linear_algebra.unitary_group ⟷ Mathlib.LinearAlgebra.UnitaryGroup

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

@@ -81,7 +81,7 @@ theorem mem_unitaryGroup_iff {A : Matrix n n α} : A ∈ Matrix.unitaryGroup n 
 theorem mem_unitaryGroup_iff' {A : Matrix n n α} : A ∈ Matrix.unitaryGroup n α ↔ star A * A = 1 :=
   by
   refine' ⟨And.left, fun hA => ⟨hA, _⟩⟩
-  rwa [mul_eq_mul, mul_eq_one_comm] at hA 
+  rwa [mul_eq_mul, mul_eq_one_comm] at hA
 #align matrix.mem_unitary_group_iff' Matrix.mem_unitaryGroup_iff'
 -/
 
@@ -280,7 +280,7 @@ theorem mem_orthogonalGroup_iff' {A : Matrix n n β} :
     A ∈ Matrix.orthogonalGroup n β ↔ star A * A = 1 :=
   by
   refine' ⟨And.left, fun hA => ⟨hA, _⟩⟩
-  rwa [mul_eq_mul, mul_eq_one_comm] at hA 
+  rwa [mul_eq_mul, mul_eq_one_comm] at hA
 #align matrix.mem_orthogonal_group_iff' Matrix.mem_orthogonalGroup_iff'
 -/
 

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

@@ -3,10 +3,10 @@ Copyright (c) 2021 Shing Tak Lam. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Shing Tak Lam
 -/
-import Mathbin.LinearAlgebra.GeneralLinearGroup
-import Mathbin.LinearAlgebra.Matrix.ToLin
-import Mathbin.LinearAlgebra.Matrix.NonsingularInverse
-import Mathbin.Algebra.Star.Unitary
+import LinearAlgebra.GeneralLinearGroup
+import LinearAlgebra.Matrix.ToLin
+import LinearAlgebra.Matrix.NonsingularInverse
+import Algebra.Star.Unitary
 
 #align_import linear_algebra.unitary_group from "leanprover-community/mathlib"@"33c67ae661dd8988516ff7f247b0be3018cdd952"
 

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

@@ -2,17 +2,14 @@
 Copyright (c) 2021 Shing Tak Lam. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Shing Tak Lam
-
-! This file was ported from Lean 3 source module linear_algebra.unitary_group
-! leanprover-community/mathlib commit 33c67ae661dd8988516ff7f247b0be3018cdd952
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.LinearAlgebra.GeneralLinearGroup
 import Mathbin.LinearAlgebra.Matrix.ToLin
 import Mathbin.LinearAlgebra.Matrix.NonsingularInverse
 import Mathbin.Algebra.Star.Unitary
 
+#align_import linear_algebra.unitary_group from "leanprover-community/mathlib"@"33c67ae661dd8988516ff7f247b0be3018cdd952"
+
 /-!
 # The Unitary Group
 

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

@@ -58,11 +58,13 @@ variable (n : Type u) [DecidableEq n] [Fintype n]
 
 variable (α : Type v) [CommRing α] [StarRing α]
 
+#print Matrix.unitaryGroup /-
 /-- `unitary_group n` is the group of `n` by `n` matrices where the star-transpose is the inverse.
 -/
 abbrev unitaryGroup :=
   unitary (Matrix n n α)
 #align matrix.unitary_group Matrix.unitaryGroup
+-/
 
 end
 
@@ -70,34 +72,45 @@ variable {n : Type u} [DecidableEq n] [Fintype n]
 
 variable {α : Type v} [CommRing α] [StarRing α]
 
+#print Matrix.mem_unitaryGroup_iff /-
 theorem mem_unitaryGroup_iff {A : Matrix n n α} : A ∈ Matrix.unitaryGroup n α ↔ A * star A = 1 :=
   by
   refine' ⟨And.right, fun hA => ⟨_, hA⟩⟩
   simpa only [mul_eq_mul, mul_eq_one_comm] using hA
 #align matrix.mem_unitary_group_iff Matrix.mem_unitaryGroup_iff
+-/
 
+#print Matrix.mem_unitaryGroup_iff' /-
 theorem mem_unitaryGroup_iff' {A : Matrix n n α} : A ∈ Matrix.unitaryGroup n α ↔ star A * A = 1 :=
   by
   refine' ⟨And.left, fun hA => ⟨hA, _⟩⟩
   rwa [mul_eq_mul, mul_eq_one_comm] at hA 
 #align matrix.mem_unitary_group_iff' Matrix.mem_unitaryGroup_iff'
+-/
 
+#print Matrix.det_of_mem_unitary /-
 theorem det_of_mem_unitary {A : Matrix n n α} (hA : A ∈ Matrix.unitaryGroup n α) :
     A.det ∈ unitary α := by
   constructor
   · simpa [star, det_transpose] using congr_arg det hA.1
   · simpa [star, det_transpose] using congr_arg det hA.2
 #align matrix.det_of_mem_unitary Matrix.det_of_mem_unitary
+-/
 
 namespace UnitaryGroup
 
+#print Matrix.UnitaryGroup.coeMatrix /-
 instance coeMatrix : Coe (unitaryGroup n α) (Matrix n n α) :=
   ⟨Subtype.val⟩
 #align matrix.unitary_group.coe_matrix Matrix.UnitaryGroup.coeMatrix
+-/
 
+#print Matrix.UnitaryGroup.coeFun /-
 instance coeFun : CoeFun (unitaryGroup n α) fun _ => n → n → α where coe A := A.val
 #align matrix.unitary_group.coe_fun Matrix.UnitaryGroup.coeFun
+-/
 
+#print Matrix.UnitaryGroup.toLin' /-
 /-- `to_lin' A` is matrix multiplication of vectors by `A`, as a linear map.
 
 After the group structure on `unitary_group n` is defined,
@@ -106,67 +119,91 @@ we show in `to_linear_equiv` that this gives a linear equivalence.
 def toLin' (A : unitaryGroup n α) :=
   Matrix.toLin' A
 #align matrix.unitary_group.to_lin' Matrix.UnitaryGroup.toLin'
+-/
 
+#print Matrix.UnitaryGroup.ext_iff /-
 theorem ext_iff (A B : unitaryGroup n α) : A = B ↔ ∀ i j, A i j = B i j :=
   Subtype.ext_iff_val.trans ⟨fun h i j => congr_fun (congr_fun h i) j, Matrix.ext⟩
 #align matrix.unitary_group.ext_iff Matrix.UnitaryGroup.ext_iff
+-/
 
+#print Matrix.UnitaryGroup.ext /-
 @[ext]
 theorem ext (A B : unitaryGroup n α) : (∀ i j, A i j = B i j) → A = B :=
   (UnitaryGroup.ext_iff A B).mpr
 #align matrix.unitary_group.ext Matrix.UnitaryGroup.ext
+-/
 
+#print Matrix.UnitaryGroup.star_mul_self /-
 @[simp]
 theorem star_mul_self (A : unitaryGroup n α) : star A ⬝ A = 1 :=
   A.2.1
 #align matrix.unitary_group.star_mul_self Matrix.UnitaryGroup.star_mul_self
+-/
 
 section CoeLemmas
 
 variable (A B : unitaryGroup n α)
 
+#print Matrix.UnitaryGroup.inv_val /-
 @[simp]
 theorem inv_val : ↑A⁻¹ = (star A : Matrix n n α) :=
   rfl
 #align matrix.unitary_group.inv_val Matrix.UnitaryGroup.inv_val
+-/
 
+#print Matrix.UnitaryGroup.inv_apply /-
 @[simp]
 theorem inv_apply : ⇑A⁻¹ = (star A : Matrix n n α) :=
   rfl
 #align matrix.unitary_group.inv_apply Matrix.UnitaryGroup.inv_apply
+-/
 
+#print Matrix.UnitaryGroup.mul_val /-
 @[simp]
 theorem mul_val : ↑(A * B) = A ⬝ B :=
   rfl
 #align matrix.unitary_group.mul_val Matrix.UnitaryGroup.mul_val
+-/
 
+#print Matrix.UnitaryGroup.mul_apply /-
 @[simp]
 theorem mul_apply : ⇑(A * B) = A ⬝ B :=
   rfl
 #align matrix.unitary_group.mul_apply Matrix.UnitaryGroup.mul_apply
+-/
 
+#print Matrix.UnitaryGroup.one_val /-
 @[simp]
 theorem one_val : ↑(1 : unitaryGroup n α) = (1 : Matrix n n α) :=
   rfl
 #align matrix.unitary_group.one_val Matrix.UnitaryGroup.one_val
+-/
 
+#print Matrix.UnitaryGroup.one_apply /-
 @[simp]
 theorem one_apply : ⇑(1 : unitaryGroup n α) = (1 : Matrix n n α) :=
   rfl
 #align matrix.unitary_group.one_apply Matrix.UnitaryGroup.one_apply
+-/
 
+#print Matrix.UnitaryGroup.toLin'_mul /-
 @[simp]
 theorem toLin'_mul : toLin' (A * B) = (toLin' A).comp (toLin' B) :=
   Matrix.toLin'_mul A B
 #align matrix.unitary_group.to_lin'_mul Matrix.UnitaryGroup.toLin'_mul
+-/
 
+#print Matrix.UnitaryGroup.toLin'_one /-
 @[simp]
 theorem toLin'_one : toLin' (1 : unitaryGroup n α) = LinearMap.id :=
   Matrix.toLin'_one
 #align matrix.unitary_group.to_lin'_one Matrix.UnitaryGroup.toLin'_one
+-/
 
 end CoeLemmas
 
+#print Matrix.UnitaryGroup.toLinearEquiv /-
 /-- `to_linear_equiv A` is matrix multiplication of vectors by `A`, as a linear equivalence. -/
 def toLinearEquiv (A : unitaryGroup n α) : (n → α) ≃ₗ[α] n → α :=
   { Matrix.toLin' A with
@@ -180,30 +217,41 @@ def toLinearEquiv (A : unitaryGroup n α) : (n → α) ≃ₗ[α] n → α :=
         (toLin' A).comp (toLin' A⁻¹) x = toLin' (A * A⁻¹) x := by rw [← to_lin'_mul]
         _ = x := by rw [mul_right_inv, to_lin'_one, id_apply] }
 #align matrix.unitary_group.to_linear_equiv Matrix.UnitaryGroup.toLinearEquiv
+-/
 
+#print Matrix.UnitaryGroup.toGL /-
 /-- `to_GL` is the map from the unitary group to the general linear group -/
 def toGL (A : unitaryGroup n α) : GeneralLinearGroup α (n → α) :=
   GeneralLinearGroup.ofLinearEquiv (toLinearEquiv A)
 #align matrix.unitary_group.to_GL Matrix.UnitaryGroup.toGL
+-/
 
+#print Matrix.UnitaryGroup.coe_toGL /-
 theorem coe_toGL (A : unitaryGroup n α) : ↑(toGL A) = toLin' A :=
   rfl
 #align matrix.unitary_group.coe_to_GL Matrix.UnitaryGroup.coe_toGL
+-/
 
+#print Matrix.UnitaryGroup.toGL_one /-
 @[simp]
 theorem toGL_one : toGL (1 : unitaryGroup n α) = 1 := by ext1 v i; rw [coe_to_GL, to_lin'_one]; rfl
 #align matrix.unitary_group.to_GL_one Matrix.UnitaryGroup.toGL_one
+-/
 
+#print Matrix.UnitaryGroup.toGL_mul /-
 @[simp]
 theorem toGL_mul (A B : unitaryGroup n α) : toGL (A * B) = toGL A * toGL B := by ext1 v i;
   rw [coe_to_GL, to_lin'_mul]; rfl
 #align matrix.unitary_group.to_GL_mul Matrix.UnitaryGroup.toGL_mul
+-/
 
+#print Matrix.UnitaryGroup.embeddingGL /-
 /-- `unitary_group.embedding_GL` is the embedding from `unitary_group n α`
 to `general_linear_group n α`. -/
 def embeddingGL : unitaryGroup n α →* GeneralLinearGroup α (n → α) :=
   ⟨fun A => toGL A, by simp, by simp⟩
 #align matrix.unitary_group.embedding_GL Matrix.UnitaryGroup.embeddingGL
+-/
 
 end UnitaryGroup
 
@@ -213,25 +261,31 @@ variable (n) (β : Type v) [CommRing β]
 
 attribute [local instance] starRingOfComm
 
+#print Matrix.orthogonalGroup /-
 /-- `orthogonal_group n` is the group of `n` by `n` matrices where the transpose is the inverse.
 -/
 abbrev orthogonalGroup :=
   unitaryGroup n β
 #align matrix.orthogonal_group Matrix.orthogonalGroup
+-/
 
+#print Matrix.mem_orthogonalGroup_iff /-
 theorem mem_orthogonalGroup_iff {A : Matrix n n β} :
     A ∈ Matrix.orthogonalGroup n β ↔ A * star A = 1 :=
   by
   refine' ⟨And.right, fun hA => ⟨_, hA⟩⟩
   simpa only [mul_eq_mul, mul_eq_one_comm] using hA
 #align matrix.mem_orthogonal_group_iff Matrix.mem_orthogonalGroup_iff
+-/
 
+#print Matrix.mem_orthogonalGroup_iff' /-
 theorem mem_orthogonalGroup_iff' {A : Matrix n n β} :
     A ∈ Matrix.orthogonalGroup n β ↔ star A * A = 1 :=
   by
   refine' ⟨And.left, fun hA => ⟨hA, _⟩⟩
   rwa [mul_eq_mul, mul_eq_one_comm] at hA 
 #align matrix.mem_orthogonal_group_iff' Matrix.mem_orthogonalGroup_iff'
+-/
 
 end OrthogonalGroup
 

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

@@ -175,12 +175,10 @@ def toLinearEquiv (A : unitaryGroup n α) : (n → α) ≃ₗ[α] n → α :=
       calc
         (toLin' A⁻¹).comp (toLin' A) x = (toLin' (A⁻¹ * A)) x := by rw [← to_lin'_mul]
         _ = x := by rw [mul_left_inv, to_lin'_one, id_apply]
-        
     right_inv := fun x =>
       calc
         (toLin' A).comp (toLin' A⁻¹) x = toLin' (A * A⁻¹) x := by rw [← to_lin'_mul]
-        _ = x := by rw [mul_right_inv, to_lin'_one, id_apply]
-         }
+        _ = x := by rw [mul_right_inv, to_lin'_one, id_apply] }
 #align matrix.unitary_group.to_linear_equiv Matrix.UnitaryGroup.toLinearEquiv
 
