algebra.star.self_adjoint | Mathlib porting status

Changes since the initial port

The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.

Changes in mathlib3

a6ece354

(last sync)

chore(algebra/star/self_adjoint): generalize a lemma to semifield (#18687)

This was missed in a previous commit, and backports a change made during forward-porting.

Diff

@@ -196,13 +196,13 @@ star_rat_cast _
 
 end division_ring
 
-section field
-variables [field R] [star_ring R]
+section semifield
+variables [semifield R] [star_ring R]
 
 lemma div {x y : R} (hx : is_self_adjoint x) (hy : is_self_adjoint y) : is_self_adjoint (x / y) :=
 by simp only [is_self_adjoint_iff, star_div', hx.star_eq, hy.star_eq]
 
-end field
+end semifield
 
 section has_smul
 variables [has_star R] [add_monoid A] [star_add_monoid A] [has_smul R A] [star_module R A]

9abfa6f0

refactor(linear_algebra/matrix/hermitian): golf and generalize (#18565)

A handful of these results can be proven trivially using results about is_self_adjoint. This also generalizes the typeclass arguments throughout the file, though largely in a mathematically meaningless way.

Diff

@@ -111,6 +111,17 @@ by simp only [is_self_adjoint_iff, star_sub, hx.star_eq, hy.star_eq]
 
 end add_group
 
+section add_comm_monoid
+variables [add_comm_monoid R] [star_add_monoid R]
+
+lemma _root_.is_self_adjoint_add_star_self (x : R) : is_self_adjoint (x + star x) :=
+by simp only [is_self_adjoint_iff, add_comm, star_add, star_star]
+
+lemma _root_.is_self_adjoint_star_add_self (x : R) : is_self_adjoint (star x + x) :=
+by simp only [is_self_adjoint_iff, add_comm, star_add, star_star]
+
+end add_comm_monoid
+
 section semigroup
 variables [semigroup R] [star_semigroup R]

30413fc8

chore(algebra): generalize typeclass arguments from field to semifield (#18597)

This generalizes some typeclass arguments from field to semifield and division_ring to division_semiring.

The proof for map_inv_nat_cast_smul had to be rewritten, as it was previously proved in terms of map_inv_int_cast_smul. The latter is now instead proved in terms of the former.

Forward-ported in https://github.com/leanprover-community/mathlib4/pull/2926

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

Diff

@@ -166,8 +166,8 @@ star_int_cast _
 
 end ring
 
-section division_ring
-variables [division_ring R] [star_ring R]
+section division_semiring
+variables [division_semiring R] [star_ring R]
 
 lemma inv {x : R} (hx : is_self_adjoint x) : is_self_adjoint x⁻¹ :=
 by simp only [is_self_adjoint_iff, star_inv', hx.star_eq]
@@ -175,6 +175,11 @@ by simp only [is_self_adjoint_iff, star_inv', hx.star_eq]
 lemma zpow {x : R} (hx : is_self_adjoint x) (n : ℤ) : is_self_adjoint (x ^ n):=
 by simp only [is_self_adjoint_iff, star_zpow₀, hx.star_eq]
 
+end division_semiring
+
+section division_ring
+variables [division_ring R] [star_ring R]
+
 lemma _root_.is_self_adjoint_rat_cast (x : ℚ) : is_self_adjoint (x : R) :=
 star_rat_cast _

1e320130

feat(analysis/normed_space/*exponential): more results about star (#18553)

These are trivial consequences of existing results.

It turns out we already had a proof about exp _ x belonging to unitary X; this weakens the conditions.

