring.{u3} L' (Semifield.toCommSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) (Algebra.toModule.{u3, u2} L' L (Semifield.toCommSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_6))))) (SMulZeroClass.toHasSmul.{u1, u2} K L (AddZeroClass.toHasZero.{u2} L (AddMonoid.toAddZeroClass.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} K L (MulZeroClass.toHasZero.{u1} K (MulZeroOneClass.toMulZeroClass.{u1} K (MonoidWithZero.toMulZeroOneClass.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (AddZeroClass.toHasZero.{u2} L (AddMonoid.toAddZeroClass.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} K L (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (AddZeroClass.toHasZero.{u2} L (AddMonoid.toAddZeroClass.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))))) (Module.toMulActionWithZero.{u1, u2} K L (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) (Algebra.toModule.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_4)))))] {E : IntermediateField.{u3, u2} L' L _inst_3 _inst_2 _inst_6} {x : L}, Iff (Membership.Mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.hasMem.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x (IntermediateField.restrictScalars.{u1, u2, u3} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 E)) (Membership.Mem.{u2, u2} L (IntermediateField.{u3, u2} L' L _inst_3 _inst_2 _inst_6) (SetLike.hasMem.{u2, u2} (IntermediateField.{u3, u2} L' L _inst_3 _inst_2 _inst_6) L (IntermediateField.setLike.{u3, u2} L' L _inst_3 _inst_2 _inst_6)) x E)
+but is expected to have type
+  forall (K : Type.{u1}) {L : Type.{u2}} {L' : Type.{u3}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_3 : Field.{u3} L'] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))] [_inst_5 : Algebra.{u1, u3} K L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3)))] [_inst_6 : Algebra.{u3, u2} L' L (Semifield.toCommSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))] [_inst_7 : IsScalarTower.{u1, u3, u2} K L' L (Algebra.toSMul.{u1, u3} K L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u3} L' (Semifield.toDivisionSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))) _inst_5) (Algebra.toSMul.{u3, u2} L' L (Semifield.toCommSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_6) (Algebra.toSMul.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4)] {E : IntermediateField.{u3, u2} L' L _inst_3 _inst_2 _inst_6} {x : L}, Iff (Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x (IntermediateField.restrictScalars.{u1, u2, u3} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 E)) (Membership.mem.{u2, u2} L (IntermediateField.{u3, u2} L' L _inst_3 _inst_2 _inst_6) (SetLike.instMembership.{u2, u2} (IntermediateField.{u3, u2} L' L _inst_3 _inst_2 _inst_6) L (IntermediateField.instSetLikeIntermediateField.{u3, u2} L' L _inst_3 _inst_2 _inst_6)) x E)
+Case conversion may be inaccurate. Consider using '#align intermediate_field.mem_restrict_scalars IntermediateField.mem_restrictScalarsₓ'. -/
 @[simp]
 theorem mem_restrictScalars {E : IntermediateField L' L} {x : L} :
     x ∈ restrictScalars K E ↔ x ∈ E :=
   Iff.rfl
 #align intermediate_field.mem_restrict_scalars IntermediateField.mem_restrictScalars
 
+/- warning: intermediate_field.restrict_scalars_injective -> IntermediateField.restrictScalars_injective is a dubious translation:
+lean 3 declaration is
+  forall (K : Type.{u1}) {L : Type.{u2}} {L' : Type.{u3}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_3 : Field.{u3} L'] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] [_inst_5 : Algebra.{u1, u3} K L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3)))] [_inst_6 : Algebra.{u3, u2} L' L (Semifield.toCommSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] [_inst_7 : IsScalarTower.{u1, u3, u2} K L' L (SMulZeroClass.toHasSmul.{u1, u3} K L' (AddZeroClass.toHasZero.{u3} L' (AddMonoid.toAddZeroClass.{u3} L' (AddCommMonoid.toAddMonoid.{u3} L' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} L' (Semiring.toNonAssocSemiring.{u3} L' (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3))))))))) (SMulWithZero.toSmulZeroClass.{u1, u3} K L' (MulZeroClass.toHasZero.{u1} K (MulZeroOneClass.toMulZeroClass.{u1} K (MonoidWithZero.toMulZeroOneClass.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (AddZeroClass.toHasZero.{u3} L' (AddMonoid.toAddZeroClass.{u3} L' (AddCommMonoid.toAddMonoid.{u3} L' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} L' (Semiring.toNonAssocSemiring.{u3} L' (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3))))))))) (MulActionWithZero.toSMulWithZero.{u1, u3} K L' (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (AddZeroClass.toHasZero.{u3} L' (AddMonoid.toAddZeroClass.{u3} L' (AddCommMonoid.toAddMonoid.{u3} L' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} L' (Semiring.toNonAssocSemiring.{u3} L' (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3))))))))) (Module.toMulActionWithZero.{u1, u3} K L' (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} L' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} L' (Semiring.toNonAssocSemiring.{u3} L' (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3)))))) (Algebra.toModule.{u1, u3} K L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u3} L' (DivisionRing.toRing.{u3} L' (Field.toDivisionRing.{u3} L' _inst_3))) _inst_5))))) (SMulZeroClass.toHasSmul.{u3, u2} L' L (AddZeroClass.toHasZero.{u2} L (AddMonoid.toAddZeroClass.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))))) (SMulWithZero.toSmulZeroClass.{u3, u2} L' L (MulZeroClass.toHasZero.{u3} L' (MulZeroOneClass.toMulZeroClass.{u3} L' (MonoidWithZero.toMulZeroOneClass.{u3} L' (Semiring.toMonoidWithZero.{u3} L' (CommSemiring.toSemiring.{u3} L' (Semifield.toCommSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))))))) (AddZeroClass.toHasZero.{u2} L (AddMonoid.toAddZeroClass.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))))) (MulActionWithZero.toSMulWithZero.{u3, u2} L' L (Semiring.toMonoidWithZero.{u3} L' (CommSemiring.toSemiring.{u3} L' (Semifield.toCommSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3)))) (AddZeroClass.toHasZero.{u2} L (AddMonoid.toAddZeroClass.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))))) (Module.toMulActionWithZero.{u3, u2} L' L (CommSemiring.toSemiring.{u3} L' (Semifield.toCommSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) (Algebra.toModule.{u3, u2} L' L (Semifield.toCommSemiring.{u3} L' (Field.toSemifield.{u3} L' _inst_3)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_6))))) (SMulZeroClass.toHasSmul.{u1, u2} K L (AddZeroClass.toHasZero.{u2} L (AddMonoid.toAddZeroClass.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} K L (MulZeroClass.toHasZero.{u1} K (MulZeroOneClass.toMulZeroClass.{u1} K (MonoidWithZero.toMulZeroOneClass.{u1} K (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (AddZeroClass.toHasZero.{u2} L (AddMonoid.toAddZeroClass.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} K L (Semiring.toMonoidWithZero.{u1} K (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (AddZeroClass.toHasZero.{u2} L (AddMonoid.toAddZeroClass.{u2} L (AddCommMonoid.toAddMonoid.{u2} L (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))))))) (Module.toMulActionWithZero.{u1, u2} K L (CommSemiring.toSemiring.{u1} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} L (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} L (Semiring.toNonAssocSemiring.{u2} L (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))))) (Algebra.toModule.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_4)))))], Function.Injective.{succ u2, succ u2} (IntermediateField.{u3, u2} L' L _inst_3 _inst_2 _inst_6) (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (IntermediateField.restrictScalars.{u1, u2, u3} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7)
+but is expected to have type
+  forall (K : Type.{u1}) {L : Type.{u3}} {L' : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u3} L] [_inst_3 : Field.{u2} L'] [_inst_4 : Algebra.{u1, u3} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u3} L (Semifield.toDivisionSemiring.{u3} L (Field.toSemifield.{u3} L _inst_2)))] [_inst_5 : Algebra.{u1, u2} K L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L' (Semifield.toDivisionSemiring.{u2} L' (Field.toSemifield.{u2} L' _inst_3)))] [_inst_6 : Algebra.{u2, u3} L' L (Semifield.toCommSemiring.{u2} L' (Field.toSemifield.{u2} L' _inst_3)) (DivisionSemiring.toSemiring.{u3} L (Semifield.toDivisionSemiring.{u3} L (Field.toSemifield.{u3} L _inst_2)))] [_inst_7 : IsScalarTower.{u1, u2, u3} K L' L (Algebra.toSMul.{u1, u2} K L' (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L' (Semifield.toDivisionSemiring.{u2} L' (Field.toSemifield.{u2} L' _inst_3))) _inst_5) (Algebra.toSMul.{u2, u3} L' L (Semifield.toCommSemiring.{u2} L' (Field.toSemifield.{u2} L' _inst_3)) (DivisionSemiring.toSemiring.{u3} L (Semifield.toDivisionSemiring.{u3} L (Field.toSemifield.{u3} L _inst_2))) _inst_6) (Algebra.toSMul.{u1, u3} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u3} L (Semifield.toDivisionSemiring.{u3} L (Field.toSemifield.{u3} L _inst_2))) _inst_4)], Function.Injective.{succ u3, succ u3} (IntermediateField.{u2, u3} L' L _inst_3 _inst_2 _inst_6) (IntermediateField.{u1, u3} K L _inst_1 _inst_2 _inst_4) (IntermediateField.restrictScalars.{u1, u3, u2} K L L' _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7)
+Case conversion may be inaccurate. Consider using '#align intermediate_field.restrict_scalars_injective IntermediateField.restrictScalars_injectiveₓ'. -/
 theorem restrictScalars_injective :
     Function.Injective (restrictScalars K : IntermediateField L' L → IntermediateField K L) :=
   fun U V H => ext fun x => by rw [← mem_restrict_scalars K, H, mem_restrict_scalars]
@@ -664,19 +1200,39 @@ section FiniteDimensional
 
 variable (F E : IntermediateField K L)
 