 /-- `to_GL` is the map from the unitary group to the general linear group -/

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

@@ -79,7 +79,7 @@ theorem mem_unitaryGroup_iff {A : Matrix n n α} : A ∈ Matrix.unitaryGroup n 
 theorem mem_unitaryGroup_iff' {A : Matrix n n α} : A ∈ Matrix.unitaryGroup n α ↔ star A * A = 1 :=
   by
   refine' ⟨And.left, fun hA => ⟨hA, _⟩⟩
-  rwa [mul_eq_mul, mul_eq_one_comm] at hA
+  rwa [mul_eq_mul, mul_eq_one_comm] at hA 
 #align matrix.mem_unitary_group_iff' Matrix.mem_unitaryGroup_iff'
 
 theorem det_of_mem_unitary {A : Matrix n n α} (hA : A ∈ Matrix.unitaryGroup n α) :
@@ -232,7 +232,7 @@ theorem mem_orthogonalGroup_iff' {A : Matrix n n β} :
     A ∈ Matrix.orthogonalGroup n β ↔ star A * A = 1 :=
   by
   refine' ⟨And.left, fun hA => ⟨hA, _⟩⟩
-  rwa [mul_eq_mul, mul_eq_one_comm] at hA
+  rwa [mul_eq_mul, mul_eq_one_comm] at hA 
 #align matrix.mem_orthogonal_group_iff' Matrix.mem_orthogonalGroup_iff'
 
 end OrthogonalGroup

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

@@ -50,7 +50,7 @@ namespace Matrix
 
 open LinearMap
 
-open Matrix
+open scoped Matrix
 
 section
 

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

@@ -58,12 +58,6 @@ variable (n : Type u) [DecidableEq n] [Fintype n]
 
 variable (α : Type v) [CommRing α] [StarRing α]
 
-/- warning: matrix.unitary_group -> Matrix.unitaryGroup is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align matrix.unitary_group Matrix.unitaryGroupₓ'. -/
 /-- `unitary_group n` is the group of `n` by `n` matrices where the star-transpose is the inverse.
 -/
 abbrev unitaryGroup :=
@@ -76,36 +70,18 @@ variable {n : Type u} [DecidableEq n] [Fintype n]
 
 variable {α : Type v} [CommRing α] [StarRing α]
 
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 theorem mem_unitaryGroup_iff {A : Matrix n n α} : A ∈ Matrix.unitaryGroup n α ↔ A * star A = 1 :=
   by
   refine' ⟨And.right, fun hA => ⟨_, hA⟩⟩
   simpa only [mul_eq_mul, mul_eq_one_comm] using hA
 #align matrix.mem_unitary_group_iff Matrix.mem_unitaryGroup_iff
 
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 theorem mem_unitaryGroup_iff' {A : Matrix n n α} : A ∈ Matrix.unitaryGroup n α ↔ star A * A = 1 :=
   by
   refine' ⟨And.left, fun hA => ⟨hA, _⟩⟩
   rwa [mul_eq_mul, mul_eq_one_comm] at hA
 #align matrix.mem_unitary_group_iff' Matrix.mem_unitaryGroup_iff'
 
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 theorem det_of_mem_unitary {A : Matrix n n α} (hA : A ∈ Matrix.unitaryGroup n α) :
     A.det ∈ unitary α := by
   constructor
@@ -115,31 +91,13 @@ theorem det_of_mem_unitary {A : Matrix n n α} (hA : A ∈ Matrix.unitaryGroup n
 
 namespace UnitaryGroup
 
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 instance coeMatrix : Coe (unitaryGroup n α) (Matrix n n α) :=
   ⟨Subtype.val⟩
 #align matrix.unitary_group.coe_matrix Matrix.UnitaryGroup.coeMatrix
 
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 instance coeFun : CoeFun (unitaryGroup n α) fun _ => n → n → α where coe A := A.val
 #align matrix.unitary_group.coe_fun Matrix.UnitaryGroup.coeFun
 
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 /-- `to_lin' A` is matrix multiplication of vectors by `A`, as a linear map.
 
 After the group structure on `unitary_group n` is defined,
@@ -149,24 +107,15 @@ def toLin' (A : unitaryGroup n α) :=
   Matrix.toLin' A
 #align matrix.unitary_group.to_lin' Matrix.UnitaryGroup.toLin'
 
-/- warning: matrix.unitary_group.ext_iff -> Matrix.UnitaryGroup.ext_iff is a dubious translation:
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 theorem ext_iff (A B : unitaryGroup n α) : A = B ↔ ∀ i j, A i j = B i j :=
   Subtype.ext_iff_val.trans ⟨fun h i j => congr_fun (congr_fun h i) j, Matrix.ext⟩
 #align matrix.unitary_group.ext_iff Matrix.UnitaryGroup.ext_iff
 
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 @[ext]
 theorem ext (A B : unitaryGroup n α) : (∀ i j, A i j = B i j) → A = B :=
   (UnitaryGroup.ext_iff A B).mpr
 #align matrix.unitary_group.ext Matrix.UnitaryGroup.ext
 
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 @[simp]
 theorem star_mul_self (A : unitaryGroup n α) : star A ⬝ A = 1 :=
   A.2.1
@@ -176,65 +125,41 @@ section CoeLemmas
 
 variable (A B : unitaryGroup n α)
 
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 @[simp]
 theorem inv_val : ↑A⁻¹ = (star A : Matrix n n α) :=
   rfl
 #align matrix.unitary_group.inv_val Matrix.UnitaryGroup.inv_val
 
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 @[simp]
 theorem inv_apply : ⇑A⁻¹ = (star A : Matrix n n α) :=
   rfl
 #align matrix.unitary_group.inv_apply Matrix.UnitaryGroup.inv_apply
 
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 @[simp]
 theorem mul_val : ↑(A * B) = A ⬝ B :=
   rfl
 #align matrix.unitary_group.mul_val Matrix.UnitaryGroup.mul_val
 
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 @[simp]
 theorem mul_apply : ⇑(A * B) = A ⬝ B :=
   rfl
 #align matrix.unitary_group.mul_apply Matrix.UnitaryGroup.mul_apply
 
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 @[simp]
 theorem one_val : ↑(1 : unitaryGroup n α) = (1 : Matrix n n α) :=
   rfl
 #align matrix.unitary_group.one_val Matrix.UnitaryGroup.one_val
 
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 @[simp]
 theorem one_apply : ⇑(1 : unitaryGroup n α) = (1 : Matrix n n α) :=
   rfl
 #align matrix.unitary_group.one_apply Matrix.UnitaryGroup.one_apply
 
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 @[simp]
 theorem toLin'_mul : toLin' (A * B) = (toLin' A).comp (toLin' B) :=
   Matrix.toLin'_mul A B
 #align matrix.unitary_group.to_lin'_mul Matrix.UnitaryGroup.toLin'_mul
 
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 @[simp]
 theorem toLin'_one : toLin' (1 : unitaryGroup n α) = LinearMap.id :=
   Matrix.toLin'_one
@@ -242,12 +167,6 @@ theorem toLin'_one : toLin' (1 : unitaryGroup n α) = LinearMap.id :=
 
 end CoeLemmas
 
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 /-- `to_linear_equiv A` is matrix multiplication of vectors by `A`, as a linear equivalence. -/
 def toLinearEquiv (A : unitaryGroup n α) : (n → α) ≃ₗ[α] n → α :=
   { Matrix.toLin' A with
@@ -264,42 +183,24 @@ def toLinearEquiv (A : unitaryGroup n α) : (n → α) ≃ₗ[α] n → α :=
          }
 #align matrix.unitary_group.to_linear_equiv Matrix.UnitaryGroup.toLinearEquiv
 
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 /-- `to_GL` is the map from the unitary group to the general linear group -/
 def toGL (A : unitaryGroup n α) : GeneralLinearGroup α (n → α) :=
   GeneralLinearGroup.ofLinearEquiv (toLinearEquiv A)
 #align matrix.unitary_group.to_GL Matrix.UnitaryGroup.toGL
 
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 theorem coe_toGL (A : unitaryGroup n α) : ↑(toGL A) = toLin' A :=
   rfl
 #align matrix.unitary_group.coe_to_GL Matrix.UnitaryGroup.coe_toGL
 
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 @[simp]
 theorem toGL_one : toGL (1 : unitaryGroup n α) = 1 := by ext1 v i; rw [coe_to_GL, to_lin'_one]; rfl
 #align matrix.unitary_group.to_GL_one Matrix.UnitaryGroup.toGL_one
 
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 @[simp]
 theorem toGL_mul (A B : unitaryGroup n α) : toGL (A * B) = toGL A * toGL B := by ext1 v i;
   rw [coe_to_GL, to_lin'_mul]; rfl
 #align matrix.unitary_group.to_GL_mul Matrix.UnitaryGroup.toGL_mul
 
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 /-- `unitary_group.embedding_GL` is the embedding from `unitary_group n α`
 to `general_linear_group n α`. -/
 def embeddingGL : unitaryGroup n α →* GeneralLinearGroup α (n → α) :=
@@ -314,24 +215,12 @@ variable (n) (β : Type v) [CommRing β]
 
 attribute [local instance] starRingOfComm
 
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 /-- `orthogonal_group n` is the group of `n` by `n` matrices where the transpose is the inverse.
 -/
 abbrev orthogonalGroup :=
   unitaryGroup n β
 #align matrix.orthogonal_group Matrix.orthogonalGroup
 
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 theorem mem_orthogonalGroup_iff {A : Matrix n n β} :
     A ∈ Matrix.orthogonalGroup n β ↔ A * star A = 1 :=
   by
@@ -339,12 +228,6 @@ theorem mem_orthogonalGroup_iff {A : Matrix n n β} :
   simpa only [mul_eq_mul, mul_eq_one_comm] using hA
 #align matrix.mem_orthogonal_group_iff Matrix.mem_orthogonalGroup_iff
 
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-Case conversion may be inaccurate. Consider using '#align matrix.mem_orthogonal_group_iff' Matrix.mem_orthogonalGroup_iff'ₓ'. -/
 theorem mem_orthogonalGroup_iff' {A : Matrix n n β} :
     A ∈ Matrix.orthogonalGroup n β ↔ star A * A = 1 :=
   by

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

@@ -286,22 +286,15 @@ theorem coe_toGL (A : unitaryGroup n α) : ↑(toGL A) = toLin' A :=
 <too large>
 Case conversion may be inaccurate. Consider using '#align matrix.unitary_group.to_GL_one Matrix.UnitaryGroup.toGL_oneₓ'. -/
 @[simp]
-theorem toGL_one : toGL (1 : unitaryGroup n α) = 1 :=
-  by
-  ext1 v i
-  rw [coe_to_GL, to_lin'_one]
-  rfl
+theorem toGL_one : toGL (1 : unitaryGroup n α) = 1 := by ext1 v i; rw [coe_to_GL, to_lin'_one]; rfl
 #align matrix.unitary_group.to_GL_one Matrix.UnitaryGroup.toGL_one
 
 /- warning: matrix.unitary_group.to_GL_mul -> Matrix.UnitaryGroup.toGL_mul is a dubious translation:
 <too large>
 Case conversion may be inaccurate. Consider using '#align matrix.unitary_group.to_GL_mul Matrix.UnitaryGroup.toGL_mulₓ'. -/
 @[simp]
-theorem toGL_mul (A B : unitaryGroup n α) : toGL (A * B) = toGL A * toGL B :=
-  by
-  ext1 v i
-  rw [coe_to_GL, to_lin'_mul]
-  rfl
+theorem toGL_mul (A B : unitaryGroup n α) : toGL (A * B) = toGL A * toGL B := by ext1 v i;
+  rw [coe_to_GL, to_lin'_mul]; rfl
 #align matrix.unitary_group.to_GL_mul Matrix.UnitaryGroup.toGL_mul
 
 /- warning: matrix.unitary_group.embedding_GL -> Matrix.UnitaryGroup.embeddingGL is a dubious translation:

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

@@ -150,20 +150,14 @@ def toLin' (A : unitaryGroup n α) :=
 #align matrix.unitary_group.to_lin' Matrix.UnitaryGroup.toLin'
 
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 Case conversion may be inaccurate. Consider using '#align matrix.unitary_group.ext_iff Matrix.UnitaryGroup.ext_iffₓ'. -/
 theorem ext_iff (A B : unitaryGroup n α) : A = B ↔ ∀ i j, A i j = B i j :=
   Subtype.ext_iff_val.trans ⟨fun h i j => congr_fun (congr_fun h i) j, Matrix.ext⟩
 #align matrix.unitary_group.ext_iff Matrix.UnitaryGroup.ext_iff
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align matrix.unitary_group.ext Matrix.UnitaryGroup.extₓ'. -/
 @[ext]
 theorem ext (A B : unitaryGroup n α) : (∀ i j, A i j = B i j) → A = B :=
@@ -171,10 +165,7 @@ theorem ext (A B : unitaryGroup n α) : (∀ i j, A i j = B i j) → A = B :=
 #align matrix.unitary_group.ext Matrix.UnitaryGroup.ext
 
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 Case conversion may be inaccurate. Consider using '#align matrix.unitary_group.star_mul_self Matrix.UnitaryGroup.star_mul_selfₓ'. -/
 @[simp]
 theorem star_mul_self (A : unitaryGroup n α) : star A ⬝ A = 1 :=
@@ -186,10 +177,7 @@ section CoeLemmas
 variable (A B : unitaryGroup n α)
 
 /- warning: matrix.unitary_group.inv_val -> Matrix.UnitaryGroup.inv_val is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align matrix.unitary_group.inv_val Matrix.UnitaryGroup.inv_valₓ'. -/
 @[simp]
 theorem inv_val : ↑A⁻¹ = (star A : Matrix n n α) :=
@@ -197,10 +185,7 @@ theorem inv_val : ↑A⁻¹ = (star A : Matrix n n α) :=
 #align matrix.unitary_group.inv_val Matrix.UnitaryGroup.inv_val
 