Diff

@@ -34,6 +34,7 @@ We also define `is_star_normal R`, a `Prop` that states that an element `x` sati
 
 ## TODO
 
+* Define `is_skew_adjoint` to match `is_self_adjoint`.
 * Define `λ z x, z * x * star z` (i.e. conjugation by `z`) as a monoid action of `R` on `R`
   (similar to the existing `conj_act` for groups), and then state the fact that `self_adjoint R` is
   invariant under it.
@@ -399,6 +400,22 @@ end has_smul
 
 end skew_adjoint
 
+/-- Scalar multiplication of a self-adjoint element by a skew-adjoint element produces a
+skew-adjoint element. -/
+lemma is_self_adjoint.smul_mem_skew_adjoint [ring R] [add_comm_group A] [module R A]
+  [star_add_monoid R] [star_add_monoid A] [star_module R A] {r : R}
+  (hr : r ∈ skew_adjoint R) {a : A} (ha : is_self_adjoint a) :
+  r • a ∈ skew_adjoint A :=
+(star_smul _ _).trans $ (congr_arg2 _ hr ha).trans $ neg_smul _ _
+
+/-- Scalar multiplication of a skew-adjoint element by a skew-adjoint element produces a
+self-adjoint element. -/
+lemma is_self_adjoint_smul_of_mem_skew_adjoint [ring R] [add_comm_group A] [module R A]
+  [star_add_monoid R] [star_add_monoid A] [star_module R A] {r : R}
+  (hr : r ∈ skew_adjoint R) {a : A} (ha : a ∈ skew_adjoint A) :
+  is_self_adjoint (r • a) :=
+(star_smul _ _).trans $ (congr_arg2 _ hr ha).trans $ neg_smul_neg _ _
+
 instance is_star_normal_zero [semiring R] [star_ring R] : is_star_normal (0 : R) :=
 ⟨by simp only [star_comm_self, star_zero]⟩

671d5d9a

feat(algebra/star/self_adjoint): add and generalize trivial lemmas (#18558)

This:

Generalizes is_self_adjoint.smul, which makes it easier to show that 0.5 • x is self-adjoint when x is, even if 0.5 is a complex number.
Generalizes is_self_adjoint.add to match matrix.is_hermitian.add (for a later refactor), along with many other lemmas.
Removes re-proofs of star_nat_cast and star_int_cast.

The first is motivated by showing that exp K m for some matrix m is positive definite if is_self_adjoint m.

Forward-ported at https://github.com/leanprover-community/mathlib4/pull/2719.

Diff

@@ -57,6 +57,10 @@ is_star_normal.star_comm_self
 
 namespace is_self_adjoint
 
+-- named to match `commute.all`
+/-- All elements are self-adjoint when `star` is trivial. -/
+lemma all [has_star R] [has_trivial_star R] (r : R) : is_self_adjoint r := star_trivial _
+
 lemma star_eq [has_star R] {x : R} (hx : is_self_adjoint x) : star x = x := hx
 
 lemma _root_.is_self_adjoint_iff [has_star R] {x : R} : is_self_adjoint x ↔ star x = x := iff.rfl
@@ -78,8 +82,8 @@ lemma star_hom_apply {F R S : Type*} [has_star R] [has_star S] [star_hom_class F
   {x : R} (hx : is_self_adjoint x) (f : F) : is_self_adjoint (f x) :=
 show star (f x) = f x, from map_star f x ▸ congr_arg f hx
 
-section add_group
-variables [add_group R] [star_add_monoid R]
+section add_monoid
+variables [add_monoid R] [star_add_monoid R]
 
 variables (R)
 
@@ -90,19 +94,24 @@ variables {R}
 lemma add {x y : R} (hx : is_self_adjoint x) (hy : is_self_adjoint y) : is_self_adjoint (x + y) :=
 by simp only [is_self_adjoint_iff, star_add, hx.star_eq, hy.star_eq]
 
+lemma bit0 {x : R} (hx : is_self_adjoint x) : is_self_adjoint (bit0 x) :=
+by simp only [is_self_adjoint_iff, star_bit0, hx.star_eq]
+
+end add_monoid
+
+section add_group
+variables [add_group R] [star_add_monoid R]
+
 lemma neg {x : R} (hx : is_self_adjoint x) : is_self_adjoint (-x) :=
 by simp only [is_self_adjoint_iff, star_neg, hx.star_eq]
 
 lemma sub {x y : R} (hx : is_self_adjoint x) (hy : is_self_adjoint y) : is_self_adjoint (x - y) :=
 by simp only [is_self_adjoint_iff, star_sub, hx.star_eq, hy.star_eq]
 