+/- warning: intermediate_field.finite_dimensional_left -> IntermediateField.finiteDimensional_left is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] (F : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) [_inst_6 : FiniteDimensional.{u1, u2} K L (Field.toDivisionRing.{u1} K _inst_1) (NonUnitalNonAssocRing.toAddCommGroup.{u2} L (NonAssocRing.toNonUnitalNonAssocRing.{u2} L (Ring.toNonAssocRing.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))))) (Algebra.toModule.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_4)], FiniteDimensional.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) F) (Field.toDivisionRing.{u1} K _inst_1) (NonUnitalNonAssocRing.toAddCommGroup.{u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) F) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) F) (Ring.toNonAssocRing.{u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) F) (DivisionRing.toRing.{u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) F) (Field.toDivisionRing.{u2} (coeSort.{succ u2, succ (succ u2)} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) F) (IntermediateField.toField.{u1, u2} K L _inst_1 _inst_2 _inst_4 F)))))) (IntermediateField.module.{u1, u2} K L _inst_1 _inst_2 _inst_4 F)
+but is expected to have type
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2)))] (F : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) [_inst_6 : FiniteDimensional.{u1, u2} K L (Field.toDivisionRing.{u1} K _inst_1) (Ring.toAddCommGroup.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) (Algebra.toModule.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u2} L (Semifield.toDivisionSemiring.{u2} L (Field.toSemifield.{u2} L _inst_2))) _inst_4)], FiniteDimensional.{u1, u2} K (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x F)) (Field.toDivisionRing.{u1} K _inst_1) (Ring.toAddCommGroup.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x F)) (DivisionRing.toRing.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x F)) (Field.toDivisionRing.{u2} (Subtype.{succ u2} L (fun (x : L) => Membership.mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x F)) (IntermediateField.toField.{u1, u2} K L _inst_1 _inst_2 _inst_4 F)))) (IntermediateField.module.{u1, u2} K L _inst_1 _inst_2 _inst_4 F)
+Case conversion may be inaccurate. Consider using '#align intermediate_field.finite_dimensional_left IntermediateField.finiteDimensional_leftₓ'. -/
 instance finiteDimensional_left [FiniteDimensional K L] : FiniteDimensional K F :=
   left K F L
 #align intermediate_field.finite_dimensional_left IntermediateField.finiteDimensional_left
 
+/- warning: intermediate_field.finite_dimensional_right -> IntermediateField.finiteDimensional_right is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align intermediate_field.finite_dimensional_right IntermediateField.finiteDimensional_rightₓ'. -/
 instance finiteDimensional_right [FiniteDimensional K L] : FiniteDimensional F L :=
   right K F L
 #align intermediate_field.finite_dimensional_right IntermediateField.finiteDimensional_right
 
+#print IntermediateField.rank_eq_rank_subalgebra /-
 @[simp]
 theorem rank_eq_rank_subalgebra : Module.rank K F.toSubalgebra = Module.rank K F :=
   rfl
 #align intermediate_field.rank_eq_rank_subalgebra IntermediateField.rank_eq_rank_subalgebra
+-/
 
+/- warning: intermediate_field.finrank_eq_finrank_subalgebra -> IntermediateField.finrank_eq_finrank_subalgebra is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align intermediate_field.finrank_eq_finrank_subalgebra IntermediateField.finrank_eq_finrank_subalgebraₓ'. -/
 @[simp]
 theorem finrank_eq_finrank_subalgebra : finrank K F.toSubalgebra = finrank K F :=
   rfl
@@ -684,24 +1240,44 @@ theorem finrank_eq_finrank_subalgebra : finrank K F.toSubalgebra = finrank K F :
 
 variable {F} {E}
 
+#print IntermediateField.toSubalgebra_eq_iff /-
 @[simp]
 theorem toSubalgebra_eq_iff : F.toSubalgebra = E.toSubalgebra ↔ F = E :=
   by
   rw [SetLike.ext_iff, SetLike.ext'_iff, Set.ext_iff]
   rfl
 #align intermediate_field.to_subalgebra_eq_iff IntermediateField.toSubalgebra_eq_iff
+-/
 
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+Case conversion may be inaccurate. Consider using '#align intermediate_field.eq_of_le_of_finrank_le IntermediateField.eq_of_le_of_finrank_leₓ'. -/
 theorem eq_of_le_of_finrank_le [FiniteDimensional K L] (h_le : F ≤ E)
     (h_finrank : finrank K E ≤ finrank K F) : F = E :=
   toSubalgebra_injective <|
     Subalgebra.toSubmodule.Injective <| eq_of_le_of_finrank_le h_le h_finrank
 #align intermediate_field.eq_of_le_of_finrank_le IntermediateField.eq_of_le_of_finrank_le
 
+/- warning: intermediate_field.eq_of_le_of_finrank_eq -> IntermediateField.eq_of_le_of_finrank_eq is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align intermediate_field.eq_of_le_of_finrank_eq IntermediateField.eq_of_le_of_finrank_eqₓ'. -/
 theorem eq_of_le_of_finrank_eq [FiniteDimensional K L] (h_le : F ≤ E)
     (h_finrank : finrank K F = finrank K E) : F = E :=
   eq_of_le_of_finrank_le h_le h_finrank.ge
 #align intermediate_field.eq_of_le_of_finrank_eq IntermediateField.eq_of_le_of_finrank_eq
 
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+Case conversion may be inaccurate. Consider using '#align intermediate_field.eq_of_le_of_finrank_le' IntermediateField.eq_of_le_of_finrank_le'ₓ'. -/
 theorem eq_of_le_of_finrank_le' [FiniteDimensional K L] (h_le : F ≤ E)
     (h_finrank : finrank F L ≤ finrank E L) : F = E :=
   by
@@ -712,6 +1288,12 @@ theorem eq_of_le_of_finrank_le' [FiniteDimensional K L] (h_le : F ≤ E)
   nlinarith
 #align intermediate_field.eq_of_le_of_finrank_le' IntermediateField.eq_of_le_of_finrank_le'
 
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+Case conversion may be inaccurate. Consider using '#align intermediate_field.eq_of_le_of_finrank_eq' IntermediateField.eq_of_le_of_finrank_eq'ₓ'. -/
 theorem eq_of_le_of_finrank_eq' [FiniteDimensional K L] (h_le : F ≤ E)
     (h_finrank : finrank F L = finrank E L) : F = E :=
   eq_of_le_of_finrank_le' h_le h_finrank.le
@@ -719,14 +1301,32 @@ theorem eq_of_le_of_finrank_eq' [FiniteDimensional K L] (h_le : F ≤ E)
 
 end FiniteDimensional
 
+/- warning: intermediate_field.is_algebraic_iff -> IntermediateField.isAlgebraic_iff is a dubious translation:
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 theorem isAlgebraic_iff {x : S} : IsAlgebraic K x ↔ IsAlgebraic K (x : L) :=
   (isAlgebraic_algebraMap_iff (algebraMap S L).Injective).symm
 #align intermediate_field.is_algebraic_iff IntermediateField.isAlgebraic_iff
 
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 theorem isIntegral_iff {x : S} : IsIntegral K x ↔ IsIntegral K (x : L) := by
   rw [← isAlgebraic_iff_isIntegral, is_algebraic_iff, isAlgebraic_iff_isIntegral]
 #align intermediate_field.is_integral_iff IntermediateField.isIntegral_iff
 
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 theorem minpoly_eq (x : S) : minpoly K x = minpoly K (x : L) :=
   by
   by_cases hx : IsIntegral K x
@@ -736,6 +1336,12 @@ theorem minpoly_eq (x : S) : minpoly K x = minpoly K (x : L) :=
 
 end IntermediateField
 
+/- warning: subalgebra_equiv_intermediate_field -> subalgebraEquivIntermediateField 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_equiv_intermediate_field subalgebraEquivIntermediateFieldₓ'. -/
 /-- If `L/K` is algebraic, the `K`-subalgebras of `L` are all fields.  -/
 def subalgebraEquivIntermediateField (alg : Algebra.IsAlgebraic K L) :
     Subalgebra K L ≃o IntermediateField K L
@@ -747,12 +1353,24 @@ def subalgebraEquivIntermediateField (alg : Algebra.IsAlgebraic K L) :
   map_rel_iff' S S' := Iff.rfl
 #align subalgebra_equiv_intermediate_field subalgebraEquivIntermediateField
 