 /- warning: matrix.unitary_group.inv_apply -> Matrix.UnitaryGroup.inv_apply is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align matrix.unitary_group.inv_apply Matrix.UnitaryGroup.inv_applyₓ'. -/
 @[simp]
 theorem inv_apply : ⇑A⁻¹ = (star A : Matrix n n α) :=
@@ -208,10 +193,7 @@ theorem inv_apply : ⇑A⁻¹ = (star A : Matrix n n α) :=
 #align matrix.unitary_group.inv_apply Matrix.UnitaryGroup.inv_apply
 
 /- warning: matrix.unitary_group.mul_val -> Matrix.UnitaryGroup.mul_val is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align matrix.unitary_group.mul_val Matrix.UnitaryGroup.mul_valₓ'. -/
 @[simp]
 theorem mul_val : ↑(A * B) = A ⬝ B :=
@@ -219,10 +201,7 @@ theorem mul_val : ↑(A * B) = A ⬝ B :=
 #align matrix.unitary_group.mul_val Matrix.UnitaryGroup.mul_val
 
 /- warning: matrix.unitary_group.mul_apply -> Matrix.UnitaryGroup.mul_apply is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align matrix.unitary_group.mul_apply Matrix.UnitaryGroup.mul_applyₓ'. -/
 @[simp]
 theorem mul_apply : ⇑(A * B) = A ⬝ B :=
@@ -230,10 +209,7 @@ theorem mul_apply : ⇑(A * B) = A ⬝ B :=
 #align matrix.unitary_group.mul_apply Matrix.UnitaryGroup.mul_apply
 
 /- warning: matrix.unitary_group.one_val -> Matrix.UnitaryGroup.one_val is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align matrix.unitary_group.one_val Matrix.UnitaryGroup.one_valₓ'. -/
 @[simp]
 theorem one_val : ↑(1 : unitaryGroup n α) = (1 : Matrix n n α) :=
@@ -241,10 +217,7 @@ theorem one_val : ↑(1 : unitaryGroup n α) = (1 : Matrix n n α) :=
 #align matrix.unitary_group.one_val Matrix.UnitaryGroup.one_val
 
 /- warning: matrix.unitary_group.one_apply -> Matrix.UnitaryGroup.one_apply is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align matrix.unitary_group.one_apply Matrix.UnitaryGroup.one_applyₓ'. -/
 @[simp]
 theorem one_apply : ⇑(1 : unitaryGroup n α) = (1 : Matrix n n α) :=
@@ -252,10 +225,7 @@ theorem one_apply : ⇑(1 : unitaryGroup n α) = (1 : Matrix n n α) :=
 #align matrix.unitary_group.one_apply Matrix.UnitaryGroup.one_apply
 
 /- warning: matrix.unitary_group.to_lin'_mul -> Matrix.UnitaryGroup.toLin'_mul is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align matrix.unitary_group.to_lin'_mul Matrix.UnitaryGroup.toLin'_mulₓ'. -/
 @[simp]
 theorem toLin'_mul : toLin' (A * B) = (toLin' A).comp (toLin' B) :=
@@ -263,10 +233,7 @@ theorem toLin'_mul : toLin' (A * B) = (toLin' A).comp (toLin' B) :=
 #align matrix.unitary_group.to_lin'_mul Matrix.UnitaryGroup.toLin'_mul
 
 /- warning: matrix.unitary_group.to_lin'_one -> Matrix.UnitaryGroup.toLin'_one is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align matrix.unitary_group.to_lin'_one Matrix.UnitaryGroup.toLin'_oneₓ'. -/
 @[simp]
 theorem toLin'_one : toLin' (1 : unitaryGroup n α) = LinearMap.id :=
@@ -309,20 +276,14 @@ def toGL (A : unitaryGroup n α) : GeneralLinearGroup α (n → α) :=
 #align matrix.unitary_group.to_GL Matrix.UnitaryGroup.toGL
 
 /- warning: matrix.unitary_group.coe_to_GL -> Matrix.UnitaryGroup.coe_toGL is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align matrix.unitary_group.coe_to_GL Matrix.UnitaryGroup.coe_toGLₓ'. -/
 theorem coe_toGL (A : unitaryGroup n α) : ↑(toGL A) = toLin' A :=
   rfl
 #align matrix.unitary_group.coe_to_GL Matrix.UnitaryGroup.coe_toGL
 
 /- warning: matrix.unitary_group.to_GL_one -> Matrix.UnitaryGroup.toGL_one is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align matrix.unitary_group.to_GL_one Matrix.UnitaryGroup.toGL_oneₓ'. -/
 @[simp]
 theorem toGL_one : toGL (1 : unitaryGroup n α) = 1 :=
@@ -333,10 +294,7 @@ theorem toGL_one : toGL (1 : unitaryGroup n α) = 1 :=
 #align matrix.unitary_group.to_GL_one Matrix.UnitaryGroup.toGL_one
 
 /- warning: matrix.unitary_group.to_GL_mul -> Matrix.UnitaryGroup.toGL_mul is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align matrix.unitary_group.to_GL_mul Matrix.UnitaryGroup.toGL_mulₓ'. -/
 @[simp]
 theorem toGL_mul (A B : unitaryGroup n α) : toGL (A * B) = toGL A * toGL B :=
@@ -347,10 +305,7 @@ theorem toGL_mul (A B : unitaryGroup n α) : toGL (A * B) = toGL A * toGL B :=
 #align matrix.unitary_group.to_GL_mul Matrix.UnitaryGroup.toGL_mul
 
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α) (Monoid.toMulOneClass.{max u2 u1} (Matrix.{u1, u1, u2} n n α) (MonoidWithZero.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Semiring.toMonoidWithZero.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.semiring.{u2, u1} n α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))))) (Matrix.{u1, u1, u2} n n α) (Submonoid.instSetLikeSubmonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Monoid.toMulOneClass.{max u2 u1} (Matrix.{u1, u1, u2} n n α) (MonoidWithZero.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Semiring.toMonoidWithZero.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.semiring.{u2, u1} n α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))))))) x (Matrix.unitaryGroup.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 α _inst_3 _inst_4))) (LinearMap.GeneralLinearGroup.{u2, max u1 u2} α (n -> α) (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.UnitaryGroup._hyg.1486 : n) => α) α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (Submonoid.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Monoid.toMulOneClass.{max u2 u1} (Matrix.{u1, u1, u2} n n α) (MonoidWithZero.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Semiring.toMonoidWithZero.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.semiring.{u2, u1} n α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))))) (Matrix.unitaryGroup.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 α _inst_3 _inst_4)) (Units.instMulOneClassUnits.{max u1 u2} (LinearMap.{u2, u2, max u1 u2, max u1 u2} α α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (RingHom.id.{u2} α (Semiring.toNonAssocSemiring.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (n -> α) (n -> α) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.UnitaryGroup._hyg.1486 : n) => α) α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.UnitaryGroup._hyg.1486 : n) => α) α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (Module.End.monoid.{u2, max u1 u2} α (n -> α) (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.UnitaryGroup._hyg.1486 : n) => α) α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align matrix.unitary_group.embedding_GL Matrix.UnitaryGroup.embeddingGLₓ'. -/
 /-- `unitary_group.embedding_GL` is the embedding from `unitary_group n α`
 to `general_linear_group n α`. -/

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

@@ -138,7 +138,7 @@ instance coeFun : CoeFun (unitaryGroup n α) fun _ => n → n → α where coe A
 lean 3 declaration is
   forall {n : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] {α : Type.{u2}} [_inst_3 : CommRing.{u2} α] [_inst_4 : StarRing.{u2} α (NonUnitalRing.toNonUnitalSemiring.{u2} α (NonUnitalCommRing.toNonUnitalRing.{u2} α (CommRing.toNonUnitalCommRing.{u2} α _inst_3)))], (coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Submonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Monoid.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.ring.{u2, u1} n α _inst_2 (fun (a : n) (b : n) => (fun (a : n) (b : n) => _inst_1 a b) a b) (CommRing.toRing.{u2} α _inst_3))))) Type.{max u1 u2} (SetLike.hasCoeToSort.{max u1 u2, max u1 u2} (Submonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Monoid.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.ring.{u2, u1} n α _inst_2 (fun (a : n) (b : n) => (fun (a : n) (b : n) => _inst_1 a b) a b) (CommRing.toRing.{u2} α _inst_3))))) (Matrix.{u1, u1, u2} n n α) (Submonoid.setLike.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Monoid.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.ring.{u2, u1} n α _inst_2 (fun (a : n) (b : n) => (fun (a : n) (b : n) => _inst_1 a b) a b) (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.unitaryGroup.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 α _inst_3 _inst_4)) -> (LinearMap.{u2, u2, max u1 u2, max u1 u2} α α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (RingHom.id.{u2} α (Semiring.toNonAssocSemiring.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (n -> α) (n -> α) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} α (Semiring.toNonAssocSemiring.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))))) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} α (Semiring.toNonAssocSemiring.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))))) (Pi.Function.module.{u1, u2, u2} n α α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} α (Semiring.toNonAssocSemiring.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (Semiring.toModule.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (Pi.Function.module.{u1, u2, u2} n α α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} α (Semiring.toNonAssocSemiring.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (Semiring.toModule.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))))
 but is expected to have type
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(CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (RingHom.id.{u2} α (Semiring.toNonAssocSemiring.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (n -> α) (n -> α) (Pi.addCommMonoid.{u1, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} α (Semiring.toNonAssocSemiring.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))))) (Pi.addCommMonoid.{u1, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} α (Semiring.toNonAssocSemiring.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))))) (Pi.module.{u1, u2, u2} n (fun 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_inst_3))))) (Subtype.val.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (fun (x : Matrix.{u1, u1, u2} n n α) => Membership.mem.{max u1 u2, max u1 u2} (Matrix.{u1, u1, u2} n n α) (Submonoid.{max u2 u1} (Matrix.{u1, u1, u2} n n α) (Monoid.toMulOneClass.{max u2 u1} (Matrix.{u1, u1, u2} n n α) (MonoidWithZero.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Semiring.toMonoidWithZero.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.semiring.{u2, u1} n α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submonoid.{max u2 u1} (Matrix.{u1, u1, u2} n n α) (Monoid.toMulOneClass.{max u2 u1} (Matrix.{u1, u1, u2} n n α) (MonoidWithZero.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Semiring.toMonoidWithZero.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.semiring.{u2, u1} n α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))))) (Matrix.{u1, u1, u2} n n α) (Submonoid.instSetLikeSubmonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Monoid.toMulOneClass.{max u2 u1} (Matrix.{u1, u1, u2} n n α) (MonoidWithZero.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Semiring.toMonoidWithZero.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.semiring.{u2, u1} n α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))))))) x (Matrix.unitaryGroup.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 α _inst_3 _inst_4)) A)
+  forall {n : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] {α : Type.{u2}} [_inst_3 : CommRing.{u2} α] [_inst_4 : StarRing.{u2} α (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} α (NonUnitalCommRing.toNonUnitalCommSemiring.{u2} α (CommRing.toNonUnitalCommRing.{u2} α _inst_3)))] (A : Subtype.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n n α) (fun (x : Matrix.{u1, u1, u2} n n α) => Membership.mem.{max u1 u2, max u1 u2} (Matrix.{u1, u1, u2} n n α) (Submonoid.{max u2 u1} (Matrix.{u1, u1, u2} n n α) (Monoid.toMulOneClass.{max u2 u1} (Matrix.{u1, u1, u2} n n α) (MonoidWithZero.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Semiring.toMonoidWithZero.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.semiring.{u2, u1} n α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submonoid.{max u2 u1} (Matrix.{u1, u1, u2} n n α) (Monoid.toMulOneClass.{max u2 u1} (Matrix.{u1, u1, u2} n n α) (MonoidWithZero.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Semiring.toMonoidWithZero.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.semiring.{u2, u1} n α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))))) (Matrix.{u1, u1, u2} n n α) (Submonoid.instSetLikeSubmonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Monoid.toMulOneClass.{max u2 u1} (Matrix.{u1, u1, u2} n n α) (MonoidWithZero.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Semiring.toMonoidWithZero.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.semiring.{u2, u1} n α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))))))) x (Matrix.unitaryGroup.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 α _inst_3 _inst_4))), (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Matrix.{u1, u1, u2} n n α) => LinearMap.{u2, u2, max u2 u1, max u2 u1} α α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (RingHom.id.{u2} α (Semiring.toNonAssocSemiring.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (n -> α) (n -> α) (Pi.addCommMonoid.{u1, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} α (Semiring.toNonAssocSemiring.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))))) (Pi.addCommMonoid.{u1, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} α (Semiring.toNonAssocSemiring.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => α) α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} α (Semiring.toNonAssocSemiring.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => α) α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} α (Semiring.toNonAssocSemiring.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (Subtype.val.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (fun (x : Matrix.{u1, u1, u2} n n α) => Membership.mem.{max u1 u2, max u1 u2} (Matrix.{u1, u1, u2} n n α) (Submonoid.{max u2 u1} (Matrix.{u1, u1, u2} n n α) (Monoid.toMulOneClass.{max u2 u1} (Matrix.{u1, u1, u2} n n α) (MonoidWithZero.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Semiring.toMonoidWithZero.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.semiring.{u2, u1} n α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submonoid.{max u2 u1} (Matrix.{u1, u1, u2} n n α) (Monoid.toMulOneClass.{max u2 u1} (Matrix.{u1, u1, u2} n n α) (MonoidWithZero.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Semiring.toMonoidWithZero.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.semiring.{u2, u1} n α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))))) (Matrix.{u1, u1, u2} n n α) (Submonoid.instSetLikeSubmonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Monoid.toMulOneClass.{max u2 u1} (Matrix.{u1, u1, u2} n n α) (MonoidWithZero.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Semiring.toMonoidWithZero.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.semiring.{u2, u1} n α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))))))) x (Matrix.unitaryGroup.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 α _inst_3 _inst_4)) A)
 Case conversion may be inaccurate. Consider using '#align matrix.unitary_group.to_lin' Matrix.UnitaryGroup.toLin'ₓ'. -/
 /-- `to_lin' A` is matrix multiplication of vectors by `A`, as a linear map.
 