-lemma bit0 {x : R} (hx : is_self_adjoint x) : is_self_adjoint (bit0 x) :=
-by simp only [is_self_adjoint_iff, star_bit0, hx.star_eq]
-
 end add_group
 
-section non_unital_semiring
-variables [non_unital_semiring R] [star_ring R]
+section semigroup
+variables [semigroup R] [star_semigroup R]
 
 lemma conjugate {x : R} (hx : is_self_adjoint x) (z : R) : is_self_adjoint (z * x * star z) :=
 by simp only [is_self_adjoint_iff, star_mul, star_star, mul_assoc, hx.star_eq]
@@ -113,10 +122,10 @@ by simp only [is_self_adjoint_iff, star_mul, star_star, mul_assoc, hx.star_eq]
 lemma is_star_normal {x : R} (hx : is_self_adjoint x) : is_star_normal x :=
 ⟨by simp only [hx.star_eq]⟩
 
-end non_unital_semiring
+end semigroup
 
-section ring
-variables [ring R] [star_ring R]
+section monoid
+variables [monoid R] [star_semigroup R]
 
 variables (R)
 
@@ -124,42 +133,66 @@ lemma _root_.is_self_adjoint_one : is_self_adjoint (1 : R) := star_one R
 
 variables {R}
 
+lemma pow {x : R} (hx : is_self_adjoint x) (n : ℕ) : is_self_adjoint (x ^ n):=
+by simp only [is_self_adjoint_iff, star_pow, hx.star_eq]
+
+end monoid
+
+section semiring
+variables [semiring R] [star_ring R]
+
 lemma bit1 {x : R} (hx : is_self_adjoint x) : is_self_adjoint (bit1 x) :=
 by simp only [is_self_adjoint_iff, star_bit1, hx.star_eq]
 
-lemma pow {x : R} (hx : is_self_adjoint x) (n : ℕ) : is_self_adjoint (x ^ n):=
-by simp only [is_self_adjoint_iff, star_pow, hx.star_eq]
+@[simp] lemma _root_.is_self_adjoint_nat_cast (n : ℕ) : is_self_adjoint (n : R) :=
+star_nat_cast _
 
-end ring
+end semiring
 
-section non_unital_comm_ring
-variables [non_unital_comm_ring R] [star_ring R]
+section comm_semigroup
+variables [comm_semigroup R] [star_semigroup R]
 
 lemma mul {x y : R} (hx : is_self_adjoint x) (hy : is_self_adjoint y) : is_self_adjoint (x * y) :=
 by simp only [is_self_adjoint_iff, star_mul', hx.star_eq, hy.star_eq]
 
-end non_unital_comm_ring
+end comm_semigroup
 
-section field
-variables [field R] [star_ring R]
+section ring
+variables [ring R] [star_ring R]
+
+@[simp] lemma _root_.is_self_adjoint_int_cast (z : ℤ) : is_self_adjoint (z : R) :=
+star_int_cast _
+
+end ring
+
+section division_ring
+variables [division_ring R] [star_ring R]
 
 lemma inv {x : R} (hx : is_self_adjoint x) : is_self_adjoint x⁻¹ :=
 by simp only [is_self_adjoint_iff, star_inv', hx.star_eq]
 
-lemma div {x y : R} (hx : is_self_adjoint x) (hy : is_self_adjoint y) : is_self_adjoint (x / y) :=
-by simp only [is_self_adjoint_iff, star_div', hx.star_eq, hy.star_eq]
-
 lemma zpow {x : R} (hx : is_self_adjoint x) (n : ℤ) : is_self_adjoint (x ^ n):=
 by simp only [is_self_adjoint_iff, star_zpow₀, hx.star_eq]
 