+/- warning: mem_subalgebra_equiv_intermediate_field -> mem_subalgebraEquivIntermediateField is a dubious translation:
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(Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (Algebra.instCompleteLatticeSubalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) => LE.le.{u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (Preorder.toLE.{u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (PartialOrder.toPreorder.{u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instPartialOrder.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (fun (_x : Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) => IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (RelHomClass.toFunLike.{u1, u1, u1} (RelIso.{u1, u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) => LE.le.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (Algebra.instCompleteLatticeSubalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) => LE.le.{u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (Preorder.toLE.{u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (PartialOrder.toPreorder.{u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instPartialOrder.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) => LE.le.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (Algebra.instCompleteLatticeSubalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) => LE.le.{u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (Preorder.toLE.{u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (PartialOrder.toPreorder.{u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instPartialOrder.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{u1, u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) => LE.le.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (Algebra.instCompleteLatticeSubalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) => LE.le.{u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (Preorder.toLE.{u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (PartialOrder.toPreorder.{u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instPartialOrder.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) (subalgebraEquivIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4 alg) S)) (Membership.mem.{u1, u1} L (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) L (Subalgebra.instSetLikeSubalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4)) x S)
+Case conversion may be inaccurate. Consider using '#align mem_subalgebra_equiv_intermediate_field mem_subalgebraEquivIntermediateFieldₓ'. -/
 @[simp]
 theorem mem_subalgebraEquivIntermediateField (alg : Algebra.IsAlgebraic K L) {S : Subalgebra K L}
     {x : L} : x ∈ subalgebraEquivIntermediateField alg S ↔ x ∈ S :=
   Iff.rfl
 #align mem_subalgebra_equiv_intermediate_field mem_subalgebraEquivIntermediateField
 
+/- warning: mem_subalgebra_equiv_intermediate_field_symm -> mem_subalgebraEquivIntermediateField_symm is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : Field.{u2} L] [_inst_4 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)))] (alg : Algebra.IsAlgebraic.{u1, u2} K L (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1)) (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2)) _inst_4) {S : IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4} {x : L}, Iff (Membership.Mem.{u2, u2} L (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_4) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_4) L (Subalgebra.setLike.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_4)) x (coeFn.{succ u2, succ u2} (OrderIso.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_4) (Preorder.toHasLe.{u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (PartialOrder.toPreorder.{u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.partialOrder.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)))) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_4) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_4) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_4) L (Subalgebra.setLike.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_4))))) (fun (_x : RelIso.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_4) (LE.le.{u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (Preorder.toHasLe.{u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (PartialOrder.toPreorder.{u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.partialOrder.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4))))) (LE.le.{u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_4) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_4) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_4) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_4) L (Subalgebra.setLike.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_4)))))) => (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) -> (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_4)) (RelIso.hasCoeToFun.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_4) (LE.le.{u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (Preorder.toHasLe.{u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (PartialOrder.toPreorder.{u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.partialOrder.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4))))) (LE.le.{u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_4) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_4) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_4) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_4) L (Subalgebra.setLike.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_4)))))) (OrderIso.symm.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_4) (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_4) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_4) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_4) L (Subalgebra.setLike.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_2))) _inst_4)))) (Preorder.toHasLe.{u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (PartialOrder.toPreorder.{u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.partialOrder.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)))) (subalgebraEquivIntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4 alg)) S)) (Membership.Mem.{u2, u2} L (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) (SetLike.hasMem.{u2, u2} (IntermediateField.{u1, u2} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.setLike.{u1, u2} K L _inst_1 _inst_2 _inst_4)) x S)
+but is expected to have type
+  forall {K : Type.{u2}} {L : Type.{u1}} [_inst_1 : Field.{u2} K] [_inst_2 : Field.{u1} L] [_inst_4 : Algebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2)))] (alg : Algebra.IsAlgebraic.{u2, u1} K L (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)) (DivisionRing.toRing.{u1} L (Field.toDivisionRing.{u1} L _inst_2)) _inst_4) {S : IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4} {x : L}, Iff (Membership.mem.{u1, u1} L (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) L (Subalgebra.instSetLikeSubalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4)) x (FunLike.coe.{succ u1, succ u1, succ u1} (RelIso.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) => LE.le.{u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (Preorder.toLE.{u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (PartialOrder.toPreorder.{u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instPartialOrder.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) => LE.le.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (Algebra.instCompleteLatticeSubalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (fun (_x : IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) => Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (RelHomClass.toFunLike.{u1, u1, u1} (RelIso.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) => LE.le.{u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (Preorder.toLE.{u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (PartialOrder.toPreorder.{u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instPartialOrder.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) => LE.le.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (Algebra.instCompleteLatticeSubalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) => LE.le.{u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (Preorder.toLE.{u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (PartialOrder.toPreorder.{u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instPartialOrder.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) => LE.le.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (Algebra.instCompleteLatticeSubalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) => LE.le.{u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (Preorder.toLE.{u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (PartialOrder.toPreorder.{u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instPartialOrder.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) => LE.le.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (Algebra.instCompleteLatticeSubalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) (OrderIso.symm.{u1, u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Subalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4) (Algebra.instCompleteLatticeSubalgebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_2))) _inst_4))))) (Preorder.toLE.{u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (PartialOrder.toPreorder.{u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instPartialOrder.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)))) (subalgebraEquivIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4 alg)) S)) (Membership.mem.{u1, u1} L (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (IntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4) L (IntermediateField.instSetLikeIntermediateField.{u2, u1} K L _inst_1 _inst_2 _inst_4)) x S)
+Case conversion may be inaccurate. Consider using '#align mem_subalgebra_equiv_intermediate_field_symm mem_subalgebraEquivIntermediateField_symmₓ'. -/
 @[simp]
 theorem mem_subalgebraEquivIntermediateField_symm (alg : Algebra.IsAlgebraic K L)
     {S : IntermediateField K L} {x : L} :

mathlib commit https://github.com/leanprover-community/mathlib/commit/d4437c68c8d350fc9d4e95e1e174409db35e30d7

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Anne Baanen
 
 ! This file was ported from Lean 3 source module field_theory.intermediate_field
-! leanprover-community/mathlib commit efed3cad43feb69219272b517de4aa4f21a81127
+! leanprover-community/mathlib commit c596622fccd6e0321979d94931c964054dea2d26
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -512,6 +512,10 @@ theorem fieldRange_val : S.val.fieldRange = S :=
   SetLike.ext' Subtype.range_val
 #align intermediate_field.field_range_val IntermediateField.fieldRange_val
 
+instance AlgHom.inhabited : Inhabited (S →ₐ[K] L) :=
+  ⟨S.val⟩
+#align intermediate_field.alg_hom.inhabited IntermediateField.AlgHom.inhabited
+
 theorem aeval_coe {R : Type _} [CommRing R] [Algebra R K] [Algebra R L] [IsScalarTower R K L]
     (x : S) (P : R[X]) : aeval (x : L) P = aeval x P :=
   by

mathlib commit https://github.com/leanprover-community/mathlib/commit/3905fa80e62c0898131285baab35559fbc4e5cda

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Anne Baanen
 
 ! This file was ported from Lean 3 source module field_theory.intermediate_field
-! leanprover-community/mathlib commit 039a089d2a4b93c761b234f3e5f5aeb752bac60f
+! leanprover-community/mathlib commit efed3cad43feb69219272b517de4aa4f21a81127
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -507,6 +507,11 @@ theorem range_val : S.val.range = S.toSubalgebra :=
   S.toSubalgebra.range_val
 #align intermediate_field.range_val IntermediateField.range_val
 
+@[simp]
+theorem fieldRange_val : S.val.fieldRange = S :=
+  SetLike.ext' Subtype.range_val
+#align intermediate_field.field_range_val IntermediateField.fieldRange_val
+
 theorem aeval_coe {R : Type _} [CommRing R] [Algebra R K] [Algebra R L] [IsScalarTower R K L]
     (x : S) (P : R[X]) : aeval (x : L) P = aeval x P :=
   by

mathlib commit https://github.com/leanprover-community/mathlib/commit/06a655b5fcfbda03502f9158bbf6c0f1400886f9

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Anne Baanen
 
 ! This file was ported from Lean 3 source module field_theory.intermediate_field
-! leanprover-community/mathlib commit 825edd3cd735e87495b0c2a2114fc3929eefce41
+! leanprover-community/mathlib commit 039a089d2a4b93c761b234f3e5f5aeb752bac60f
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -664,9 +664,9 @@ instance finiteDimensional_right [FiniteDimensional K L] : FiniteDimensional F L
 #align intermediate_field.finite_dimensional_right IntermediateField.finiteDimensional_right
 
 @[simp]
-theorem dim_eq_dim_subalgebra : Module.rank K F.toSubalgebra = Module.rank K F :=
+theorem rank_eq_rank_subalgebra : Module.rank K F.toSubalgebra = Module.rank K F :=
   rfl
-#align intermediate_field.dim_eq_dim_subalgebra IntermediateField.dim_eq_dim_subalgebra
+#align intermediate_field.rank_eq_rank_subalgebra IntermediateField.rank_eq_rank_subalgebra
 
 @[simp]
 theorem finrank_eq_finrank_subalgebra : finrank K F.toSubalgebra = finrank K F :=

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

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

@@ -234,9 +234,9 @@ protected theorem zsmul_mem {x : L} (hx : x ∈ S) (n : ℤ) : n • x ∈ S :=
   zsmul_mem hx n
 #align intermediate_field.zsmul_mem IntermediateField.zsmul_mem
 
-protected theorem coe_int_mem (n : ℤ) : (n : L) ∈ S :=
-  coe_int_mem S n
-#align intermediate_field.coe_int_mem IntermediateField.coe_int_mem
+protected theorem intCast_mem (n : ℤ) : (n : L) ∈ S :=
+  intCast_mem S n
+#align intermediate_field.coe_int_mem IntermediateField.intCast_mem
 
 protected theorem coe_add (x y : S) : (↑(x + y) : L) = ↑x + ↑y :=
   rfl
@@ -268,8 +268,12 @@ protected theorem coe_pow (x : S) (n : ℕ) : (↑(x ^ n : S) : L) = (x : L) ^ n
 
 end InheritedLemmas
 
-theorem coe_nat_mem (n : ℕ) : (n : L) ∈ S := by simpa using coe_int_mem S n
-#align intermediate_field.coe_nat_mem IntermediateField.coe_nat_mem
+theorem natCast_mem (n : ℕ) : (n : L) ∈ S := by simpa using intCast_mem S n
+#align intermediate_field.coe_nat_mem IntermediateField.natCast_mem
+
+-- 2024-04-05
+@[deprecated _root_.natCast_mem] alias coe_nat_mem := natCast_mem
+@[deprecated _root_.intCast_mem] alias coe_int_mem := intCast_mem
 
 end IntermediateField
 

The few useful lemmas can go to Data.Subtype.Basic and the other ones can be deleted.