@@ -255,7 +255,7 @@ theorem one_apply : ⇑(1 : unitaryGroup n α) = (1 : Matrix n n α) :=
 lean 3 declaration is
   forall {n : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] {α : Type.{u2}} [_inst_3 : CommRing.{u2} α] [_inst_4 : StarRing.{u2} α (NonUnitalRing.toNonUnitalSemiring.{u2} α (NonUnitalCommRing.toNonUnitalRing.{u2} α (CommRing.toNonUnitalCommRing.{u2} α _inst_3)))] (A : coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Submonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Monoid.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.ring.{u2, u1} n α _inst_2 (fun (a : n) (b : n) => (fun (a : n) (b : n) => _inst_1 a b) a b) (CommRing.toRing.{u2} α _inst_3))))) Type.{max u1 u2} (SetLike.hasCoeToSort.{max u1 u2, max u1 u2} (Submonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Monoid.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.ring.{u2, u1} n α _inst_2 (fun (a : n) (b : n) => (fun (a : n) (b : n) => _inst_1 a b) a b) (CommRing.toRing.{u2} α _inst_3))))) (Matrix.{u1, u1, u2} n n α) (Submonoid.setLike.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Monoid.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.ring.{u2, u1} n α _inst_2 (fun (a : n) (b : n) => (fun (a : n) (b : n) => _inst_1 a b) a b) (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.unitaryGroup.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 α _inst_3 _inst_4)) (B : coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Submonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Monoid.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.ring.{u2, u1} n α _inst_2 (fun (a : n) (b : n) => (fun (a : n) (b : n) => _inst_1 a b) a b) (CommRing.toRing.{u2} α _inst_3))))) Type.{max u1 u2} (SetLike.hasCoeToSort.{max u1 u2, max u1 u2} (Submonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Monoid.toMulOneClass.{max u1 u2} (Matrix.{u1, 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α) (n -> α) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} α (Semiring.toNonAssocSemiring.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))))) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} α (Semiring.toNonAssocSemiring.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))))) (Pi.Function.module.{u1, u2, u2} n α α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} α (Semiring.toNonAssocSemiring.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (Semiring.toModule.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (Pi.Function.module.{u1, u2, u2} n α α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} α (Semiring.toNonAssocSemiring.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (Semiring.toModule.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (Matrix.UnitaryGroup.toLin'.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 α _inst_3 _inst_4 (HMul.hMul.{max u1 u2, max u1 u2, max u1 u2} (coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Submonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Monoid.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.ring.{u2, u1} n α _inst_2 (fun (a : n) (b : n) => (fun (a : n) (b : n) => _inst_1 a b) a b) (CommRing.toRing.{u2} α _inst_3))))) Type.{max u1 u2} (SetLike.hasCoeToSort.{max u1 u2, max u1 u2} (Submonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Monoid.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.ring.{u2, u1} n α _inst_2 (fun (a : n) (b : n) => (fun (a : n) (b : n) => _inst_1 a b) a b) (CommRing.toRing.{u2} α _inst_3))))) (Matrix.{u1, u1, u2} n n α) (Submonoid.setLike.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Monoid.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.ring.{u2, u1} n α _inst_2 (fun (a : n) (b : n) => (fun (a : n) (b : n) => _inst_1 a b) a b) (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.unitaryGroup.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 α _inst_3 _inst_4)) (coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Submonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Monoid.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.ring.{u2, u1} n α _inst_2 (fun (a : n) (b : n) => (fun (a : n) (b : n) => _inst_1 a b) a b) (CommRing.toRing.{u2} α _inst_3))))) Type.{max u1 u2} (SetLike.hasCoeToSort.{max u1 u2, max u1 u2} (Submonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Monoid.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.ring.{u2, u1} n α _inst_2 (fun (a : n) (b : n) => (fun (a : n) (b : n) => _inst_1 a b) a b) (CommRing.toRing.{u2} α _inst_3))))) (Matrix.{u1, u1, u2} n n α) (Submonoid.setLike.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Monoid.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.ring.{u2, u1} n α _inst_2 (fun (a : n) (b : n) => (fun (a : n) (b : n) => _inst_1 a b) a b) (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.unitaryGroup.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 α _inst_3 _inst_4)) (coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Submonoid.{max u1 u2} 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(Matrix.unitaryGroup.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 α _inst_3 _inst_4)) (instHMul.{max u1 u2} (coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Submonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Monoid.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.ring.{u2, u1} n α _inst_2 (fun (a : n) (b : n) => (fun (a : n) (b : n) => _inst_1 a b) a b) (CommRing.toRing.{u2} α _inst_3))))) Type.{max u1 u2} (SetLike.hasCoeToSort.{max u1 u2, max u1 u2} (Submonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Monoid.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.ring.{u2, u1} n α _inst_2 (fun (a : n) (b : n) => (fun (a : n) (b : n) => _inst_1 a b) a b) (CommRing.toRing.{u2} α _inst_3))))) (Matrix.{u1, u1, u2} n n α) (Submonoid.setLike.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Monoid.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 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(CommRing.toCommSemiring.{u2} α _inst_3)) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} α (Semiring.toNonAssocSemiring.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))))) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} α (Semiring.toNonAssocSemiring.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))))) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} α (Semiring.toNonAssocSemiring.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))))) (Pi.Function.module.{u1, u2, u2} n α α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} α (Semiring.toNonAssocSemiring.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (Semiring.toModule.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (Pi.Function.module.{u1, u2, u2} n α α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} α (Semiring.toNonAssocSemiring.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (Semiring.toModule.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (Pi.Function.module.{u1, u2, u2} n α α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} α (Semiring.toNonAssocSemiring.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (Semiring.toModule.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (RingHom.id.{u2} α (Semiring.toNonAssocSemiring.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (RingHom.id.{u2} α (Semiring.toNonAssocSemiring.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (RingHom.id.{u2} α (Semiring.toNonAssocSemiring.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (RingHomCompTriple.right_ids.{u2, u2} α α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (RingHom.id.{u2} α (Semiring.toNonAssocSemiring.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (Matrix.UnitaryGroup.toLin'.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 α _inst_3 _inst_4 A) (Matrix.UnitaryGroup.toLin'.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 α _inst_3 _inst_4 B))
 but is expected to have type
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b) _inst_2 α _inst_3 _inst_4))) A B))) (Matrix.UnitaryGroup.toLin'.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 α _inst_3 _inst_4 (HMul.hMul.{max u1 u2, max u1 u2, max u1 u2} (Subtype.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n n α) (fun (x : Matrix.{u1, u1, u2} n n α) => Membership.mem.{max u1 u2, max u1 u2} (Matrix.{u1, u1, u2} n n α) (Submonoid.{max u2 u1} (Matrix.{u1, u1, u2} n n α) (Monoid.toMulOneClass.{max u2 u1} (Matrix.{u1, u1, u2} n n α) (MonoidWithZero.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Semiring.toMonoidWithZero.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.semiring.{u2, u1} n α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submonoid.{max u2 u1} (Matrix.{u1, u1, u2} n n α) (Monoid.toMulOneClass.{max u2 u1} (Matrix.{u1, u1, u2} n n α) (MonoidWithZero.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Semiring.toMonoidWithZero.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.semiring.{u2, u1} n α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))))) (Matrix.{u1, u1, u2} n n α) (Submonoid.instSetLikeSubmonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Monoid.toMulOneClass.{max u2 u1} (Matrix.{u1, u1, u2} n n α) (MonoidWithZero.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Semiring.toMonoidWithZero.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.semiring.{u2, u1} n α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))))))) x (Matrix.unitaryGroup.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 α _inst_3 _inst_4))) (Subtype.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n n α) (fun (x : Matrix.{u1, u1, u2} n n α) => Membership.mem.{max u1 u2, max u1 u2} (Matrix.{u1, u1, u2} n n α) (Submonoid.{max u2 u1} (Matrix.{u1, u1, u2} n n α) (Monoid.toMulOneClass.{max u2 u1} (Matrix.{u1, u1, u2} n n α) (MonoidWithZero.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Semiring.toMonoidWithZero.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.semiring.{u2, u1} n α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submonoid.{max u2 u1} (Matrix.{u1, u1, u2} n n α) (Monoid.toMulOneClass.{max u2 u1} (Matrix.{u1, u1, u2} n n α) (MonoidWithZero.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Semiring.toMonoidWithZero.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.semiring.{u2, u1} n α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))))) (Matrix.{u1, u1, u2} n n α) (Submonoid.instSetLikeSubmonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Monoid.toMulOneClass.{max u2 u1} (Matrix.{u1, u1, u2} n n α) (MonoidWithZero.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Semiring.toMonoidWithZero.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.semiring.{u2, u1} n α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))))))) x (Matrix.unitaryGroup.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 α _inst_3 _inst_4))) (Subtype.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n n α) (fun (x : Matrix.{u1, u1, u2} n n α) => Membership.mem.{max u1 u2, max u1 u2} (Matrix.{u1, u1, u2} n n α) (Submonoid.{max u2 u1} (Matrix.{u1, u1, u2} n n α) (Monoid.toMulOneClass.{max u2 u1} (Matrix.{u1, u1, u2} n n α) (MonoidWithZero.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Semiring.toMonoidWithZero.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.semiring.{u2, u1} n α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submonoid.{max u2 u1} (Matrix.{u1, u1, 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Matrix.{u1, u1, u2} n n α) => Membership.mem.{max u1 u2, max u1 u2} (Matrix.{u1, u1, u2} n n α) (Submonoid.{max u2 u1} (Matrix.{u1, u1, u2} n n α) (Monoid.toMulOneClass.{max u2 u1} (Matrix.{u1, u1, u2} n n α) (MonoidWithZero.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Semiring.toMonoidWithZero.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.semiring.{u2, u1} n α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submonoid.{max u2 u1} (Matrix.{u1, u1, u2} n n α) (Monoid.toMulOneClass.{max u2 u1} (Matrix.{u1, u1, u2} n n α) (MonoidWithZero.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Semiring.toMonoidWithZero.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.semiring.{u2, u1} n α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))))) (Matrix.{u1, u1, u2} n n α) (Submonoid.instSetLikeSubmonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Monoid.toMulOneClass.{max u2 u1} (Matrix.{u1, u1, u2} n n α) (MonoidWithZero.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Semiring.toMonoidWithZero.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.semiring.{u2, u1} n α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))))))) x (Matrix.unitaryGroup.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 α _inst_3 _inst_4))) (Submonoid.mul.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Monoid.toMulOneClass.{max u2 u1} (Matrix.{u1, u1, u2} n n α) (MonoidWithZero.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Semiring.toMonoidWithZero.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.semiring.{u2, u1} n α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))))) (Matrix.unitaryGroup.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 α _inst_3 _inst_4))) A B)) (LinearMap.comp.{u2, u2, u2, max u1 u2, max u1 u2, max u1 u2} α α α (n -> α) (n -> α) (n -> α) (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} α (Semiring.toNonAssocSemiring.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))))) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} α (Semiring.toNonAssocSemiring.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))))) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} α (Semiring.toNonAssocSemiring.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => α) α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} α (Semiring.toNonAssocSemiring.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => α) α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} α (Semiring.toNonAssocSemiring.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => α) α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} α (Semiring.toNonAssocSemiring.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (RingHom.id.{u2} α (Semiring.toNonAssocSemiring.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (RingHom.id.{u2} α (Semiring.toNonAssocSemiring.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (RingHom.id.{u2} α (Semiring.toNonAssocSemiring.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (RingHomCompTriple.ids.{u2, u2} α α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (RingHom.id.{u2} α (Semiring.toNonAssocSemiring.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (Matrix.UnitaryGroup.toLin'.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 α _inst_3 _inst_4 A) (Matrix.UnitaryGroup.toLin'.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 α _inst_3 _inst_4 B))
 Case conversion may be inaccurate. Consider using '#align matrix.unitary_group.to_lin'_mul Matrix.UnitaryGroup.toLin'_mulₓ'. -/
 @[simp]
 theorem toLin'_mul : toLin' (A * B) = (toLin' A).comp (toLin' B) :=
@@ -266,7 +266,7 @@ theorem toLin'_mul : toLin' (A * B) = (toLin' A).comp (toLin' B) :=
 lean 3 declaration is
   forall {n : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] {α : Type.{u2}} [_inst_3 : CommRing.{u2} α] [_inst_4 : StarRing.{u2} α (NonUnitalRing.toNonUnitalSemiring.{u2} α (NonUnitalCommRing.toNonUnitalRing.{u2} α (CommRing.toNonUnitalCommRing.{u2} α _inst_3)))], Eq.{succ (max u1 u2)} (LinearMap.{u2, u2, max u1 u2, max u1 u2} α α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (RingHom.id.{u2} α (Semiring.toNonAssocSemiring.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (n -> α) (n -> α) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} α (Semiring.toNonAssocSemiring.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))))) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} α (Semiring.toNonAssocSemiring.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))))) (Pi.Function.module.{u1, u2, u2} n α α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} α (Semiring.toNonAssocSemiring.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (Semiring.toModule.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (Pi.Function.module.{u1, u2, u2} n α α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} α (Semiring.toNonAssocSemiring.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (Semiring.toModule.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (Matrix.UnitaryGroup.toLin'.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 α _inst_3 _inst_4 (OfNat.ofNat.{max u1 u2} (coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Submonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Monoid.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.ring.{u2, u1} n α _inst_2 (fun (a : n) (b : n) => (fun (a : n) (b : n) => _inst_1 a b) a b) (CommRing.toRing.{u2} α _inst_3))))) Type.{max u1 u2} (SetLike.hasCoeToSort.{max u1 u2, max u1 u2} (Submonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Monoid.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.ring.{u2, u1} n α _inst_2 (fun (a : n) (b : n) => (fun (a : n) (b : n) => _inst_1 a b) a b) (CommRing.toRing.{u2} α _inst_3))))) (Matrix.{u1, u1, u2} n n α) (Submonoid.setLike.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Monoid.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.ring.{u2, u1} n α _inst_2 (fun (a : n) (b : n) => (fun (a : n) (b : n) => _inst_1 a b) a b) (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.unitaryGroup.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 α _inst_3 _inst_4)) 1 (OfNat.mk.{max u1 u2} (coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Submonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Monoid.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.ring.{u2, u1} n α _inst_2 (fun (a : n) (b : n) => (fun (a : n) (b : n) => _inst_1 a b) a b) (CommRing.toRing.{u2} α _inst_3))))) Type.{max u1 u2} (SetLike.hasCoeToSort.{max u1 u2, max u1 u2} (Submonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Monoid.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.ring.{u2, u1} n α _inst_2 (fun (a : n) (b : n) => (fun (a : n) (b : n) => _inst_1 a b) a b) (CommRing.toRing.{u2} α _inst_3))))) (Matrix.{u1, u1, u2} n n α) (Submonoid.setLike.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Monoid.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.ring.{u2, u1} n α _inst_2 (fun (a : n) (b : n) => (fun (a : n) (b : n) => _inst_1 a b) a b) (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.unitaryGroup.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 α _inst_3 _inst_4)) 1 (One.one.{max u1 u2} (coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Submonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Monoid.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.ring.{u2, u1} n α _inst_2 (fun (a : n) (b : n) => (fun (a : n) (b : n) => _inst_1 a b) a b) (CommRing.toRing.{u2} α _inst_3))))) Type.{max u1 u2} (SetLike.hasCoeToSort.{max u1 u2, max u1 u2} (Submonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Monoid.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.ring.{u2, u1} n α _inst_2 (fun (a : n) (b : n) => (fun (a : n) (b : n) => _inst_1 a b) a b) (CommRing.toRing.{u2} α _inst_3))))) (Matrix.{u1, u1, u2} n n α) (Submonoid.setLike.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Monoid.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.ring.{u2, u1} n α _inst_2 (fun (a : n) (b : n) => (fun (a : n) (b : n) => _inst_1 a b) a b) (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.unitaryGroup.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 α _inst_3 _inst_4)) (Submonoid.one.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Monoid.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.ring.{u2, u1} n α _inst_2 (fun (a : n) (b : n) => (fun (a : n) (b : n) => _inst_1 a b) a b) (CommRing.toRing.{u2} α _inst_3)))) (Matrix.unitaryGroup.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 α _inst_3 _inst_4)))))) (LinearMap.id.{u2, max u1 u2} α (n -> α) (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} α (Semiring.toNonAssocSemiring.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))))) (Pi.Function.module.{u1, u2, u2} n α α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} α (Semiring.toNonAssocSemiring.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (Semiring.toModule.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))))
 but is expected to have type
-  forall {n : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] {α : Type.{u2}} [_inst_3 : CommRing.{u2} α] [_inst_4 : StarRing.{u2} α (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} α (NonUnitalCommRing.toNonUnitalCommSemiring.{u2} α (CommRing.toNonUnitalCommRing.{u2} α _inst_3)))], Eq.{max (succ u1) (succ u2)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Matrix.{u1, u1, u2} n n α) => LinearMap.{u2, u2, max u2 u1, max u2 u1} α α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (RingHom.id.{u2} α (Semiring.toNonAssocSemiring.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (n -> α) (n -> α) (Pi.addCommMonoid.{u1, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} α (Semiring.toNonAssocSemiring.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))))) (Pi.addCommMonoid.{u1, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} α (Semiring.toNonAssocSemiring.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => α) α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} α (Semiring.toNonAssocSemiring.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => α) α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} α (Semiring.toNonAssocSemiring.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (Subtype.val.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (fun (x : Matrix.{u1, u1, u2} n n α) => Membership.mem.{max u1 u2, max u1 u2} (Matrix.{u1, u1, u2} n n α) (Submonoid.{max u2 u1} (Matrix.{u1, u1, u2} n n α) (Monoid.toMulOneClass.{max u2 u1} (Matrix.{u1, u1, u2} n n α) (MonoidWithZero.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Semiring.toMonoidWithZero.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.semiring.{u2, u1} n α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submonoid.{max u2 u1} (Matrix.{u1, u1, u2} n n α) (Monoid.toMulOneClass.{max u2 u1} (Matrix.{u1, u1, u2} n n α) (MonoidWithZero.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Semiring.toMonoidWithZero.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.semiring.{u2, u1} n α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))))) (Matrix.{u1, u1, u2} n n α) (Submonoid.instSetLikeSubmonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Monoid.toMulOneClass.{max u2 u1} (Matrix.{u1, u1, u2} n n α) (MonoidWithZero.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Semiring.toMonoidWithZero.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.semiring.{u2, u1} n α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))))))) x (Matrix.unitaryGroup.{u1, u2} n (fun (a : 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_inst_4))) (Submonoid.one.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Monoid.toMulOneClass.{max u2 u1} (Matrix.{u1, u1, u2} n n α) (MonoidWithZero.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Semiring.toMonoidWithZero.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.semiring.{u2, u1} n α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))))) (Matrix.unitaryGroup.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 α _inst_3 _inst_4))))) (LinearMap.id.{u2, max u1 u2} α (n -> α) (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} α (Semiring.toNonAssocSemiring.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => α) α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} α (Semiring.toNonAssocSemiring.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))))
+  forall {n : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] {α : Type.{u2}} [_inst_3 : CommRing.{u2} α] [_inst_4 : StarRing.{u2} α (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} α (NonUnitalCommRing.toNonUnitalCommSemiring.{u2} α (CommRing.toNonUnitalCommRing.{u2} α _inst_3)))], Eq.{max (succ u1) (succ u2)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Matrix.{u1, u1, u2} n n α) => LinearMap.{u2, u2, max u2 u1, max u2 u1} α α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (RingHom.id.{u2} α (Semiring.toNonAssocSemiring.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (n -> α) (n -> α) (Pi.addCommMonoid.{u1, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} α 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_inst_4))) (Submonoid.one.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Monoid.toMulOneClass.{max u2 u1} (Matrix.{u1, u1, u2} n n α) (MonoidWithZero.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Semiring.toMonoidWithZero.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.semiring.{u2, u1} n α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))))) (Matrix.unitaryGroup.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 α _inst_3 _inst_4))))) (LinearMap.id.{u2, max u1 u2} α (n -> α) (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} α (Semiring.toNonAssocSemiring.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => α) α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} α (Semiring.toNonAssocSemiring.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))))
 Case conversion may be inaccurate. Consider using '#align matrix.unitary_group.to_lin'_one Matrix.UnitaryGroup.toLin'_oneₓ'. -/
 @[simp]
 theorem toLin'_one : toLin' (1 : unitaryGroup n α) = LinearMap.id :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/33c67ae661dd8988516ff7f247b0be3018cdd952