+lemma _root_.is_self_adjoint_rat_cast (x : ℚ) : is_self_adjoint (x : R) :=
+star_rat_cast _
+
+end division_ring
+
+section field
+variables [field R] [star_ring R]
+
+lemma div {x y : R} (hx : is_self_adjoint x) (hy : is_self_adjoint y) : is_self_adjoint (x / y) :=
+by simp only [is_self_adjoint_iff, star_div', hx.star_eq, hy.star_eq]
+
 end field
 
 section has_smul
-variables [has_star R] [has_trivial_star R] [add_group A] [star_add_monoid A]
+variables [has_star R] [add_monoid A] [star_add_monoid A] [has_smul R A] [star_module R A]
 
-lemma smul [has_smul R A] [star_module R A] (r : R) {x : A} (hx : is_self_adjoint x) :
+lemma smul {r : R} (hr : is_self_adjoint r) {x : A} (hx : is_self_adjoint x) :
   is_self_adjoint (r • x) :=
-by simp only [is_self_adjoint_iff, star_smul, star_trivial, hx.star_eq]
+by simp only [is_self_adjoint_iff, star_smul, hr.star_eq, hx.star_eq]
 
 end has_smul
 
@@ -208,16 +241,10 @@ instance : has_one (self_adjoint R) := ⟨⟨1, is_self_adjoint_one R⟩⟩
 instance [nontrivial R] : nontrivial (self_adjoint R) := ⟨⟨0, 1, subtype.ne_of_val_ne zero_ne_one⟩⟩
 
 instance : has_nat_cast (self_adjoint R) :=
-⟨λ n, ⟨n, nat.rec_on n (by simp [zero_mem])
-  (λ k hk, (@nat.cast_succ R _ k).symm ▸ add_mem hk (is_self_adjoint_one R))⟩⟩
+⟨λ n, ⟨n, is_self_adjoint_nat_cast _⟩⟩
 
 instance : has_int_cast (self_adjoint R) :=
-⟨λ n, ⟨n,
-  begin
-    cases n;
-    simp [show ↑n ∈ self_adjoint R, from (n : self_adjoint R).2],
-    refine add_mem (is_self_adjoint_one R).neg (n : self_adjoint R).2.neg,
-  end ⟩ ⟩
+⟨λ n, ⟨n, is_self_adjoint_int_cast _⟩ ⟩
 
 instance : has_pow (self_adjoint R) ℕ :=
 ⟨λ x n, ⟨(x : R) ^ n, x.prop.pow n⟩⟩
@@ -266,18 +293,14 @@ instance : has_pow (self_adjoint R) ℤ :=
 
 @[simp, norm_cast] lemma coe_zpow (x : self_adjoint R) (z : ℤ) : ↑(x ^ z) = (x : R) ^ z := rfl
 
-lemma rat_cast_mem : ∀ (x : ℚ), is_self_adjoint (x : R)
-| ⟨a, b, h1, h2⟩ :=
-  by rw [is_self_adjoint, rat.cast_mk', star_mul', star_inv', star_nat_cast, star_int_cast]
-
 instance : has_rat_cast (self_adjoint R) :=
-⟨λ n, ⟨n, rat_cast_mem n⟩⟩
+⟨λ n, ⟨n, is_self_adjoint_rat_cast n⟩⟩
 
 @[simp, norm_cast] lemma coe_rat_cast (x : ℚ) : ↑(x : self_adjoint R) = (x : R) :=
 rfl
 
 instance has_qsmul : has_smul ℚ (self_adjoint R) :=
-⟨λ a x, ⟨a • x, by rw rat.smul_def; exact (rat_cast_mem a).mul x.prop⟩⟩
+⟨λ a x, ⟨a • x, by rw rat.smul_def; exact is_self_adjoint.mul (is_self_adjoint_rat_cast a) x.prop⟩⟩
 
 @[simp, norm_cast] lemma coe_rat_smul (x : self_adjoint R) (a : ℚ) : ↑(a • x) = a • (x : R) :=
 rfl
@@ -294,7 +317,7 @@ section has_smul
 variables [has_star R] [has_trivial_star R] [add_group A] [star_add_monoid A]
 
 instance [has_smul R A] [star_module R A] : has_smul R (self_adjoint A) :=
-⟨λ r x, ⟨r • x, x.prop.smul r⟩⟩
+⟨λ r x, ⟨r • x, (is_self_adjoint.all _).smul x.prop⟩⟩
 