@@ -301,7 +301,7 @@ def Subalgebra.toIntermediateField' (S : Subalgebra K L) (hS : IsField S) : Inte
     · rw [hx0, inv_zero]
       exact S.zero_mem
     letI hS' := hS.toField
-    obtain ⟨y, hy⟩ := hS.mul_inv_cancel (show (⟨x, hx⟩ : S) ≠ 0 from Subtype.ne_of_val_ne hx0)
+    obtain ⟨y, hy⟩ := hS.mul_inv_cancel (show (⟨x, hx⟩ : S) ≠ 0 from Subtype.coe_ne_coe.1 hx0)
     rw [Subtype.ext_iff, S.coe_mul, S.coe_one, Subtype.coe_mk, mul_eq_one_iff_inv_eq₀ hx0] at hy
     exact hy.symm ▸ y.2
 #align subalgebra.to_intermediate_field' Subalgebra.toIntermediateField'

Homogenises porting notes via capitalisation and addition of whitespace.

It makes the following changes:

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

@@ -634,7 +634,7 @@ def lift {F : IntermediateField K L} (E : IntermediateField K F) : IntermediateF
   E.map (val F)
 #align intermediate_field.lift IntermediateField.lift
 
---Porting note: change from `HasLiftT` to `CoeOut`
+-- Porting note: change from `HasLiftT` to `CoeOut`
 instance hasLift {F : IntermediateField K L} :
     CoeOut (IntermediateField K F) (IntermediateField K L) :=
   ⟨lift⟩

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

@@ -80,7 +80,7 @@ instance : SubfieldClass (IntermediateField K L) L where
   one_mem {s} := s.one_mem'
   inv_mem {s} := s.inv_mem' _
 
---@[simp] Porting note: simp can prove it
+--@[simp] Porting note (#10618): simp can prove it
 theorem mem_carrier {s : IntermediateField K L} {x : L} : x ∈ s.carrier ↔ x ∈ s :=
   Iff.rfl
 #align intermediate_field.mem_carrier IntermediateField.mem_carrier
@@ -342,7 +342,7 @@ theorem coe_sum {ι : Type*} [Fintype ι] (f : ι → S) : (↑(∑ i, f i) : L)
     · rw [Finset.sum_insert hi, AddMemClass.coe_add, H, Finset.sum_insert hi]
 #align intermediate_field.coe_sum IntermediateField.coe_sum
 
-@[norm_cast] --Porting note: `simp` can prove it
+@[norm_cast] --Porting note (#10618): `simp` can prove it
 theorem coe_prod {ι : Type*} [Fintype ι] (f : ι → S) : (↑(∏ i, f i) : L) = ∏ i, (f i : L) := by
   classical
     induction' (Finset.univ : Finset ι) using Finset.induction_on with i s hi H

These instances don't seem to be necessary (and there's evidence in a porting note that one of them used to be).

@@ -372,25 +372,13 @@ theorem coe_smul {R} [Semiring R] [SMul R K] [Module R L] [IsScalarTower R K L]
   rfl
 #align intermediate_field.coe_smul IntermediateField.coe_smul
 
-/- More general form of `IntermediateField.algebra`.
-
-This instance should have low priority since it is slow to fail:
-before failing, it will cause a search through all `SMul K' K` instances,
-which can quickly get expensive.
--/
-instance (priority := 500) algebra' {K'} [CommSemiring K'] [SMul K' K] [Algebra K' L]
-    [IsScalarTower K' K L] :
-    Algebra K' S :=
-  S.toSubalgebra.algebra'
-#align intermediate_field.algebra' IntermediateField.algebra'
+#noalign intermediate_field.algebra'
 
 instance algebra : Algebra K S :=
   inferInstanceAs (Algebra K S.toSubsemiring)
 #align intermediate_field.algebra IntermediateField.algebra
 
-instance toAlgebra {R : Type*} [Semiring R] [Algebra L R] : Algebra S R :=
-  S.toSubalgebra.toAlgebra
-#align intermediate_field.to_algebra IntermediateField.toAlgebra
+#noalign intermediate_field.to_algebra
 
 @[simp] lemma algebraMap_apply (x : S) : algebraMap S L x = x := rfl
 

Add map_injective and lift_injective for IntermediateField. Also minize the imports

@@ -3,8 +3,6 @@ Copyright (c) 2020 Anne Baanen. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Anne Baanen
 -/
-import Mathlib.FieldTheory.Minpoly.Field
-import Mathlib.FieldTheory.Subfield
 import Mathlib.FieldTheory.Tower
 
 #align_import field_theory.intermediate_field from "leanprover-community/mathlib"@"c596622fccd6e0321979d94931c964054dea2d26"
@@ -611,6 +609,12 @@ theorem toSubalgebra_injective :
   rw [← mem_toSubalgebra, ← mem_toSubalgebra, h]
 #align intermediate_field.to_subalgebra_injective IntermediateField.toSubalgebra_injective
 
+theorem map_injective (f : L →ₐ[K] L'):
+    Function.Injective (map f) := by
+  intro _ _ h
+  rwa [← toSubalgebra_injective.eq_iff, toSubalgebra_map, toSubalgebra_map,
+    (Subalgebra.map_injective f.injective).eq_iff, toSubalgebra_injective.eq_iff] at h
+
 variable (S)
 
 theorem set_range_subset : Set.range (algebraMap K L) ⊆ S :=
@@ -648,6 +652,9 @@ instance hasLift {F : IntermediateField K L} :
   ⟨lift⟩
 #align intermediate_field.has_lift IntermediateField.hasLift
 
+theorem lift_injective (F : IntermediateField K L) : Function.Injective F.lift :=
+  map_injective F.val
+
 section RestrictScalars
 
 variable (K)

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

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

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

@@ -374,7 +374,14 @@ theorem coe_smul {R} [Semiring R] [SMul R K] [Module R L] [IsScalarTower R K L]
   rfl
 #align intermediate_field.coe_smul IntermediateField.coe_smul
 
-instance algebra' {K'} [CommSemiring K'] [SMul K' K] [Algebra K' L] [IsScalarTower K' K L] :
+/- More general form of `IntermediateField.algebra`.
+
+This instance should have low priority since it is slow to fail:
+before failing, it will cause a search through all `SMul K' K` instances,
+which can quickly get expensive.
+-/
+instance (priority := 500) algebra' {K'} [CommSemiring K'] [SMul K' K] [Algebra K' L]
+    [IsScalarTower K' K L] :
     Algebra K' S :=
   S.toSubalgebra.algebra'
 #align intermediate_field.algebra' IntermediateField.algebra'

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

@@ -460,7 +460,7 @@ theorem gc_map_comap (f :L →ₐ[K] L') : GaloisConnection (map f) (comap f) :=
   fun _ _ ↦ map_le_iff_le_comap
 
 /-- Given an equivalence `e : L ≃ₐ[K] L'` of `K`-field extensions and an intermediate
-field `E` of `L/K`, `intermediate_field_equiv_map e E` is the induced equivalence
+field `E` of `L/K`, `intermediateFieldMap e E` is the induced equivalence
 between `E` and `E.map e` -/
 def intermediateFieldMap (e : L ≃ₐ[K] L') (E : IntermediateField K L) : E ≃ₐ[K] E.map e.toAlgHom :=
   e.subalgebraMap E.toSubalgebra

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

@@ -387,6 +387,10 @@ instance toAlgebra {R : Type*} [Semiring R] [Algebra L R] : Algebra S R :=
   S.toSubalgebra.toAlgebra
 #align intermediate_field.to_algebra IntermediateField.toAlgebra
 
+@[simp] lemma algebraMap_apply (x : S) : algebraMap S L x = x := rfl
+
+@[simp] lemma coe_algebraMap_apply (x : K) : ↑(algebraMap K S x) = algebraMap K L x := rfl
+
 instance isScalarTower_bot {R : Type*} [Semiring R] [Algebra L R] : IsScalarTower S L R :=
   IsScalarTower.subalgebra _ _ _ S.toSubalgebra
 #align intermediate_field.is_scalar_tower_bot IntermediateField.isScalarTower_bot

Removes manual letI/haveI that appear in four proofs of #9041

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

@@ -401,6 +401,14 @@ instance isScalarTower_mid' : IsScalarTower K S L :=
   S.isScalarTower_mid
 #align intermediate_field.is_scalar_tower_mid' IntermediateField.isScalarTower_mid'
 
+section shortcut_instances
+variable {E} [Field E] [Algebra L E] (T : IntermediateField S E) {S}
+instance : Algebra S T := T.algebra
+instance : Module S T := Algebra.toModule
+instance : SMul S T := Algebra.toSMul
+instance [Algebra K E] [IsScalarTower K L E] : IsScalarTower K S T := T.isScalarTower
+end shortcut_instances
+
 /-- Given `f : L →ₐ[K] L'`, `S.comap f` is the intermediate field between `K` and `L`
   such that `f x ∈ S ↔ x ∈ S.comap f`. -/
 def comap (f : L →ₐ[K] L') (S : IntermediateField K L') : IntermediateField K L where