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Shing Tak Lam
 
 ! This file was ported from Lean 3 source module linear_algebra.unitary_group
-! leanprover-community/mathlib commit 2705404e701abc6b3127da906f40bae062a169c9
+! leanprover-community/mathlib commit 33c67ae661dd8988516ff7f247b0be3018cdd952
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -16,6 +16,9 @@ import Mathbin.Algebra.Star.Unitary
 /-!
 # The Unitary Group
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file defines elements of the unitary group `unitary_group n α`, where `α` is a `star_ring`.
 This consists of all `n` by `n` matrices with entries in `α` such that the star-transpose is its
 inverse. In addition, we define the group structure on `unitary_group n α`, and the embedding into

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

@@ -55,6 +55,12 @@ variable (n : Type u) [DecidableEq n] [Fintype n]
 
 variable (α : Type v) [CommRing α] [StarRing α]
 
+/- warning: matrix.unitary_group -> Matrix.unitaryGroup is a dubious translation:
+lean 3 declaration is
+  forall (n : Type.{u1}) [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] (α : Type.{u2}) [_inst_3 : CommRing.{u2} α] [_inst_4 : StarRing.{u2} α (NonUnitalRing.toNonUnitalSemiring.{u2} α (NonUnitalCommRing.toNonUnitalRing.{u2} α (CommRing.toNonUnitalCommRing.{u2} α _inst_3)))], Submonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Monoid.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.ring.{u2, u1} n α _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toRing.{u2} α _inst_3))))
+but is expected to have type
+  forall (n : Type.{u1}) [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] (α : Type.{u2}) [_inst_3 : CommRing.{u2} α] [_inst_4 : StarRing.{u2} α (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} α (NonUnitalCommRing.toNonUnitalCommSemiring.{u2} α (CommRing.toNonUnitalCommRing.{u2} α _inst_3)))], Submonoid.{max u2 u1} (Matrix.{u1, u1, u2} n n α) (Monoid.toMulOneClass.{max u2 u1} (Matrix.{u1, u1, u2} n n α) (MonoidWithZero.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Semiring.toMonoidWithZero.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.semiring.{u2, u1} n α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))))
+Case conversion may be inaccurate. Consider using '#align matrix.unitary_group Matrix.unitaryGroupₓ'. -/
 /-- `unitary_group n` is the group of `n` by `n` matrices where the star-transpose is the inverse.
 -/
 abbrev unitaryGroup :=
@@ -67,18 +73,36 @@ variable {n : Type u} [DecidableEq n] [Fintype n]
 
 variable {α : Type v} [CommRing α] [StarRing α]
 
+/- warning: matrix.mem_unitary_group_iff -> Matrix.mem_unitaryGroup_iff is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align matrix.mem_unitary_group_iff Matrix.mem_unitaryGroup_iffₓ'. -/
 theorem mem_unitaryGroup_iff {A : Matrix n n α} : A ∈ Matrix.unitaryGroup n α ↔ A * star A = 1 :=
   by
   refine' ⟨And.right, fun hA => ⟨_, hA⟩⟩
   simpa only [mul_eq_mul, mul_eq_one_comm] using hA
 #align matrix.mem_unitary_group_iff Matrix.mem_unitaryGroup_iff
 
+/- warning: matrix.mem_unitary_group_iff' -> Matrix.mem_unitaryGroup_iff' is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align matrix.mem_unitary_group_iff' Matrix.mem_unitaryGroup_iff'ₓ'. -/
 theorem mem_unitaryGroup_iff' {A : Matrix n n α} : A ∈ Matrix.unitaryGroup n α ↔ star A * A = 1 :=
   by
   refine' ⟨And.left, fun hA => ⟨hA, _⟩⟩
   rwa [mul_eq_mul, mul_eq_one_comm] at hA
 #align matrix.mem_unitary_group_iff' Matrix.mem_unitaryGroup_iff'
 
+/- warning: matrix.det_of_mem_unitary -> Matrix.det_of_mem_unitary is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align matrix.det_of_mem_unitary Matrix.det_of_mem_unitaryₓ'. -/
 theorem det_of_mem_unitary {A : Matrix n n α} (hA : A ∈ Matrix.unitaryGroup n α) :
     A.det ∈ unitary α := by
   constructor
@@ -88,13 +112,31 @@ theorem det_of_mem_unitary {A : Matrix n n α} (hA : A ∈ Matrix.unitaryGroup n
 
 namespace UnitaryGroup
 
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+Case conversion may be inaccurate. Consider using '#align matrix.unitary_group.coe_matrix Matrix.UnitaryGroup.coeMatrixₓ'. -/
 instance coeMatrix : Coe (unitaryGroup n α) (Matrix n n α) :=
   ⟨Subtype.val⟩
-#align matrix.unitary_group.coe_matrix Matrix.unitaryGroup.coeMatrix
-
+#align matrix.unitary_group.coe_matrix Matrix.UnitaryGroup.coeMatrix
+
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+Case conversion may be inaccurate. Consider using '#align matrix.unitary_group.coe_fun Matrix.UnitaryGroup.coeFunₓ'. -/
 instance coeFun : CoeFun (unitaryGroup n α) fun _ => n → n → α where coe A := A.val
-#align matrix.unitary_group.coe_fun Matrix.unitaryGroup.coeFun
-
+#align matrix.unitary_group.coe_fun Matrix.UnitaryGroup.coeFun
+
+/- warning: matrix.unitary_group.to_lin' -> Matrix.UnitaryGroup.toLin' is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align matrix.unitary_group.to_lin' Matrix.UnitaryGroup.toLin'ₓ'. -/
 /-- `to_lin' A` is matrix multiplication of vectors by `A`, as a linear map.
 
 After the group structure on `unitary_group n` is defined,
@@ -102,68 +144,140 @@ we show in `to_linear_equiv` that this gives a linear equivalence.
 -/
 def toLin' (A : unitaryGroup n α) :=
   Matrix.toLin' A
-#align matrix.unitary_group.to_lin' Matrix.unitaryGroup.toLin'
-
+#align matrix.unitary_group.to_lin' Matrix.UnitaryGroup.toLin'
+
+/- warning: matrix.unitary_group.ext_iff -> Matrix.UnitaryGroup.ext_iff 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 matrix.unitary_group.ext_iff Matrix.UnitaryGroup.ext_iffₓ'. -/
 theorem ext_iff (A B : unitaryGroup n α) : A = B ↔ ∀ i j, A i j = B i j :=
   Subtype.ext_iff_val.trans ⟨fun h i j => congr_fun (congr_fun h i) j, Matrix.ext⟩
-#align matrix.unitary_group.ext_iff Matrix.unitaryGroup.ext_iff
-
+#align matrix.unitary_group.ext_iff Matrix.UnitaryGroup.ext_iff
+
+/- warning: matrix.unitary_group.ext -> Matrix.UnitaryGroup.ext 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 matrix.unitary_group.ext Matrix.UnitaryGroup.extₓ'. -/
 @[ext]
 theorem ext (A B : unitaryGroup n α) : (∀ i j, A i j = B i j) → A = B :=
-  (unitaryGroup.ext_iff A B).mpr
-#align matrix.unitary_group.ext Matrix.unitaryGroup.ext
-
+  (UnitaryGroup.ext_iff A B).mpr
+#align matrix.unitary_group.ext Matrix.UnitaryGroup.ext
+
+/- warning: matrix.unitary_group.star_mul_self -> Matrix.UnitaryGroup.star_mul_self is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align matrix.unitary_group.star_mul_self Matrix.UnitaryGroup.star_mul_selfₓ'. -/
 @[simp]
 theorem star_mul_self (A : unitaryGroup n α) : star A ⬝ A = 1 :=
   A.2.1
-#align matrix.unitary_group.star_mul_self Matrix.unitaryGroup.star_mul_self
+#align matrix.unitary_group.star_mul_self Matrix.UnitaryGroup.star_mul_self
 
 section CoeLemmas
 
 variable (A B : unitaryGroup n α)
 