 @[simp, norm_cast] lemma coe_smul [has_smul R A] [star_module R A] (r : R) (x : self_adjoint A) :
   ↑(r • x) = r • (x : A) := rfl

f93c1193

(first ported)

Changes in mathlib3port

mathlib3

mathlib3port

a6ece354

bump to nightly-2024-04-07-08

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

b03b8656

Diff

@@ -483,25 +483,25 @@ theorem val_ratCast (x : ℚ) : ↑(x : selfAdjoint R) = (x : R) :=
 #align self_adjoint.coe_rat_cast selfAdjoint.val_ratCast
 -/
 
-#print selfAdjoint.instQSMul /-
-instance instQSMul : SMul ℚ (selfAdjoint R) :=
+#print selfAdjoint.instSMulRat /-
+instance instSMulRat : SMul ℚ (selfAdjoint R) :=
   ⟨fun a x =>
     ⟨a • x, by rw [Rat.smul_def] <;> exact IsSelfAdjoint.mul (isSelfAdjoint_ratCast a) x.prop⟩⟩
-#align self_adjoint.has_qsmul selfAdjoint.instQSMul
+#align self_adjoint.has_qsmul selfAdjoint.instSMulRat
 -/
 
-#print selfAdjoint.val_rat_smul /-
+#print selfAdjoint.val_qsmul /-
 @[simp, norm_cast]
-theorem val_rat_smul (x : selfAdjoint R) (a : ℚ) : ↑(a • x) = a • (x : R) :=
+theorem val_qsmul (x : selfAdjoint R) (a : ℚ) : ↑(a • x) = a • (x : R) :=
   rfl
-#align self_adjoint.coe_rat_smul selfAdjoint.val_rat_smul
+#align self_adjoint.coe_rat_smul selfAdjoint.val_qsmul
 -/
 
 instance : Field (selfAdjoint R) :=
   Function.Injective.field _ Subtype.coe_injective (selfAdjoint R).val_zero val_one
     (selfAdjoint R).val_add val_mul (selfAdjoint R).val_neg (selfAdjoint R).val_neg_eq_neg_val
     val_inv val_div (selfAdjoint R).val_nsmul_eq_nsmul_val (selfAdjoint R).val_zsmul_eq_zsmul_val
-    val_rat_smul val_pow val_zpow (fun _ => rfl) (fun _ => rfl) val_ratCast
+    val_qsmul val_pow val_zpow (fun _ => rfl) (fun _ => rfl) val_ratCast
 
 end Field

a6ece354

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -586,7 +586,7 @@ theorem conjugate' {x : R} (hx : x ∈ skewAdjoint R) (z : R) : star z * x * z 
 
 #print skewAdjoint.isStarNormal_of_mem /-
 theorem isStarNormal_of_mem {x : R} (hx : x ∈ skewAdjoint R) : IsStarNormal x :=
-  ⟨by simp only [mem_iff] at hx ; simp only [hx, Commute.neg_left]⟩
+  ⟨by simp only [mem_iff] at hx; simp only [hx, Commute.neg_left]⟩
 #align skew_adjoint.is_star_normal_of_mem skewAdjoint.isStarNormal_of_mem
 -/

a6ece354

bump to nightly-2024-01-18-06

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

d4b8c2fa

Diff

@@ -659,11 +659,11 @@ instance isStarNormal_one [Monoid R] [StarMul R] : IsStarNormal (1 : R) :=
 #align is_star_normal_one isStarNormal_one
 -/
 
-#print isStarNormal_star_self /-
-instance isStarNormal_star_self [Monoid R] [StarMul R] {x : R} [IsStarNormal x] :
+#print IsStarNormal.star /-
+instance IsStarNormal.star [Monoid R] [StarMul R] {x : R} [IsStarNormal x] :
     IsStarNormal (star x) :=
   ⟨show star (star x) * star x = star x * star (star x) by rw [star_star, star_comm_self']⟩
-#align is_star_normal_star_self isStarNormal_star_self
+#align is_star_normal_star_self IsStarNormal.star
 -/
 