• generalize IntermediateField.eq_of_le_of_finrank_{le|eq}: the condition FiniteDimensional K L is generalized to FiniteDimensional K E (credits: @riccardobrasca)
• generalize IntermediateField.eq_of_le_of_finrank_{le|eq}': the condition FiniteDimensional K L is generalized to FiniteDimensional F L (original proof credits: @riccardobrasca)
• add Subalgebra.eq_of_le_of_finrank_{le|eq}
• add IntermediateField.extendScalars and its basic properties

@@ -675,6 +675,55 @@ end RestrictScalars
 /-- This was formerly an instance called `lift2_alg`, but an instance above already provides it. -/
 example {F : IntermediateField K L} {E : IntermediateField F L} : Algebra K E := by infer_instance
 
+section ExtendScalars
+
+variable {F E E' : IntermediateField K L} (h : F ≤ E) (h' : F ≤ E') {x : L}
+
+/-- If `F ≤ E` are two intermediate fields of `L / K`, then `E` is also an intermediate field of
+`L / F`. It can be viewed as an inverse to `IntermediateField.restrictScalars`. -/
+def extendScalars : IntermediateField F L := E.toSubfield.toIntermediateField fun ⟨_, hf⟩ ↦ h hf
+
+@[simp]
+theorem coe_extendScalars : (extendScalars h : Set L) = (E : Set L) := rfl
+
+@[simp]
+theorem extendScalars_toSubfield : (extendScalars h).toSubfield = E.toSubfield :=
+  SetLike.coe_injective rfl
+
+@[simp]
+theorem mem_extendScalars : x ∈ extendScalars h ↔ x ∈ E := Iff.rfl
+
+@[simp]
+theorem extendScalars_restrictScalars : (extendScalars h).restrictScalars K = E := rfl
+
+theorem extendScalars_le_extendScalars_iff : extendScalars h ≤ extendScalars h' ↔ E ≤ E' := Iff.rfl
+
+theorem extendScalars_le_iff (E' : IntermediateField F L) :
+    extendScalars h ≤ E' ↔ E ≤ E'.restrictScalars K := Iff.rfl
+
+theorem le_extendScalars_iff (E' : IntermediateField F L) :
+    E' ≤ extendScalars h ↔ E'.restrictScalars K ≤ E := Iff.rfl
+
+variable (F)
+
+/-- `IntermediateField.extendScalars` is an order isomorphism from
+`{ E : IntermediateField K L // F ≤ E }` to `IntermediateField F L`. Its inverse is
+`IntermediateField.restrictScalars`. -/
+def extendScalars.orderIso : { E : IntermediateField K L // F ≤ E } ≃o IntermediateField F L where
+  toFun E := extendScalars E.2
+  invFun E := ⟨E.restrictScalars K, fun x hx ↦ E.algebraMap_mem ⟨x, hx⟩⟩
+  left_inv E := rfl
+  right_inv E := rfl
+  map_rel_iff' {E E'} := by
+    simp only [Equiv.coe_fn_mk]
+    exact extendScalars_le_extendScalars_iff _ _
+
+theorem extendScalars_injective :
+    Function.Injective fun E : { E : IntermediateField K L // F ≤ E } ↦ extendScalars E.2 :=
+  (extendScalars.orderIso F).injective
+
+end ExtendScalars
+
 end Tower
 
 section FiniteDimensional
@@ -707,27 +756,45 @@ theorem toSubalgebra_eq_iff : F.toSubalgebra = E.toSubalgebra ↔ F = E := by
   rfl
 #align intermediate_field.to_subalgebra_eq_iff IntermediateField.toSubalgebra_eq_iff
 
-nonrec theorem eq_of_le_of_finrank_le [FiniteDimensional K L] (h_le : F ≤ E)
+/-- If `F ≤ E` are two intermediate fields of `L / K` such that `[E : K] ≤ [F : K]` are finite,
+then `F = E`. -/
+theorem eq_of_le_of_finrank_le [hfin : FiniteDimensional K E] (h_le : F ≤ E)
     (h_finrank : finrank K E ≤ finrank K F) : F = E :=
-  toSubalgebra_injective <|
-    Subalgebra.toSubmodule.injective <| eq_of_le_of_finrank_le h_le h_finrank
+  haveI : Module.Finite K E.toSubalgebra := hfin
+  toSubalgebra_injective <| Subalgebra.eq_of_le_of_finrank_le h_le h_finrank
 #align intermediate_field.eq_of_le_of_finrank_le IntermediateField.eq_of_le_of_finrank_le
 
-theorem eq_of_le_of_finrank_eq [FiniteDimensional K L] (h_le : F ≤ E)
+/-- If `F ≤ E` are two intermediate fields of `L / K` such that `[F : K] = [E : K]` are finite,
+then `F = E`. -/
+theorem eq_of_le_of_finrank_eq [FiniteDimensional K E] (h_le : F ≤ E)
     (h_finrank : finrank K F = finrank K E) : F = E :=
   eq_of_le_of_finrank_le h_le h_finrank.ge
 #align intermediate_field.eq_of_le_of_finrank_eq IntermediateField.eq_of_le_of_finrank_eq
 
-theorem eq_of_le_of_finrank_le' [FiniteDimensional K L] (h_le : F ≤ E)
+-- If `F ≤ E` are two intermediate fields of a finite extension `L / K` such that
+-- `[L : F] ≤ [L : E]`, then `F = E`. Marked as private since it's a direct corollary of
+-- `eq_of_le_of_finrank_le'` (the `FiniteDimensional K L` implies `FiniteDimensional F L`
+-- automatically by typeclass resolution).
+private theorem eq_of_le_of_finrank_le'' [FiniteDimensional K L] (h_le : F ≤ E)
     (h_finrank : finrank F L ≤ finrank E L) : F = E := by
   apply eq_of_le_of_finrank_le h_le
   have h1 := finrank_mul_finrank K F L
   have h2 := finrank_mul_finrank K E L
   have h3 : 0 < finrank E L := finrank_pos
   nlinarith
+
+/-- If `F ≤ E` are two intermediate fields of `L / K` such that `[L : F] ≤ [L : E]` are finite,
+then `F = E`. -/
+theorem eq_of_le_of_finrank_le' [FiniteDimensional F L] (h_le : F ≤ E)
+    (h_finrank : finrank F L ≤ finrank E L) : F = E := by
+  refine le_antisymm h_le (fun l hl ↦ ?_)
+  rwa [← mem_extendScalars (le_refl F), eq_of_le_of_finrank_le''
+    ((extendScalars_le_extendScalars_iff (le_refl F) h_le).2 h_le) h_finrank, mem_extendScalars]
 #align intermediate_field.eq_of_le_of_finrank_le' IntermediateField.eq_of_le_of_finrank_le'
 
-theorem eq_of_le_of_finrank_eq' [FiniteDimensional K L] (h_le : F ≤ E)
+/-- If `F ≤ E` are two intermediate fields of `L / K` such that `[L : F] = [L : E]` are finite,
+then `F = E`. -/
+theorem eq_of_le_of_finrank_eq' [FiniteDimensional F L] (h_le : F ≤ E)
     (h_finrank : finrank F L = finrank E L) : F = E :=
   eq_of_le_of_finrank_le' h_le h_finrank.le
 #align intermediate_field.eq_of_le_of_finrank_eq' IntermediateField.eq_of_le_of_finrank_eq'

Main changes are to the file NormalClosure:

• Introduce predicate IsNormalClosure to characterize normal closures L/F of a field extension K/F by the conditions that every minimal polynomial of an element of K over F splits in L, and that L is generated by roots of such polynomials. (When K/F is not necessarily algebraic, the conditions actually says L/F is a normal closure of the algebraic closure of F in K over F.

• IsNormalClosure.normal: a normal closure is always normal.

• isNormalClosure_iff : if K/F is algebraic, the "generated by roots" condition in IsNormalClosure can be replaced by "generated by images of embeddings". To prove it, we split out the two inclusions in restrictScalars_eq_iSup_adjoin and golf its proof. restrictScalars_eq_iSup_adjoin is renamed to normalClosure_eq_iSup_adjoin as it has nothing to do with restrictScalars.

• IsNormalClosure.lift: a normal closure of K/F embeds into any L/F such that the minpolys of K/F splits in L/F.

• IsNormalClosure.equiv: normal closures are unique up to F-algebra isomorphisms.

• isNormalClosure_normalClosure: normalClosure F K L is a valid normal closure if K/F is algebraic and all minpolys of K/F splits in L/F; in particular, if there is at least one F-embedding of K into L, and L/F is normal.

• Algebra.IsAlgebraic.cardinal_mk_algHom_le_of_splits: if every minpoly of K/F splits in L/F, then L is maximal w.r.t. F-embeddings of K, in the sense that K →ₐ[F] L achieves maximal cardinality.

In the file Normal:

• splits_of_mem_adjoin: If a set of algebraic elements in a field extension K/F have minimal polynomials that split in another extension L/F, then all minimal polynomials in the intermediate field generated by the set also split in L/F. This is in preparation for connecting IsNormalClosure and IsSplittingField.

In the file IntermediateField:

• Add comap and show it forms a Galois connection with map.

In the file FieldTheory/Adjoin:

• Add map_sup/iSup lemmas that follow from the Galois connection, plus an additional convenience lemma.

In the file RingTheory/Algebraic: add a lemma AlgHom.isAlgebraic_of_injective.