+/- warning: matrix.unitary_group.inv_val -> Matrix.UnitaryGroup.inv_val is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align matrix.unitary_group.inv_val Matrix.UnitaryGroup.inv_valₓ'. -/
 @[simp]
 theorem inv_val : ↑A⁻¹ = (star A : Matrix n n α) :=
   rfl
-#align matrix.unitary_group.inv_val Matrix.unitaryGroup.inv_val
-
+#align matrix.unitary_group.inv_val Matrix.UnitaryGroup.inv_val
+
+/- warning: matrix.unitary_group.inv_apply -> Matrix.UnitaryGroup.inv_apply is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align matrix.unitary_group.inv_apply Matrix.UnitaryGroup.inv_applyₓ'. -/
 @[simp]
 theorem inv_apply : ⇑A⁻¹ = (star A : Matrix n n α) :=
   rfl
-#align matrix.unitary_group.inv_apply Matrix.unitaryGroup.inv_apply
-
+#align matrix.unitary_group.inv_apply Matrix.UnitaryGroup.inv_apply
+
+/- warning: matrix.unitary_group.mul_val -> Matrix.UnitaryGroup.mul_val is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align matrix.unitary_group.mul_val Matrix.UnitaryGroup.mul_valₓ'. -/
 @[simp]
 theorem mul_val : ↑(A * B) = A ⬝ B :=
   rfl
-#align matrix.unitary_group.mul_val Matrix.unitaryGroup.mul_val
-
+#align matrix.unitary_group.mul_val Matrix.UnitaryGroup.mul_val
+
+/- warning: matrix.unitary_group.mul_apply -> Matrix.UnitaryGroup.mul_apply is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align matrix.unitary_group.mul_apply Matrix.UnitaryGroup.mul_applyₓ'. -/
 @[simp]
 theorem mul_apply : ⇑(A * B) = A ⬝ B :=
   rfl
-#align matrix.unitary_group.mul_apply Matrix.unitaryGroup.mul_apply
-
+#align matrix.unitary_group.mul_apply Matrix.UnitaryGroup.mul_apply
+
+/- warning: matrix.unitary_group.one_val -> Matrix.UnitaryGroup.one_val 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 matrix.unitary_group.one_val Matrix.UnitaryGroup.one_valₓ'. -/
 @[simp]
 theorem one_val : ↑(1 : unitaryGroup n α) = (1 : Matrix n n α) :=
   rfl
-#align matrix.unitary_group.one_val Matrix.unitaryGroup.one_val
-
+#align matrix.unitary_group.one_val Matrix.UnitaryGroup.one_val
+
+/- warning: matrix.unitary_group.one_apply -> Matrix.UnitaryGroup.one_apply 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 matrix.unitary_group.one_apply Matrix.UnitaryGroup.one_applyₓ'. -/
 @[simp]
 theorem one_apply : ⇑(1 : unitaryGroup n α) = (1 : Matrix n n α) :=
   rfl
-#align matrix.unitary_group.one_apply Matrix.unitaryGroup.one_apply
-
+#align matrix.unitary_group.one_apply Matrix.UnitaryGroup.one_apply
+
+/- warning: matrix.unitary_group.to_lin'_mul -> Matrix.UnitaryGroup.toLin'_mul is a dubious translation:
+lean 3 declaration is
+  forall {n : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] {α : Type.{u2}} [_inst_3 : CommRing.{u2} α] [_inst_4 : StarRing.{u2} α (NonUnitalRing.toNonUnitalSemiring.{u2} α (NonUnitalCommRing.toNonUnitalRing.{u2} α (CommRing.toNonUnitalCommRing.{u2} α _inst_3)))] (A : coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Submonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Monoid.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.ring.{u2, u1} n α _inst_2 (fun (a : n) (b : n) => (fun (a : n) (b : n) => _inst_1 a b) a b) (CommRing.toRing.{u2} α _inst_3))))) Type.{max u1 u2} (SetLike.hasCoeToSort.{max u1 u2, max u1 u2} (Submonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Monoid.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.ring.{u2, u1} n α _inst_2 (fun (a : n) (b : n) => (fun (a : n) (b : n) => _inst_1 a b) a b) (CommRing.toRing.{u2} α _inst_3))))) (Matrix.{u1, u1, u2} n n α) (Submonoid.setLike.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Monoid.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.ring.{u2, u1} n α _inst_2 (fun (a : n) (b : n) => (fun (a : n) (b : n) => _inst_1 a b) a b) (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.unitaryGroup.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 α _inst_3 _inst_4)) (B : coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Submonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Monoid.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.ring.{u2, u1} n α _inst_2 (fun (a : n) (b : n) => (fun (a : n) (b : n) => _inst_1 a b) a b) (CommRing.toRing.{u2} α _inst_3))))) Type.{max u1 u2} (SetLike.hasCoeToSort.{max u1 u2, max u1 u2} (Submonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Monoid.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.ring.{u2, u1} n α _inst_2 (fun (a : n) (b : n) => (fun (a : n) (b : n) => _inst_1 a b) a b) (CommRing.toRing.{u2} α _inst_3))))) (Matrix.{u1, u1, u2} n n α) (Submonoid.setLike.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Monoid.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.ring.{u2, u1} n α _inst_2 (fun (a : n) (b : n) => (fun (a : n) (b : n) => _inst_1 a b) a b) (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.unitaryGroup.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 α _inst_3 _inst_4)), Eq.{succ (max u1 u2)} (LinearMap.{u2, u2, max u1 u2, max u1 u2} α α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (RingHom.id.{u2} α (Semiring.toNonAssocSemiring.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (n -> α) (n -> α) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} α (Semiring.toNonAssocSemiring.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))))) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} α (Semiring.toNonAssocSemiring.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))))) (Pi.Function.module.{u1, u2, u2} n α α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} α (Semiring.toNonAssocSemiring.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (Semiring.toModule.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (Pi.Function.module.{u1, u2, u2} n α α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} α (Semiring.toNonAssocSemiring.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (Semiring.toModule.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (Matrix.UnitaryGroup.toLin'.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 α _inst_3 _inst_4 (HMul.hMul.{max u1 u2, max u1 u2, max u1 u2} (coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Submonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Monoid.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.ring.{u2, u1} n α _inst_2 (fun (a : n) (b : n) => (fun (a : n) (b : n) => _inst_1 a b) a b) (CommRing.toRing.{u2} α _inst_3))))) Type.{max u1 u2} (SetLike.hasCoeToSort.{max u1 u2, max u1 u2} (Submonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Monoid.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.ring.{u2, u1} n α _inst_2 (fun (a : n) (b : n) => (fun (a : n) (b : n) => _inst_1 a b) a b) (CommRing.toRing.{u2} α _inst_3))))) (Matrix.{u1, u1, u2} n n α) (Submonoid.setLike.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Monoid.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.ring.{u2, u1} n α _inst_2 (fun (a : n) (b : n) => (fun (a : n) (b : n) => _inst_1 a b) a b) (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.unitaryGroup.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 α _inst_3 _inst_4)) (coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Submonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Monoid.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.ring.{u2, u1} n α _inst_2 (fun (a : n) (b : n) => (fun (a : n) (b : n) => _inst_1 a b) a b) (CommRing.toRing.{u2} α _inst_3))))) Type.{max u1 u2} (SetLike.hasCoeToSort.{max u1 u2, max u1 u2} (Submonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Monoid.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.ring.{u2, u1} n α _inst_2 (fun (a : n) (b : n) => (fun (a : n) (b : n) => _inst_1 a b) a b) (CommRing.toRing.{u2} α _inst_3))))) (Matrix.{u1, u1, u2} n n α) (Submonoid.setLike.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Monoid.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.ring.{u2, u1} n α _inst_2 (fun (a : n) (b : n) => (fun (a : n) (b : n) => _inst_1 a b) a b) (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.unitaryGroup.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 α _inst_3 _inst_4)) (coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Submonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Monoid.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.ring.{u2, u1} n α _inst_2 (fun (a : n) (b : n) => (fun (a : n) (b : n) => _inst_1 a b) a b) (CommRing.toRing.{u2} α _inst_3))))) Type.{max u1 u2} (SetLike.hasCoeToSort.{max u1 u2, max u1 u2} (Submonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Monoid.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.ring.{u2, u1} n α _inst_2 (fun (a : n) (b : n) => (fun (a : n) (b : n) => _inst_1 a b) a b) (CommRing.toRing.{u2} α _inst_3))))) (Matrix.{u1, u1, u2} n n α) (Submonoid.setLike.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Monoid.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.ring.{u2, u1} n α _inst_2 (fun (a : n) (b : n) => (fun (a : n) (b : n) => _inst_1 a b) a b) (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.unitaryGroup.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 α _inst_3 _inst_4)) (instHMul.{max u1 u2} (coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Submonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Monoid.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.ring.{u2, u1} n α _inst_2 (fun (a : n) (b : n) => (fun (a : n) (b : n) => _inst_1 a b) a b) (CommRing.toRing.{u2} α _inst_3))))) Type.{max u1 u2} (SetLike.hasCoeToSort.{max u1 u2, max u1 u2} (Submonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Monoid.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.ring.{u2, u1} n α _inst_2 (fun (a : n) (b : n) => (fun (a : n) (b : n) => _inst_1 a b) a b) (CommRing.toRing.{u2} α _inst_3))))) (Matrix.{u1, u1, u2} n n α) (Submonoid.setLike.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Monoid.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.ring.{u2, u1} n α _inst_2 (fun (a : n) (b : n) => (fun (a : n) (b : n) => _inst_1 a b) a b) (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.unitaryGroup.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 α _inst_3 _inst_4)) (Submonoid.mul.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Monoid.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.ring.{u2, u1} n α _inst_2 (fun (a : n) (b : n) => (fun (a : n) (b : n) => _inst_1 a b) a b) (CommRing.toRing.{u2} α _inst_3)))) (Matrix.unitaryGroup.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 α _inst_3 _inst_4))) A B)) (LinearMap.comp.{u2, u2, u2, max u1 u2, max u1 u2, max u1 u2} α α α (n -> α) (n -> α) (n -> α) (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} α (Semiring.toNonAssocSemiring.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))))) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} α (Semiring.toNonAssocSemiring.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))))) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} α (Semiring.toNonAssocSemiring.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))))) (Pi.Function.module.{u1, u2, u2} n α α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} α (Semiring.toNonAssocSemiring.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (Semiring.toModule.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (Pi.Function.module.{u1, u2, u2} n α α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} α (Semiring.toNonAssocSemiring.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (Semiring.toModule.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (Pi.Function.module.{u1, u2, u2} n α α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} α (Semiring.toNonAssocSemiring.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (Semiring.toModule.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (RingHom.id.{u2} α (Semiring.toNonAssocSemiring.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (RingHom.id.{u2} α (Semiring.toNonAssocSemiring.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (RingHom.id.{u2} α (Semiring.toNonAssocSemiring.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (RingHomCompTriple.right_ids.{u2, u2} α α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (RingHom.id.{u2} α (Semiring.toNonAssocSemiring.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (Matrix.UnitaryGroup.toLin'.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 α _inst_3 _inst_4 A) (Matrix.UnitaryGroup.toLin'.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 α _inst_3 _inst_4 B))
+but is expected to have type
+  forall {n : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] {α : Type.{u2}} [_inst_3 : CommRing.{u2} α] [_inst_4 : StarRing.{u2} α (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} α (NonUnitalCommRing.toNonUnitalCommSemiring.{u2} α (CommRing.toNonUnitalCommRing.{u2} α _inst_3)))] (A : Subtype.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n n α) (fun (x : Matrix.{u1, u1, u2} n n α) => Membership.mem.{max u1 u2, max u1 u2} (Matrix.{u1, u1, u2} n n α) (Submonoid.{max u2 u1} (Matrix.{u1, u1, u2} n n α) (Monoid.toMulOneClass.{max u2 u1} (Matrix.{u1, u1, u2} n n α) (MonoidWithZero.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Semiring.toMonoidWithZero.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.semiring.{u2, u1} n α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submonoid.{max u2 u1} (Matrix.{u1, u1, u2} n n α) (Monoid.toMulOneClass.{max 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+Case conversion may be inaccurate. Consider using '#align matrix.unitary_group.to_lin'_mul Matrix.UnitaryGroup.toLin'_mulₓ'. -/
 @[simp]
 theorem toLin'_mul : toLin' (A * B) = (toLin' A).comp (toLin' B) :=
   Matrix.toLin'_mul A B
-#align matrix.unitary_group.to_lin'_mul Matrix.unitaryGroup.toLin'_mul
-
+#align matrix.unitary_group.to_lin'_mul Matrix.UnitaryGroup.toLin'_mul
+
+/- warning: matrix.unitary_group.to_lin'_one -> Matrix.UnitaryGroup.toLin'_one is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align matrix.unitary_group.to_lin'_one Matrix.UnitaryGroup.toLin'_oneₓ'. -/
 @[simp]
 theorem toLin'_one : toLin' (1 : unitaryGroup n α) = LinearMap.id :=
   Matrix.toLin'_one
-#align matrix.unitary_group.to_lin'_one Matrix.unitaryGroup.toLin'_one
+#align matrix.unitary_group.to_lin'_one Matrix.UnitaryGroup.toLin'_one
 