 #print TrivialStar.isStarNormal /-

a6ece354

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,8 +3,8 @@ Copyright (c) 2021 Frédéric Dupuis. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Frédéric Dupuis
 -/
-import Mathbin.Algebra.Star.Basic
-import Mathbin.GroupTheory.Subgroup.Basic
+import Algebra.Star.Basic
+import GroupTheory.Subgroup.Basic
 
 #align_import algebra.star.self_adjoint from "leanprover-community/mathlib"@"a6ece35404f60597c651689c1b46ead86de5ac1b"

a6ece354

bump to nightly-2023-09-02-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/442a83d738cb208d3600056c489be16900ba701d

a4ca67cb

Diff

@@ -98,14 +98,14 @@ theorem star_iff [InvolutiveStar R] {x : R} : IsSelfAdjoint (star x) ↔ IsSelfA
 
 #print IsSelfAdjoint.star_mul_self /-
 @[simp]
-theorem star_mul_self [Semigroup R] [StarSemigroup R] (x : R) : IsSelfAdjoint (star x * x) := by
+theorem star_mul_self [Semigroup R] [StarMul R] (x : R) : IsSelfAdjoint (star x * x) := by
   simp only [IsSelfAdjoint, star_mul, star_star]
 #align is_self_adjoint.star_mul_self IsSelfAdjoint.star_mul_self
 -/
 
 #print IsSelfAdjoint.mul_star_self /-
 @[simp]
-theorem mul_star_self [Semigroup R] [StarSemigroup R] (x : R) : IsSelfAdjoint (x * star x) := by
+theorem mul_star_self [Semigroup R] [StarMul R] (x : R) : IsSelfAdjoint (x * star x) := by
   simpa only [star_star] using star_mul_self (star x)
 #align is_self_adjoint.mul_star_self IsSelfAdjoint.mul_star_self
 -/
@@ -184,7 +184,7 @@ end AddCommMonoid
 
 section Semigroup
 
-variable [Semigroup R] [StarSemigroup R]
+variable [Semigroup R] [StarMul R]
 
 #print IsSelfAdjoint.conjugate /-
 theorem conjugate {x : R} (hx : IsSelfAdjoint x) (z : R) : IsSelfAdjoint (z * x * star z) := by
@@ -208,7 +208,7 @@ end Semigroup
 
 section Monoid
 
-variable [Monoid R] [StarSemigroup R]
+variable [Monoid R] [StarMul R]
 
 variable (R)
 
@@ -249,7 +249,7 @@ end Semiring
 
 section CommSemigroup
 
-variable [CommSemigroup R] [StarSemigroup R]
+variable [CommSemigroup R] [StarMul R]
 
 #print IsSelfAdjoint.mul /-
 theorem mul {x y : R} (hx : IsSelfAdjoint x) (hy : IsSelfAdjoint y) : IsSelfAdjoint (x * y) := by
@@ -654,13 +654,13 @@ instance isStarNormal_zero [Semiring R] [StarRing R] : IsStarNormal (0 : R) :=
 -/
 
 #print isStarNormal_one /-
-instance isStarNormal_one [Monoid R] [StarSemigroup R] : IsStarNormal (1 : R) :=
+instance isStarNormal_one [Monoid R] [StarMul R] : IsStarNormal (1 : R) :=
   ⟨by simp only [star_comm_self, star_one]⟩
 #align is_star_normal_one isStarNormal_one
 -/
 
 #print isStarNormal_star_self /-
-instance isStarNormal_star_self [Monoid R] [StarSemigroup R] {x : R} [IsStarNormal x] :
+instance isStarNormal_star_self [Monoid R] [StarMul R] {x : R} [IsStarNormal x] :
     IsStarNormal (star x) :=
   ⟨show star (star x) * star x = star x * star (star x) by rw [star_star, star_comm_self']⟩
 #align is_star_normal_star_self isStarNormal_star_self
@@ -668,15 +668,15 @@ instance isStarNormal_star_self [Monoid R] [StarSemigroup R] {x : R} [IsStarNorm
 