Co-authored-by: Jz Pan <acme_pjz@hotmail.com>

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

@@ -401,7 +401,13 @@ instance isScalarTower_mid' : IsScalarTower K S L :=
   S.isScalarTower_mid
 #align intermediate_field.is_scalar_tower_mid' IntermediateField.isScalarTower_mid'
 
-/-- If `f : L →+* L'` fixes `K`, `S.map f` is the intermediate field between `L'` and `K`
+/-- Given `f : L →ₐ[K] L'`, `S.comap f` is the intermediate field between `K` and `L`
+  such that `f x ∈ S ↔ x ∈ S.comap f`. -/
+def comap (f : L →ₐ[K] L') (S : IntermediateField K L') : IntermediateField K L where
+  __ := S.toSubalgebra.comap f
+  inv_mem' x hx := show f x⁻¹ ∈ S by rw [map_inv₀ f x]; exact S.inv_mem hx
+
+/-- Given `f : L →ₐ[K] L'`, `S.map f` is the intermediate field between `K` and `L'`
 such that `x ∈ S ↔ f x ∈ S.map f`. -/
 def map (f : L →ₐ[K] L') (S : IntermediateField K L) : IntermediateField K L' where
   __ := S.toSubalgebra.map f
@@ -433,6 +439,14 @@ theorem map_mono (f : L →ₐ[K] L') {S T : IntermediateField K L} (h : S ≤ T
     S.map f ≤ T.map f :=
   SetLike.coe_mono (Set.image_subset f h)
 
+theorem map_le_iff_le_comap {f : L →ₐ[K] L'}
+    {s : IntermediateField K L} {t : IntermediateField K L'} :
+    s.map f ≤ t ↔ s ≤ t.comap f :=
+  Set.image_subset_iff
+
+theorem gc_map_comap (f :L →ₐ[K] L') : GaloisConnection (map f) (comap f) :=
+  fun _ _ ↦ map_le_iff_le_comap
+
 /-- Given an equivalence `e : L ≃ₐ[K] L'` of `K`-field extensions and an intermediate
 field `E` of `L/K`, `intermediate_field_equiv_map e E` is the induced equivalence
 between `E` and `E.map e` -/

This eliminates (fun a ↦ β) α in the type when applying a FunLike.

Co-authored-by: Matthew Ballard <matt@mrb.email> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

@@ -533,9 +533,7 @@ theorem coe_isIntegral_iff {R : Type*} [CommRing R] [Algebra R K] [Algebra R L]
     refine' ⟨P, hPmo, (injective_iff_map_eq_zero _).1 (algebraMap (↥S) L).injective _ _⟩
     letI : IsScalarTower R S L := IsScalarTower.of_algebraMap_eq (congr_fun rfl)
     rw [eval₂_eq_eval_map, ← eval₂_at_apply, eval₂_eq_eval_map, Polynomial.map_map, ←
-      --Porting note: very strange that I have to `rw` twice with `eval₂_eq_eval_map`.
-      -- The first `rw` does nothing
-      IsScalarTower.algebraMap_eq, ← eval₂_eq_eval_map, ← eval₂_eq_eval_map]
+      IsScalarTower.algebraMap_eq, ← eval₂_eq_eval_map]
     exact hProot
   · obtain ⟨P, hPmo, hProot⟩ := h
     refine' ⟨P, hPmo, _⟩

@@ -403,13 +403,11 @@ instance isScalarTower_mid' : IsScalarTower K S L :=
 
 /-- If `f : L →+* L'` fixes `K`, `S.map f` is the intermediate field between `L'` and `K`
 such that `x ∈ S ↔ f x ∈ S.map f`. -/
-def map (f : L →ₐ[K] L') (S : IntermediateField K L) : IntermediateField K L' :=
-  {
-    S.toSubalgebra.map
-      f with
-    inv_mem' := by
-      rintro _ ⟨x, hx, rfl⟩
-      exact ⟨x⁻¹, S.inv_mem hx, map_inv₀ f x⟩ }
+def map (f : L →ₐ[K] L') (S : IntermediateField K L) : IntermediateField K L' where
+  __ := S.toSubalgebra.map f
+  inv_mem' := by
+    rintro _ ⟨x, hx, rfl⟩
+    exact ⟨x⁻¹, S.inv_mem hx, map_inv₀ f x⟩
 #align intermediate_field.map IntermediateField.map
 
 @[simp]
@@ -417,6 +415,14 @@ theorem coe_map (f : L →ₐ[K] L') : (S.map f : Set L') = f '' S :=
   rfl
 #align intermediate_field.coe_map IntermediateField.coe_map
 
+@[simp]
+theorem toSubalgebra_map (f : L →ₐ[K] L') : (S.map f).toSubalgebra = S.toSubalgebra.map f :=
+  rfl
+
+@[simp]
+theorem toSubfield_map (f : L →ₐ[K] L') : (S.map f).toSubfield = S.toSubfield.map f :=
+  rfl
+
 theorem map_map {K L₁ L₂ L₃ : Type*} [Field K] [Field L₁] [Algebra K L₁] [Field L₂] [Algebra K L₂]
     [Field L₃] [Algebra K L₃] (E : IntermediateField K L₁) (f : L₁ →ₐ[K] L₂) (g : L₂ →ₐ[K] L₃) :
     (E.map f).map g = E.map (g.comp f) :=
@@ -567,8 +573,9 @@ theorem coe_inclusion {E F : IntermediateField K L} (hEF : E ≤ F) (e : E) :
 
 variable {S}
 
-theorem toSubalgebra_injective {S S' : IntermediateField K L}
-    (h : S.toSubalgebra = S'.toSubalgebra) : S = S' := by
+theorem toSubalgebra_injective :
+    Function.Injective (IntermediateField.toSubalgebra : IntermediateField K L → _) := by
+  intro S S' h
   ext
   rw [← mem_toSubalgebra, ← mem_toSubalgebra, h]
 #align intermediate_field.to_subalgebra_injective IntermediateField.toSubalgebra_injective

This reverts commit f3695eb2.

@@ -436,13 +436,15 @@ def intermediateFieldMap (e : L ≃ₐ[K] L') (E : IntermediateField K L) : E 
 
 /- We manually add these two simp lemmas because `@[simps]` before `intermediate_field_map`
   led to a timeout. -/
-@[simp]
+-- This lemma has always been bad, but the linter only noticed after lean4#2644.
+@[simp, nolint simpNF]
 theorem intermediateFieldMap_apply_coe (e : L ≃ₐ[K] L') (E : IntermediateField K L) (a : E) :
     ↑(intermediateFieldMap e E a) = e a :=
   rfl
 #align intermediate_field.intermediate_field_map_apply_coe IntermediateField.intermediateFieldMap_apply_coe
 
-@[simp]
+-- This lemma has always been bad, but the linter only noticed after lean4#2644.
+@[simp, nolint simpNF]
 theorem intermediateFieldMap_symm_apply_coe (e : L ≃ₐ[K] L') (E : IntermediateField K L)
     (a : E.map e.toAlgHom) : ↑((intermediateFieldMap e E).symm a) = e.symm a :=
   rfl

This reverts commit 26eb2b0a.

@@ -436,15 +436,13 @@ def intermediateFieldMap (e : L ≃ₐ[K] L') (E : IntermediateField K L) : E 
 
 /- We manually add these two simp lemmas because `@[simps]` before `intermediate_field_map`
   led to a timeout. -/
--- This lemma has always been bad, but the linter only noticed after lean4#2644.
-@[simp, nolint simpNF]
+@[simp]
 theorem intermediateFieldMap_apply_coe (e : L ≃ₐ[K] L') (E : IntermediateField K L) (a : E) :
     ↑(intermediateFieldMap e E a) = e a :=
   rfl
 #align intermediate_field.intermediate_field_map_apply_coe IntermediateField.intermediateFieldMap_apply_coe
 
--- This lemma has always been bad, but the linter only noticed after lean4#2644.
-@[simp, nolint simpNF]
+@[simp]
 theorem intermediateFieldMap_symm_apply_coe (e : L ≃ₐ[K] L') (E : IntermediateField K L)
     (a : E.map e.toAlgHom) : ↑((intermediateFieldMap e E).symm a) = e.symm a :=
   rfl

This includes all the changes from #7606.