 end CoeLemmas
 
+/- warning: matrix.unitary_group.to_linear_equiv -> Matrix.UnitaryGroup.toLinearEquiv is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align matrix.unitary_group.to_linear_equiv Matrix.UnitaryGroup.toLinearEquivₓ'. -/
 /-- `to_linear_equiv A` is matrix multiplication of vectors by `A`, as a linear equivalence. -/
 def toLinearEquiv (A : unitaryGroup n α) : (n → α) ≃ₗ[α] n → α :=
   { Matrix.toLin' A with
@@ -178,38 +292,68 @@ def toLinearEquiv (A : unitaryGroup n α) : (n → α) ≃ₗ[α] n → α :=
         (toLin' A).comp (toLin' A⁻¹) x = toLin' (A * A⁻¹) x := by rw [← to_lin'_mul]
         _ = x := by rw [mul_right_inv, to_lin'_one, id_apply]
          }
-#align matrix.unitary_group.to_linear_equiv Matrix.unitaryGroup.toLinearEquiv
-
+#align matrix.unitary_group.to_linear_equiv Matrix.UnitaryGroup.toLinearEquiv
+
+/- warning: matrix.unitary_group.to_GL -> Matrix.UnitaryGroup.toGL is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align matrix.unitary_group.to_GL Matrix.UnitaryGroup.toGLₓ'. -/
 /-- `to_GL` is the map from the unitary group to the general linear group -/
 def toGL (A : unitaryGroup n α) : GeneralLinearGroup α (n → α) :=
   GeneralLinearGroup.ofLinearEquiv (toLinearEquiv A)
-#align matrix.unitary_group.to_GL Matrix.unitaryGroup.toGL
-
+#align matrix.unitary_group.to_GL Matrix.UnitaryGroup.toGL
+
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(Semiring.toModule.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3))))))))) (Matrix.UnitaryGroup.toGL.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 α _inst_3 _inst_4 A)) (Matrix.UnitaryGroup.toLin'.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 α _inst_3 _inst_4 A)
+but is expected to have type
+  forall {n : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] {α : Type.{u2}} [_inst_3 : CommRing.{u2} α] [_inst_4 : StarRing.{u2} α (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} α (NonUnitalCommRing.toNonUnitalCommSemiring.{u2} α (CommRing.toNonUnitalCommRing.{u2} α _inst_3)))] (A : Subtype.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n n α) (fun (x : Matrix.{u1, u1, u2} n n α) => Membership.mem.{max u1 u2, max u1 u2} (Matrix.{u1, u1, u2} n n α) (Submonoid.{max u2 u1} (Matrix.{u1, u1, u2} n n α) (Monoid.toMulOneClass.{max u2 u1} (Matrix.{u1, u1, u2} n n α) (MonoidWithZero.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Semiring.toMonoidWithZero.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.semiring.{u2, u1} n α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submonoid.{max u2 u1} (Matrix.{u1, u1, u2} n n α) (Monoid.toMulOneClass.{max 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NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.UnitaryGroup._hyg.1291 : n) => α) α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (Module.End.monoid.{u2, max u1 u2} α (n -> α) (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (Pi.addCommMonoid.{u1, u2} n (fun (a._@.Mathlib.LinearAlgebra.UnitaryGroup._hyg.1291 : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.UnitaryGroup._hyg.1291 : n) => α) α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (Matrix.UnitaryGroup.toGL.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 α _inst_3 _inst_4 A)) (Matrix.UnitaryGroup.toLin'.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 α _inst_3 _inst_4 A)
+Case conversion may be inaccurate. Consider using '#align matrix.unitary_group.coe_to_GL Matrix.UnitaryGroup.coe_toGLₓ'. -/
 theorem coe_toGL (A : unitaryGroup n α) : ↑(toGL A) = toLin' A :=
   rfl
-#align matrix.unitary_group.coe_to_GL Matrix.unitaryGroup.coe_toGL
-
+#align matrix.unitary_group.coe_to_GL Matrix.UnitaryGroup.coe_toGL
+
+/- warning: matrix.unitary_group.to_GL_one -> Matrix.UnitaryGroup.toGL_one is a dubious translation:
+lean 3 declaration is
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(NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.Function.module.{u1, u2, u2} n α α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Semiring.toModule.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Pi.Function.module.{u1, u2, u2} n α α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Semiring.toModule.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Module.End.monoid.{u2, max u1 u2} α (n -> α) (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.Function.module.{u1, u2, u2} n α α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Semiring.toModule.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3))))))))))
+but is expected to have type
+  forall {n : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] {α : Type.{u2}} [_inst_3 : CommRing.{u2} α] [_inst_4 : StarRing.{u2} α (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} α (NonUnitalCommRing.toNonUnitalCommSemiring.{u2} α (CommRing.toNonUnitalCommRing.{u2} α _inst_3)))], Eq.{max (succ u1) (succ u2)} (LinearMap.GeneralLinearGroup.{u2, max u1 u2} α (n -> α) (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.UnitaryGroup._hyg.1291 : n) => α) α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (Matrix.UnitaryGroup.toGL.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 α _inst_3 _inst_4 (OfNat.ofNat.{max u1 u2} (Subtype.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n n α) (fun (x : Matrix.{u1, u1, u2} n n α) => Membership.mem.{max u1 u2, max u1 u2} (Matrix.{u1, u1, u2} n n α) (Submonoid.{max u2 u1} (Matrix.{u1, u1, u2} n n α) (Monoid.toMulOneClass.{max u2 u1} (Matrix.{u1, u1, u2} n n α) (MonoidWithZero.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Semiring.toMonoidWithZero.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.semiring.{u2, u1} n α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))))) (SetLike.instMembership.{max 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b)))))) (Matrix.{u1, u1, u2} n n α) (Submonoid.instSetLikeSubmonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Monoid.toMulOneClass.{max u2 u1} (Matrix.{u1, u1, u2} n n α) (MonoidWithZero.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Semiring.toMonoidWithZero.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.semiring.{u2, u1} n α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))))))) x (Matrix.unitaryGroup.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 α _inst_3 _inst_4))) (Submonoid.one.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Monoid.toMulOneClass.{max u2 u1} (Matrix.{u1, u1, u2} n n α) (MonoidWithZero.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Semiring.toMonoidWithZero.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.semiring.{u2, u1} n α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))))) (Matrix.unitaryGroup.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 α _inst_3 _inst_4))))) (OfNat.ofNat.{max u1 u2} (LinearMap.GeneralLinearGroup.{u2, max u1 u2} α (n -> α) (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.UnitaryGroup._hyg.1291 : n) => α) α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) 1 (One.toOfNat1.{max u1 u2} (LinearMap.GeneralLinearGroup.{u2, max u1 u2} α (n -> α) (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (Pi.addCommMonoid.{u1, u2} n (fun (a._@.Mathlib.LinearAlgebra.UnitaryGroup._hyg.1291 : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.UnitaryGroup._hyg.1291 : n) => α) α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (InvOneClass.toOne.{max u1 u2} (LinearMap.GeneralLinearGroup.{u2, max u1 u2} α (n -> α) (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.UnitaryGroup._hyg.1291 : n) => α) α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (DivInvOneMonoid.toInvOneClass.{max u1 u2} (LinearMap.GeneralLinearGroup.{u2, max u1 u2} α (n -> α) (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.UnitaryGroup._hyg.1291 : n) => α) α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) 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(CommRing.toCommSemiring.{u2} α _inst_3))))) (Group.toDivisionMonoid.{max u1 u2} (LinearMap.GeneralLinearGroup.{u2, max u1 u2} α (n -> α) (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (Pi.addCommMonoid.{u1, u2} n (fun (a._@.Mathlib.LinearAlgebra.UnitaryGroup._hyg.1291 : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.UnitaryGroup._hyg.1291 : n) => α) α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (Units.instGroupUnits.{max u1 u2} (LinearMap.{u2, u2, max u1 u2, max u1 u2} α α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (RingHom.id.{u2} α (Semiring.toNonAssocSemiring.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (n -> α) (n -> α) (Pi.addCommMonoid.{u1, u2} n (fun (a._@.Mathlib.LinearAlgebra.UnitaryGroup._hyg.1291 : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.addCommMonoid.{u1, u2} n (fun (a._@.Mathlib.LinearAlgebra.UnitaryGroup._hyg.1291 : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.UnitaryGroup._hyg.1291 : n) => α) α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.UnitaryGroup._hyg.1291 : n) => α) α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α 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_inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))))))))))
+Case conversion may be inaccurate. Consider using '#align matrix.unitary_group.to_GL_one Matrix.UnitaryGroup.toGL_oneₓ'. -/
 @[simp]
 theorem toGL_one : toGL (1 : unitaryGroup n α) = 1 :=
   by
   ext1 v i
   rw [coe_to_GL, to_lin'_one]
   rfl
-#align matrix.unitary_group.to_GL_one Matrix.unitaryGroup.toGL_one
-
+#align matrix.unitary_group.to_GL_one Matrix.UnitaryGroup.toGL_one
+
+/- warning: matrix.unitary_group.to_GL_mul -> Matrix.UnitaryGroup.toGL_mul is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align matrix.unitary_group.to_GL_mul Matrix.UnitaryGroup.toGL_mulₓ'. -/
 @[simp]
 theorem toGL_mul (A B : unitaryGroup n α) : toGL (A * B) = toGL A * toGL B :=
   by
   ext1 v i
   rw [coe_to_GL, to_lin'_mul]
   rfl
-#align matrix.unitary_group.to_GL_mul Matrix.unitaryGroup.toGL_mul
-
+#align matrix.unitary_group.to_GL_mul Matrix.UnitaryGroup.toGL_mul
+
+/- warning: matrix.unitary_group.embedding_GL -> Matrix.UnitaryGroup.embeddingGL is a dubious translation:
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+but is expected to have type
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(CommRing.toCommSemiring.{u2} α _inst_3)) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.UnitaryGroup._hyg.1486 : n) => α) α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (Submonoid.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Monoid.toMulOneClass.{max u2 u1} (Matrix.{u1, u1, u2} n n α) (MonoidWithZero.toMonoid.{max 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α _inst_3)))))) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.UnitaryGroup._hyg.1486 : n) => α) α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.UnitaryGroup._hyg.1486 : n) => α) α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (Module.End.monoid.{u2, max u1 u2} α (n -> α) (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.UnitaryGroup._hyg.1486 : n) => α) α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))))
+Case conversion may be inaccurate. Consider using '#align matrix.unitary_group.embedding_GL Matrix.UnitaryGroup.embeddingGLₓ'. -/
 /-- `unitary_group.embedding_GL` is the embedding from `unitary_group n α`
 to `general_linear_group n α`. -/
 def embeddingGL : unitaryGroup n α →* GeneralLinearGroup α (n → α) :=
   ⟨fun A => toGL A, by simp, by simp⟩
-#align matrix.unitary_group.embedding_GL Matrix.unitaryGroup.embeddingGL
+#align matrix.unitary_group.embedding_GL Matrix.UnitaryGroup.embeddingGL
 
 end UnitaryGroup
 
@@ -219,12 +363,24 @@ variable (n) (β : Type v) [CommRing β]
 
 attribute [local instance] starRingOfComm
 
+/- warning: matrix.orthogonal_group -> Matrix.orthogonalGroup is a dubious translation:
+lean 3 declaration is
+  forall (n : Type.{u1}) [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] (β : Type.{u2}) [_inst_5 : CommRing.{u2} β], Submonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n β) (Monoid.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} n n β) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n β) (Matrix.ring.{u2, u1} n β _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toRing.{u2} β _inst_5))))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align matrix.orthogonal_group Matrix.orthogonalGroupₓ'. -/
 /-- `orthogonal_group n` is the group of `n` by `n` matrices where the transpose is the inverse.
 -/
 abbrev orthogonalGroup :=
   unitaryGroup n β
 #align matrix.orthogonal_group Matrix.orthogonalGroup
 
+/- warning: matrix.mem_orthogonal_group_iff -> Matrix.mem_orthogonalGroup_iff is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align matrix.mem_orthogonal_group_iff Matrix.mem_orthogonalGroup_iffₓ'. -/
 theorem mem_orthogonalGroup_iff {A : Matrix n n β} :
     A ∈ Matrix.orthogonalGroup n β ↔ A * star A = 1 :=
   by
@@ -232,6 +388,12 @@ theorem mem_orthogonalGroup_iff {A : Matrix n n β} :
   simpa only [mul_eq_mul, mul_eq_one_comm] using hA
 #align matrix.mem_orthogonal_group_iff Matrix.mem_orthogonalGroup_iff
 