 #print TrivialStar.isStarNormal /-
 -- see Note [lower instance priority]
-instance (priority := 100) TrivialStar.isStarNormal [Monoid R] [StarSemigroup R] [TrivialStar R]
-    {x : R} : IsStarNormal x :=
+instance (priority := 100) TrivialStar.isStarNormal [Monoid R] [StarMul R] [TrivialStar R] {x : R} :
+    IsStarNormal x :=
   ⟨by rw [star_trivial]⟩
 #align has_trivial_star.is_star_normal TrivialStar.isStarNormal
 -/
 
 #print CommMonoid.isStarNormal /-
 -- see Note [lower instance priority]
-instance (priority := 100) CommMonoid.isStarNormal [CommMonoid R] [StarSemigroup R] {x : R} :
+instance (priority := 100) CommMonoid.isStarNormal [CommMonoid R] [StarMul R] {x : R} :
     IsStarNormal x :=
   ⟨mul_comm _ _⟩
 #align comm_monoid.is_star_normal CommMonoid.isStarNormal

a6ece354

bump to nightly-2023-08-23-23

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

f612b9e0

Diff

@@ -436,7 +436,7 @@ variable [CommRing R] [StarRing R]
 
 instance : CommRing (selfAdjoint R) :=
   Function.Injective.commRing _ Subtype.coe_injective (selfAdjoint R).val_zero val_one
-    (selfAdjoint R).val_add val_mul (selfAdjoint R).coeNeg (selfAdjoint R).val_neg_eq_neg_val
+    (selfAdjoint R).val_add val_mul (selfAdjoint R).val_neg (selfAdjoint R).val_neg_eq_neg_val
     (selfAdjoint R).val_nsmul_eq_nsmul_val (selfAdjoint R).val_zsmul_eq_zsmul_val val_pow
     (fun _ => rfl) fun _ => rfl
 
@@ -499,7 +499,7 @@ theorem val_rat_smul (x : selfAdjoint R) (a : ℚ) : ↑(a • x) = a • (x : R
 
 instance : Field (selfAdjoint R) :=
   Function.Injective.field _ Subtype.coe_injective (selfAdjoint R).val_zero val_one
-    (selfAdjoint R).val_add val_mul (selfAdjoint R).coeNeg (selfAdjoint R).val_neg_eq_neg_val
+    (selfAdjoint R).val_add val_mul (selfAdjoint R).val_neg (selfAdjoint R).val_neg_eq_neg_val
     val_inv val_div (selfAdjoint R).val_nsmul_eq_nsmul_val (selfAdjoint R).val_zsmul_eq_zsmul_val
     val_rat_smul val_pow val_zpow (fun _ => rfl) (fun _ => rfl) val_ratCast

a6ece354

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,15 +2,12 @@
 Copyright (c) 2021 Frédéric Dupuis. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Frédéric Dupuis
-
-! This file was ported from Lean 3 source module algebra.star.self_adjoint
-! leanprover-community/mathlib commit a6ece35404f60597c651689c1b46ead86de5ac1b
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.Star.Basic
 import Mathbin.GroupTheory.Subgroup.Basic
 
+#align_import algebra.star.self_adjoint from "leanprover-community/mathlib"@"a6ece35404f60597c651689c1b46ead86de5ac1b"
+
 /-!
 # Self-adjoint, skew-adjoint and normal elements of a star additive group

a6ece354

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -99,21 +99,27 @@ theorem star_iff [InvolutiveStar R] {x : R} : IsSelfAdjoint (star x) ↔ IsSelfA
 #align is_self_adjoint.star_iff IsSelfAdjoint.star_iff
 -/
 