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

@@ -436,13 +436,15 @@ def intermediateFieldMap (e : L ≃ₐ[K] L') (E : IntermediateField K L) : E 
 
 /- We manually add these two simp lemmas because `@[simps]` before `intermediate_field_map`
   led to a timeout. -/
-@[simp]
+-- This lemma has always been bad, but the linter only noticed after lean4#2644.
+@[simp, nolint simpNF]
 theorem intermediateFieldMap_apply_coe (e : L ≃ₐ[K] L') (E : IntermediateField K L) (a : E) :
     ↑(intermediateFieldMap e E a) = e a :=
   rfl
 #align intermediate_field.intermediate_field_map_apply_coe IntermediateField.intermediateFieldMap_apply_coe
 
-@[simp]
+-- This lemma has always been bad, but the linter only noticed after lean4#2644.
+@[simp, nolint simpNF]
 theorem intermediateFieldMap_symm_apply_coe (e : L ≃ₐ[K] L') (E : IntermediateField K L)
     (a : E.map e.toAlgHom) : ↑((intermediateFieldMap e E).symm a) = e.symm a :=
   rfl

Also changes the repetitive names minpoly.minpoly_algHom/Equiv to minpoly.algHom/Equiv_eq

@@ -721,10 +721,8 @@ theorem isIntegral_iff {x : S} : IsIntegral K x ↔ IsIntegral K (x : L) := by
   rw [← isAlgebraic_iff_isIntegral, isAlgebraic_iff, isAlgebraic_iff_isIntegral]
 #align intermediate_field.is_integral_iff IntermediateField.isIntegral_iff
 
-theorem minpoly_eq (x : S) : minpoly K x = minpoly K (x : L) := by
-  by_cases hx : IsIntegral K x
-  · exact minpoly.eq_of_algebraMap_eq (algebraMap S L).injective hx rfl
-  · exact (minpoly.eq_zero hx).trans (minpoly.eq_zero (mt isIntegral_iff.mpr hx)).symm
+theorem minpoly_eq (x : S) : minpoly K x = minpoly K (x : L) :=
+  (minpoly.algebraMap_eq (algebraMap S L).injective x).symm
 #align intermediate_field.minpoly_eq IntermediateField.minpoly_eq
 
 end IntermediateField

This PR adds API and changes the definition of the normal closure of $F\leq K\leq L$ to be an intermediate field of L/F, rather than an intermediate field of L/K. For example, I think it would be more common to say that the normal closure of $\mathbb{Q}(\sqrt[3]{2})/\mathbb{Q}$ is $\mathbb{Q}(\sqrt[3]{2},\zeta_3)/\mathbb{Q}$ rather than $\mathbb{Q}(\sqrt[3]{2},\zeta_3)/\mathbb{Q}(\sqrt[3]{2})$. This change also means that the normal closure goes from being a dependent function (K : Type) → IntermediateField K L to being a non-dependent function Type → IntermediateField F L, making it easier to compare across the Galois corespondence.

Supersedes https://github.com/leanprover-community/mathlib/pull/18971

Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Thomas Browning <tb65536@users.noreply.github.com>

@@ -423,6 +423,10 @@ theorem map_map {K L₁ L₂ L₃ : Type*} [Field K] [Field L₁] [Algebra K L
   SetLike.coe_injective <| Set.image_image _ _ _
 #align intermediate_field.map_map IntermediateField.map_map
 
+theorem map_mono (f : L →ₐ[K] L') {S T : IntermediateField K L} (h : S ≤ T) :
+    S.map f ≤ T.map f :=
+  SetLike.coe_mono (Set.image_subset f h)
+
 /-- Given an equivalence `e : L ≃ₐ[K] L'` of `K`-field extensions and an intermediate
 field `E` of `L/K`, `intermediate_field_equiv_map e E` is the induced equivalence
 between `E` and `E.map e` -/

We clean up heart beat bumps after #6474.

@@ -664,15 +664,11 @@ instance finiteDimensional_right [FiniteDimensional K L] : FiniteDimensional F L
   right K F L
 #align intermediate_field.finite_dimensional_right IntermediateField.finiteDimensional_right
 
---Porting note: increased heartbeats
-set_option synthInstance.maxHeartbeats 25000 in
 @[simp]
 theorem rank_eq_rank_subalgebra : Module.rank K F.toSubalgebra = Module.rank K F :=
   rfl
 #align intermediate_field.rank_eq_rank_subalgebra IntermediateField.rank_eq_rank_subalgebra
 
---Porting note: increased heartbeats
-set_option synthInstance.maxHeartbeats 25000 in
 @[simp]
 theorem finrank_eq_finrank_subalgebra : finrank K F.toSubalgebra = finrank K F :=
   rfl

@@ -47,7 +47,6 @@ variable (K L L' : Type*) [Field K] [Field L] [Field L'] [Algebra K L] [Algebra
 /-- `S : IntermediateField K L` is a subset of `L` such that there is a field
 tower `L / S / K`. -/
 structure IntermediateField extends Subalgebra K L where
-  neg_mem' : ∀ x ∈ carrier, -x ∈ carrier
   inv_mem' : ∀ x ∈ carrier, x⁻¹ ∈ carrier
 #align intermediate_field IntermediateField
 
@@ -59,22 +58,26 @@ variable (S : IntermediateField K L)
 
 namespace IntermediateField
 
+instance : SetLike (IntermediateField K L) L :=
+  ⟨fun S => S.toSubalgebra.carrier, by
+    rintro ⟨⟨⟩⟩ ⟨⟨⟩⟩
+    simp ⟩
+
+protected theorem neg_mem {x : L} (hx : x ∈ S) : -x ∈ S := by
+  show -x ∈S.toSubalgebra; simpa
+#align intermediate_field.neg_mem IntermediateField.neg_mem
+
 /-- Reinterpret an `IntermediateField` as a `Subfield`. -/
 def toSubfield : Subfield L :=
   { S.toSubalgebra with
-    neg_mem' := S.neg_mem' _,
+    neg_mem' := S.neg_mem,
     inv_mem' := S.inv_mem' }
 #align intermediate_field.to_subfield IntermediateField.toSubfield
 
-instance : SetLike (IntermediateField K L) L :=
-  ⟨fun S => S.toSubalgebra.carrier, by
-    rintro ⟨⟨⟩⟩ ⟨⟨⟩⟩
-    simp ⟩
-
 instance : SubfieldClass (IntermediateField K L) L where
   add_mem {s} := s.add_mem'
   zero_mem {s} := s.zero_mem'
-  neg_mem {s} := s.neg_mem' _
+  neg_mem {s} := s.neg_mem
   mul_mem {s} := s.mul_mem'
   one_mem {s} := s.one_mem'
   inv_mem {s} := s.inv_mem' _
@@ -101,8 +104,8 @@ theorem coe_toSubfield : (S.toSubfield : Set L) = S :=
 #align intermediate_field.coe_to_subfield IntermediateField.coe_toSubfield
 
 @[simp]
-theorem mem_mk (s : Subsemiring L) (hK : ∀ x, algebraMap K L x ∈ s) (hn hi) (x : L) :
-    x ∈ IntermediateField.mk (Subalgebra.mk s hK) hn hi ↔ x ∈ s :=
+theorem mem_mk (s : Subsemiring L) (hK : ∀ x, algebraMap K L x ∈ s) (hi) (x : L) :
+    x ∈ IntermediateField.mk (Subalgebra.mk s hK) hi ↔ x ∈ s :=
   Iff.rfl
 #align intermediate_field.mem_mk IntermediateField.mem_mkₓ
 
@@ -121,9 +124,6 @@ definitional equalities. -/
 protected def copy (S : IntermediateField K L) (s : Set L) (hs : s = ↑S) : IntermediateField K L
     where
   toSubalgebra := S.toSubalgebra.copy s (hs : s = S.toSubalgebra.carrier)
-  neg_mem' :=
-    have hs' : (S.toSubalgebra.copy s hs).carrier = S.toSubalgebra.carrier := hs
-    hs'.symm ▸ S.neg_mem'
   inv_mem' :=
     have hs' : (S.toSubalgebra.copy s hs).carrier = S.toSubalgebra.carrier := hs
     hs'.symm ▸ S.inv_mem'
@@ -184,11 +184,6 @@ protected theorem sub_mem {x y : L} : x ∈ S → y ∈ S → x - y ∈ S :=
   sub_mem
 #align intermediate_field.sub_mem IntermediateField.sub_mem
 
-/-- An intermediate field is closed under negation. -/
-protected theorem neg_mem {x : L} : x ∈ S → -x ∈ S :=
-  neg_mem
-#align intermediate_field.neg_mem IntermediateField.neg_mem
-
 /-- An intermediate field is closed under inverses. -/
 protected theorem inv_mem {x : L} : x ∈ S → x⁻¹ ∈ S :=
   inv_mem
@@ -284,7 +279,6 @@ end IntermediateField
 def Subalgebra.toIntermediateField (S : Subalgebra K L) (inv_mem : ∀ x ∈ S, x⁻¹ ∈ S) :
     IntermediateField K L :=
   { S with
-    neg_mem' := fun _ => S.neg_mem
     inv_mem' := inv_mem }
 #align subalgebra.to_intermediate_field Subalgebra.toIntermediateField
 
@@ -332,8 +326,7 @@ theorem toIntermediateField'_toSubalgebra (S : IntermediateField K L) :
 def Subfield.toIntermediateField (S : Subfield L) (algebra_map_mem : ∀ x, algebraMap K L x ∈ S) :
     IntermediateField K L :=
   { S with
-    algebraMap_mem' := algebra_map_mem
-    neg_mem' := fun _ => S.neg_mem' }
+    algebraMap_mem' := algebra_map_mem }
 #align subfield.to_intermediate_field Subfield.toIntermediateField
 
 namespace IntermediateField
@@ -416,8 +409,7 @@ def map (f : L →ₐ[K] L') (S : IntermediateField K L) : IntermediateField K L
       f with
     inv_mem' := by
       rintro _ ⟨x, hx, rfl⟩
-      exact ⟨x⁻¹, S.inv_mem hx, map_inv₀ f x⟩
-    neg_mem' := fun x hx => (S.toSubalgebra.map f).neg_mem hx }
+      exact ⟨x⁻¹, S.inv_mem hx, map_inv₀ f x⟩ }
 #align intermediate_field.map IntermediateField.map
 
 @[simp]
@@ -461,8 +453,7 @@ variable (f : L →ₐ[K] L')
 /-- The range of an algebra homomorphism, as an intermediate field. -/
 @[simps toSubalgebra]
 def fieldRange : IntermediateField K L' :=
-  { f.range, (f : L →+* L').fieldRange with
-    neg_mem' := fun _ => (f : L →+* L').fieldRange.neg_mem' }
+  { f.range, (f : L →+* L').fieldRange with }
 #align alg_hom.field_range AlgHom.fieldRange
 
 @[simp]
@@ -622,8 +613,7 @@ variable [Algebra L' L] [IsScalarTower K L' L]
 `L`, reinterpret `E` as a `K`-intermediate field of `L`. -/
 def restrictScalars (E : IntermediateField L' L) : IntermediateField K L :=
   { E.toSubfield, E.toSubalgebra.restrictScalars K with
-    carrier := E.carrier,
-    neg_mem' := fun _ => E.neg_mem, }
+    carrier := E.carrier }
 #align intermediate_field.restrict_scalars IntermediateField.restrictScalars
 
 @[simp]

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

This has nice performance benefits.