+/- warning: matrix.mem_orthogonal_group_iff' -> Matrix.mem_orthogonalGroup_iff' is a dubious translation:
+lean 3 declaration is
+  forall (n : Type.{u1}) [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] (β : Type.{u2}) [_inst_5 : CommRing.{u2} β] {A : Matrix.{u1, u1, u2} n n β}, Iff (Membership.Mem.{max u1 u2, max u1 u2} (Matrix.{u1, u1, u2} n n β) (Submonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n β) (Monoid.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} n n β) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n β) (Matrix.ring.{u2, u1} n β _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toRing.{u2} β _inst_5))))) (SetLike.hasMem.{max u1 u2, max u1 u2} (Submonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n β) (Monoid.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} n n β) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n β) (Matrix.ring.{u2, u1} n β _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toRing.{u2} β _inst_5))))) (Matrix.{u1, u1, u2} n n β) (Submonoid.setLike.{max u1 u2} (Matrix.{u1, u1, u2} n n β) (Monoid.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} n n β) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n β) (Matrix.ring.{u2, u1} n β _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toRing.{u2} β _inst_5)))))) A (Matrix.orthogonalGroup.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 β _inst_5)) (Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n n β) (HMul.hMul.{max u1 u2, max u1 u2, max u1 u2} (Matrix.{u1, u1, u2} n n β) (Matrix.{u1, u1, u2} n n β) (Matrix.{u1, u1, u2} n n β) (instHMul.{max u1 u2} (Matrix.{u1, u1, u2} n n β) (Matrix.hasMul.{u2, u1} n β _inst_2 (Distrib.toHasMul.{u2} β (Ring.toDistrib.{u2} β (CommRing.toRing.{u2} β _inst_5))) (AddCommGroup.toAddCommMonoid.{u2} β (NonUnitalNonAssocRing.toAddCommGroup.{u2} β (NonAssocRing.toNonUnitalNonAssocRing.{u2} β (Ring.toNonAssocRing.{u2} β (CommRing.toRing.{u2} β _inst_5))))))) (Star.star.{max u1 u2} (Matrix.{u1, u1, u2} n n β) (Matrix.hasStar.{u2, u1} n β (InvolutiveStar.toHasStar.{u2} β (StarAddMonoid.toHasInvolutiveStar.{u2} β (AddCommMonoid.toAddMonoid.{u2} β (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} β (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} β (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} β (CommSemiring.toNonUnitalCommSemiring.{u2} β (CommRing.toCommSemiring.{u2} β _inst_5)))))) (StarRing.toStarAddMonoid.{u2} β (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} β (CommSemiring.toNonUnitalCommSemiring.{u2} β (CommRing.toCommSemiring.{u2} β _inst_5))) (starRingOfComm.{u2} β (CommRing.toCommSemiring.{u2} β _inst_5)))))) A) A) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n n β) 1 (OfNat.mk.{max u1 u2} (Matrix.{u1, u1, u2} n n β) 1 (One.one.{max u1 u2} (Matrix.{u1, u1, u2} n n β) (Matrix.hasOne.{u2, u1} n β (fun (a : n) (b : n) => _inst_1 a b) (MulZeroClass.toHasZero.{u2} β (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} β (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} β (NonAssocRing.toNonUnitalNonAssocRing.{u2} β (Ring.toNonAssocRing.{u2} β (CommRing.toRing.{u2} β _inst_5)))))) (AddMonoidWithOne.toOne.{u2} β (AddGroupWithOne.toAddMonoidWithOne.{u2} β (AddCommGroupWithOne.toAddGroupWithOne.{u2} β (Ring.toAddCommGroupWithOne.{u2} β (CommRing.toRing.{u2} β _inst_5))))))))))
+but is expected to have type
+  forall (n : Type.{u1}) [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] (β : Type.{u2}) [_inst_5 : CommRing.{u2} β] {A : Matrix.{u1, u1, u2} n n β}, Iff (Membership.mem.{max u1 u2, max u1 u2} (Matrix.{u1, u1, u2} n n β) (Submonoid.{max u2 u1} (Matrix.{u1, u1, u2} n n β) (Monoid.toMulOneClass.{max u2 u1} (Matrix.{u1, u1, u2} n n β) (MonoidWithZero.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n β) (Semiring.toMonoidWithZero.{max u1 u2} (Matrix.{u1, u1, u2} n n β) (Matrix.semiring.{u2, u1} n β (CommSemiring.toSemiring.{u2} β (CommRing.toCommSemiring.{u2} β _inst_5)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submonoid.{max u2 u1} (Matrix.{u1, u1, u2} n n β) (Monoid.toMulOneClass.{max u2 u1} (Matrix.{u1, u1, u2} n n β) (MonoidWithZero.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n β) (Semiring.toMonoidWithZero.{max u1 u2} (Matrix.{u1, u1, u2} n n β) (Matrix.semiring.{u2, u1} n β (CommSemiring.toSemiring.{u2} β (CommRing.toCommSemiring.{u2} β _inst_5)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))))) (Matrix.{u1, u1, u2} n n β) (Submonoid.instSetLikeSubmonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n β) (Monoid.toMulOneClass.{max u2 u1} (Matrix.{u1, u1, u2} n n β) (MonoidWithZero.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n β) (Semiring.toMonoidWithZero.{max u1 u2} (Matrix.{u1, u1, u2} n n β) (Matrix.semiring.{u2, u1} n β (CommSemiring.toSemiring.{u2} β (CommRing.toCommSemiring.{u2} β _inst_5)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))))))) A (Matrix.orthogonalGroup.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 β _inst_5)) (Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n β) (HMul.hMul.{max u1 u2, max u1 u2, max u1 u2} (Matrix.{u1, u1, u2} n n β) (Matrix.{u1, u1, u2} n n β) (Matrix.{u1, u1, u2} n n β) (instHMul.{max u1 u2} (Matrix.{u1, u1, u2} n n β) (Matrix.instMulMatrix.{u2, u1} n β _inst_2 (NonUnitalNonAssocRing.toMul.{u2} β (NonAssocRing.toNonUnitalNonAssocRing.{u2} β (Ring.toNonAssocRing.{u2} β (CommRing.toRing.{u2} β _inst_5)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} β (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} β (NonAssocRing.toNonUnitalNonAssocRing.{u2} β (Ring.toNonAssocRing.{u2} β (CommRing.toRing.{u2} β _inst_5))))))) (Star.star.{max u1 u2} (Matrix.{u1, u1, u2} n n β) (Matrix.instStarMatrix.{u2, u1} n β (InvolutiveStar.toStar.{u2} β (StarAddMonoid.toInvolutiveStar.{u2} β (AddMonoidWithOne.toAddMonoid.{u2} β (AddGroupWithOne.toAddMonoidWithOne.{u2} β (Ring.toAddGroupWithOne.{u2} β (CommRing.toRing.{u2} β _inst_5)))) (StarRing.toStarAddMonoid.{u2} β (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} β (NonUnitalCommRing.toNonUnitalCommSemiring.{u2} β (CommRing.toNonUnitalCommRing.{u2} β _inst_5))) (starRingOfComm.{u2} β (CommRing.toCommSemiring.{u2} β _inst_5)))))) A) A) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n n β) 1 (One.toOfNat1.{max u1 u2} (Matrix.{u1, u1, u2} n n β) (Matrix.one.{u2, u1} n β (fun (a : n) (b : n) => _inst_1 a b) (CommMonoidWithZero.toZero.{u2} β (CommSemiring.toCommMonoidWithZero.{u2} β (CommRing.toCommSemiring.{u2} β _inst_5))) (Semiring.toOne.{u2} β (CommSemiring.toSemiring.{u2} β (CommRing.toCommSemiring.{u2} β _inst_5)))))))
+Case conversion may be inaccurate. Consider using '#align matrix.mem_orthogonal_group_iff' Matrix.mem_orthogonalGroup_iff'ₓ'. -/
 theorem mem_orthogonalGroup_iff' {A : Matrix n n β} :
     A ∈ Matrix.orthogonalGroup n β ↔ star A * A = 1 :=
   by

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

Co-authored-by: Bergschaf <christian.k@netcom-mail.de> Co-authored-by: bergschaf <christian.k@netcom-mail.de>

@@ -198,6 +198,22 @@ set_option linter.uppercaseLean3 false in
 
 end UnitaryGroup
 
+section specialUnitaryGroup
+
+variable (n) (α)
+
+/--`Matrix.specialUnitaryGroup` is the group of unitary `n` by `n` matrices where the determinant
+is 1. (This definition is only correct if 2 is invertible.)-/
+abbrev specialUnitaryGroup := unitaryGroup n α ⊓ MonoidHom.mker detMonoidHom
+
+variable {n} {α}
+
+theorem mem_specialUnitaryGroup_iff :
+    A ∈ specialUnitaryGroup n α ↔ A ∈ unitaryGroup n α ∧ A.det = 1 :=
+  Iff.rfl
+
+end specialUnitaryGroup
+
 section OrthogonalGroup
 
 variable (n) (β : Type v) [CommRing β]
@@ -226,4 +242,22 @@ theorem mem_orthogonalGroup_iff' {A : Matrix n n β} :
 
 end OrthogonalGroup
 
+section specialOrthogonalGroup
+
+variable (n) (β : Type v) [CommRing β]
+
+attribute [local instance] starRingOfComm
+
+/-- `Matrix.specialOrthogonalGroup n` is the group of orthogonal `n` by `n` where the determinant
+is one. (This definition is only correct if 2 is invertible.)-/
+abbrev specialOrthogonalGroup := specialUnitaryGroup n β
+
+variable {n} {β} {A : Matrix n n β}
+
+theorem mem_specialOrthogonalGroup_iff :
+    A ∈ specialOrthogonalGroup n β ↔ A ∈ orthogonalGroup n β ∧ A.det = 1 :=
+  Iff.rfl
+
+end specialOrthogonalGroup
+
 end Matrix

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

@@ -145,7 +145,7 @@ theorem toLin'_one : toLin' (1 : unitaryGroup n α) = LinearMap.id :=
 
 end CoeLemmas
 
--- Porting note: todo: redefine `toGL`/`embeddingGL` as in this example:
+-- Porting note (#11215): TODO: redefine `toGL`/`embeddingGL` as in this example:
 example : unitaryGroup n α →* GeneralLinearGroup α (n → α) :=
   .toHomUnits ⟨⟨toLin', toLin'_one⟩, toLin'_mul⟩
 -- Porting note: then we can get `toLinearEquiv` from `GeneralLinearGroup.toLinearEquiv`
@@ -202,7 +202,7 @@ section OrthogonalGroup
 
 variable (n) (β : Type v) [CommRing β]
 
--- Porting note: todo: will lemmas about `Matrix.orthogonalGroup` work without making
+-- Porting note (#11215): TODO: will lemmas about `Matrix.orthogonalGroup` work without making
 -- `starRingOfComm` a local instance? E.g., can we talk about unitary group and orthogonal group
 -- at the same time?
 attribute [local instance] starRingOfComm

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".

@@ -145,10 +145,10 @@ theorem toLin'_one : toLin' (1 : unitaryGroup n α) = LinearMap.id :=
 
 end CoeLemmas
 
--- porting note: todo: redefine `toGL`/`embeddingGL` as in this example:
+-- Porting note: todo: redefine `toGL`/`embeddingGL` as in this example:
 example : unitaryGroup n α →* GeneralLinearGroup α (n → α) :=
   .toHomUnits ⟨⟨toLin', toLin'_one⟩, toLin'_mul⟩
--- porting note: then we can get `toLinearEquiv` from `GeneralLinearGroup.toLinearEquiv`
+-- Porting note: then we can get `toLinearEquiv` from `GeneralLinearGroup.toLinearEquiv`
 
 /-- `Matrix.unitaryGroup.toLinearEquiv A` is matrix multiplication of vectors by `A`, as a linear
 equivalence. -/

The main difficulty here is that * has a slightly difference precedence to ⬝. notably around smul and neg.

The other annoyance is that ↑U ⬝ A ⬝ ↑U⁻¹ : Matrix m m 𝔸 now has to be written U.val * A * (U⁻¹).val in order to typecheck.

A downside of this change to consider: if you have a goal of A * (B * C) = (A * B) * C, mul_assoc now gives the illusion of matching, when in fact Matrix.mul_assoc is needed. Previously the distinct symbol made it easy to avoid this mistake.

On the flipside, there is now no need to rewrite by Matrix.mul_eq_mul all the time (indeed, the lemma is now removed).

@@ -65,12 +65,12 @@ variable {α : Type v} [CommRing α] [StarRing α] {A : Matrix n n α}
 
 theorem mem_unitaryGroup_iff : A ∈ Matrix.unitaryGroup n α ↔ A * star A = 1 := by
   refine' ⟨And.right, fun hA => ⟨_, hA⟩⟩
-  simpa only [mul_eq_mul, mul_eq_one_comm] using hA
+  simpa only [mul_eq_one_comm] using hA
 #align matrix.mem_unitary_group_iff Matrix.mem_unitaryGroup_iff
 
 theorem mem_unitaryGroup_iff' : A ∈ Matrix.unitaryGroup n α ↔ star A * A = 1 := by
   refine' ⟨And.left, fun hA => ⟨hA, _⟩⟩
-  rwa [mul_eq_mul, mul_eq_one_comm] at hA
+  rwa [mul_eq_one_comm] at hA
 #align matrix.mem_unitary_group_iff' Matrix.mem_unitaryGroup_iff'
 
 theorem det_of_mem_unitary {A : Matrix n n α} (hA : A ∈ Matrix.unitaryGroup n α) :
@@ -107,8 +107,7 @@ theorem ext (A B : unitaryGroup n α) : (∀ i j, A i j = B i j) → A = B :=
   (UnitaryGroup.ext_iff A B).mpr
 #align matrix.unitary_group.ext Matrix.UnitaryGroup.ext
 
-@[simp]
-theorem star_mul_self (A : unitaryGroup n α) : star A.1 ⬝ A.1 = 1 :=
+theorem star_mul_self (A : unitaryGroup n α) : star A.1 * A.1 = 1 :=
   A.2.1
 #align matrix.unitary_group.star_mul_self Matrix.UnitaryGroup.star_mul_self
 
@@ -122,10 +121,10 @@ variable (A B : unitaryGroup n α)
 @[simp] theorem inv_apply : ⇑A⁻¹ = (star A : Matrix n n α) := rfl
 #align matrix.unitary_group.inv_apply Matrix.UnitaryGroup.inv_apply
 
-@[simp] theorem mul_val : ↑(A * B) = A.1 ⬝ B.1 := rfl
+@[simp] theorem mul_val : ↑(A * B) = A.1 * B.1 := rfl
 #align matrix.unitary_group.mul_val Matrix.UnitaryGroup.mul_val
 
-@[simp] theorem mul_apply : ⇑(A * B) = A.1 ⬝ B.1 := rfl
+@[simp] theorem mul_apply : ⇑(A * B) = A.1 * B.1 := rfl
 #align matrix.unitary_group.mul_apply Matrix.UnitaryGroup.mul_apply
 
 @[simp] theorem one_val : ↑(1 : unitaryGroup n α) = (1 : Matrix n n α) := rfl
@@ -216,16 +215,15 @@ abbrev orthogonalGroup := unitaryGroup n β
 theorem mem_orthogonalGroup_iff {A : Matrix n n β} :
     A ∈ Matrix.orthogonalGroup n β ↔ A * star A = 1 := by
   refine' ⟨And.right, fun hA => ⟨_, hA⟩⟩
-  simpa only [mul_eq_mul, mul_eq_one_comm] using hA
+  simpa only [mul_eq_one_comm] using hA
 #align matrix.mem_orthogonal_group_iff Matrix.mem_orthogonalGroup_iff
 
 theorem mem_orthogonalGroup_iff' {A : Matrix n n β} :
     A ∈ Matrix.orthogonalGroup n β ↔ star A * A = 1 := by
   refine' ⟨And.left, fun hA => ⟨hA, _⟩⟩
-  rwa [mul_eq_mul, mul_eq_one_comm] at hA
+  rwa [mul_eq_one_comm] at hA
 #align matrix.mem_orthogonal_group_iff' Matrix.mem_orthogonalGroup_iff'
 
 end OrthogonalGroup
 
 end Matrix
-

• depends on: #5966

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

@@ -2,17 +2,14 @@
 Copyright (c) 2021 Shing Tak Lam. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Shing Tak Lam
-
-! This file was ported from Lean 3 source module linear_algebra.unitary_group
-! leanprover-community/mathlib commit 2705404e701abc6b3127da906f40bae062a169c9
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.LinearAlgebra.GeneralLinearGroup
 import Mathlib.LinearAlgebra.Matrix.ToLin
 import Mathlib.LinearAlgebra.Matrix.NonsingularInverse
 import Mathlib.Algebra.Star.Unitary
 
+#align_import linear_algebra.unitary_group from "leanprover-community/mathlib"@"2705404e701abc6b3127da906f40bae062a169c9"
+
 /-!
 # The Unitary Group
 

I use name unitaryGroup (because it's a Submonoid, not a Type _) and namespace UnitaryGroup. Should I change either of these names?

Also, I don't know how to fix the timeout in the simpNF linter.

Co-authored-by: Matthew Ballard <matt@mrb.email>