@@ -42,7 +42,7 @@ open FiniteDimensional Polynomial
 
 open BigOperators Polynomial
 
-variable (K L L' : Type _) [Field K] [Field L] [Field L'] [Algebra K L] [Algebra K L']
+variable (K L L' : Type*) [Field K] [Field L] [Field L'] [Algebra K L] [Algebra K L']
 
 /-- `S : IntermediateField K L` is a subset of `L` such that there is a field
 tower `L / S / K`. -/
@@ -221,14 +221,14 @@ protected theorem multiset_sum_mem (m : Multiset L) : (∀ a ∈ m, a ∈ S) →
 
 /-- Product of elements of an intermediate field indexed by a `Finset` is in the intermediate_field.
 -/
-protected theorem prod_mem {ι : Type _} {t : Finset ι} {f : ι → L} (h : ∀ c ∈ t, f c ∈ S) :
+protected theorem prod_mem {ι : Type*} {t : Finset ι} {f : ι → L} (h : ∀ c ∈ t, f c ∈ S) :
     (∏ i in t, f i) ∈ S :=
   prod_mem h
 #align intermediate_field.prod_mem IntermediateField.prod_mem
 
 /-- Sum of elements in an `IntermediateField` indexed by a `Finset` is in the `IntermediateField`.
 -/
-protected theorem sum_mem {ι : Type _} {t : Finset ι} {f : ι → L} (h : ∀ c ∈ t, f c ∈ S) :
+protected theorem sum_mem {ι : Type*} {t : Finset ι} {f : ι → L} (h : ∀ c ∈ t, f c ∈ S) :
     (∑ i in t, f i) ∈ S :=
   sum_mem h
 #align intermediate_field.sum_mem IntermediateField.sum_mem
@@ -344,7 +344,7 @@ instance toField : Field S :=
 #align intermediate_field.to_field IntermediateField.toField
 
 @[simp, norm_cast]
-theorem coe_sum {ι : Type _} [Fintype ι] (f : ι → S) : (↑(∑ i, f i) : L) = ∑ i, (f i : L) := by
+theorem coe_sum {ι : Type*} [Fintype ι] (f : ι → S) : (↑(∑ i, f i) : L) = ∑ i, (f i : L) := by
   classical
     induction' (Finset.univ : Finset ι) using Finset.induction_on with i s hi H
     · simp
@@ -352,7 +352,7 @@ theorem coe_sum {ι : Type _} [Fintype ι] (f : ι → S) : (↑(∑ i, f i) : L
 #align intermediate_field.coe_sum IntermediateField.coe_sum
 
 @[norm_cast] --Porting note: `simp` can prove it
-theorem coe_prod {ι : Type _} [Fintype ι] (f : ι → S) : (↑(∏ i, f i) : L) = ∏ i, (f i : L) := by
+theorem coe_prod {ι : Type*} [Fintype ι] (f : ι → S) : (↑(∏ i, f i) : L) = ∏ i, (f i : L) := by
   classical
     induction' (Finset.univ : Finset ι) using Finset.induction_on with i s hi H
     · simp
@@ -390,15 +390,15 @@ instance algebra : Algebra K S :=
   inferInstanceAs (Algebra K S.toSubsemiring)
 #align intermediate_field.algebra IntermediateField.algebra
 
-instance toAlgebra {R : Type _} [Semiring R] [Algebra L R] : Algebra S R :=
+instance toAlgebra {R : Type*} [Semiring R] [Algebra L R] : Algebra S R :=
   S.toSubalgebra.toAlgebra
 #align intermediate_field.to_algebra IntermediateField.toAlgebra
 
-instance isScalarTower_bot {R : Type _} [Semiring R] [Algebra L R] : IsScalarTower S L R :=
+instance isScalarTower_bot {R : Type*} [Semiring R] [Algebra L R] : IsScalarTower S L R :=
   IsScalarTower.subalgebra _ _ _ S.toSubalgebra
 #align intermediate_field.is_scalar_tower_bot IntermediateField.isScalarTower_bot
 
-instance isScalarTower_mid {R : Type _} [Semiring R] [Algebra L R] [Algebra K R]
+instance isScalarTower_mid {R : Type*} [Semiring R] [Algebra L R] [Algebra K R]
     [IsScalarTower K L R] : IsScalarTower K S R :=
   IsScalarTower.subalgebra' _ _ _ S.toSubalgebra
 #align intermediate_field.is_scalar_tower_mid IntermediateField.isScalarTower_mid
@@ -425,7 +425,7 @@ theorem coe_map (f : L →ₐ[K] L') : (S.map f : Set L') = f '' S :=
   rfl
 #align intermediate_field.coe_map IntermediateField.coe_map
 
-theorem map_map {K L₁ L₂ L₃ : Type _} [Field K] [Field L₁] [Algebra K L₁] [Field L₂] [Algebra K L₂]
+theorem map_map {K L₁ L₂ L₃ : Type*} [Field K] [Field L₁] [Algebra K L₁] [Field L₂] [Algebra K L₂]
     [Field L₃] [Algebra K L₃] (E : IntermediateField K L₁) (f : L₁ →ₐ[K] L₂) (g : L₂ →ₐ[K] L₃) :
     (E.map f).map g = E.map (g.comp f) :=
   SetLike.coe_injective <| Set.image_image _ _ _
@@ -514,7 +514,7 @@ instance AlgHom.inhabited : Inhabited (S →ₐ[K] L) :=
   ⟨S.val⟩
 #align intermediate_field.alg_hom.inhabited IntermediateField.AlgHom.inhabited
 
-theorem aeval_coe {R : Type _} [CommRing R] [Algebra R K] [Algebra R L] [IsScalarTower R K L]
+theorem aeval_coe {R : Type*} [CommRing R] [Algebra R K] [Algebra R L] [IsScalarTower R K L]
     (x : S) (P : R[X]) : aeval (x : L) P = aeval x P := by
   refine' Polynomial.induction_on' P (fun f g hf hg => _) fun n r => _
   · rw [aeval_add, aeval_add, AddMemClass.coe_add, hf, hg]
@@ -523,7 +523,7 @@ theorem aeval_coe {R : Type _} [CommRing R] [Algebra R K] [Algebra R L] [IsScala
     rfl
 #align intermediate_field.aeval_coe IntermediateField.aeval_coe
 
-theorem coe_isIntegral_iff {R : Type _} [CommRing R] [Algebra R K] [Algebra R L]
+theorem coe_isIntegral_iff {R : Type*} [CommRing R] [Algebra R K] [Algebra R L]
     [IsScalarTower R K L] {x : S} : IsIntegral R (x : L) ↔ IsIntegral R x := by
   refine' ⟨fun h => _, fun h => _⟩
   · obtain ⟨P, hPmo, hProot⟩ := h

• depends on: #5966

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

@@ -2,16 +2,13 @@
 Copyright (c) 2020 Anne Baanen. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Anne Baanen
-
-! This file was ported from Lean 3 source module field_theory.intermediate_field
-! leanprover-community/mathlib commit c596622fccd6e0321979d94931c964054dea2d26
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.FieldTheory.Minpoly.Field
 import Mathlib.FieldTheory.Subfield
 import Mathlib.FieldTheory.Tower
 
+#align_import field_theory.intermediate_field from "leanprover-community/mathlib"@"c596622fccd6e0321979d94931c964054dea2d26"
+
 /-!
 # Intermediate fields
 

Part 2 of #5001

@@ -217,7 +217,7 @@ protected theorem multiset_prod_mem (m : Multiset L) : (∀ a ∈ m, a ∈ S) 
   multiset_prod_mem m
 #align intermediate_field.multiset_prod_mem IntermediateField.multiset_prod_mem
 
-/-- Sum of a multiset of elements in a `IntermediateField` is in the `IntermediateField`. -/
+/-- Sum of a multiset of elements in an `IntermediateField` is in the `IntermediateField`. -/
 protected theorem multiset_sum_mem (m : Multiset L) : (∀ a ∈ m, a ∈ S) → m.sum ∈ S :=
   multiset_sum_mem m
 #align intermediate_field.multiset_sum_mem IntermediateField.multiset_sum_mem
@@ -229,7 +229,7 @@ protected theorem prod_mem {ι : Type _} {t : Finset ι} {f : ι → L} (h : ∀
   prod_mem h
 #align intermediate_field.prod_mem IntermediateField.prod_mem
 
-/-- Sum of elements in a `IntermediateField` indexed by a `Finset` is in the `IntermediateField`.
+/-- Sum of elements in an `IntermediateField` indexed by a `Finset` is in the `IntermediateField`.
 -/
 protected theorem sum_mem {ι : Type _} {t : Finset ι} {f : ι → L} (h : ∀ c ∈ t, f c ∈ S) :
     (∑ i in t, f i) ∈ S :=