+#print IsSelfAdjoint.star_mul_self /-
 @[simp]
 theorem star_mul_self [Semigroup R] [StarSemigroup R] (x : R) : IsSelfAdjoint (star x * x) := by
   simp only [IsSelfAdjoint, star_mul, star_star]
 #align is_self_adjoint.star_mul_self IsSelfAdjoint.star_mul_self
+-/
 
+#print IsSelfAdjoint.mul_star_self /-
 @[simp]
 theorem mul_star_self [Semigroup R] [StarSemigroup R] (x : R) : IsSelfAdjoint (x * star x) := by
   simpa only [star_star] using star_mul_self (star x)
 #align is_self_adjoint.mul_star_self IsSelfAdjoint.mul_star_self
+-/
 
+#print IsSelfAdjoint.starHom_apply /-
 /-- Functions in a `star_hom_class` preserve self-adjoint elements. -/
 theorem starHom_apply {F R S : Type _} [Star R] [Star S] [StarHomClass F R S] {x : R}
     (hx : IsSelfAdjoint x) (f : F) : IsSelfAdjoint (f x) :=
   show star (f x) = f x from map_star f x ▸ congr_arg f hx
 #align is_self_adjoint.star_hom_apply IsSelfAdjoint.starHom_apply
+-/
 
 section AddMonoid
 
@@ -121,19 +127,25 @@ variable [AddMonoid R] [StarAddMonoid R]
 
 variable (R)
 
+#print isSelfAdjoint_zero /-
 theorem isSelfAdjoint_zero : IsSelfAdjoint (0 : R) :=
   star_zero R
 #align is_self_adjoint_zero isSelfAdjoint_zero
+-/
 
 variable {R}
 
+#print IsSelfAdjoint.add /-
 theorem add {x y : R} (hx : IsSelfAdjoint x) (hy : IsSelfAdjoint y) : IsSelfAdjoint (x + y) := by
   simp only [isSelfAdjoint_iff, star_add, hx.star_eq, hy.star_eq]
 #align is_self_adjoint.add IsSelfAdjoint.add
+-/
 
+#print IsSelfAdjoint.bit0 /-
 theorem bit0 {x : R} (hx : IsSelfAdjoint x) : IsSelfAdjoint (bit0 x) := by
   simp only [isSelfAdjoint_iff, star_bit0, hx.star_eq]
 #align is_self_adjoint.bit0 IsSelfAdjoint.bit0
+-/
 
 end AddMonoid
 
@@ -141,13 +153,17 @@ section AddGroup
 
 variable [AddGroup R] [StarAddMonoid R]
 
+#print IsSelfAdjoint.neg /-
 theorem neg {x : R} (hx : IsSelfAdjoint x) : IsSelfAdjoint (-x) := by
   simp only [isSelfAdjoint_iff, star_neg, hx.star_eq]
 #align is_self_adjoint.neg IsSelfAdjoint.neg
+-/
 
+#print IsSelfAdjoint.sub /-
 theorem sub {x y : R} (hx : IsSelfAdjoint x) (hy : IsSelfAdjoint y) : IsSelfAdjoint (x - y) := by
   simp only [isSelfAdjoint_iff, star_sub, hx.star_eq, hy.star_eq]
 #align is_self_adjoint.sub IsSelfAdjoint.sub
+-/
 
 end AddGroup
 
@@ -155,13 +171,17 @@ section AddCommMonoid
 
 variable [AddCommMonoid R] [StarAddMonoid R]
 
+#print isSelfAdjoint_add_star_self /-
 theorem isSelfAdjoint_add_star_self (x : R) : IsSelfAdjoint (x + star x) := by
   simp only [isSelfAdjoint_iff, add_comm, star_add, star_star]
 #align is_self_adjoint_add_star_self isSelfAdjoint_add_star_self
+-/
 
+#print isSelfAdjoint_star_add_self /-
 theorem isSelfAdjoint_star_add_self (x : R) : IsSelfAdjoint (star x + x) := by
   simp only [isSelfAdjoint_iff, add_comm, star_add, star_star]
 #align is_self_adjoint_star_add_self isSelfAdjoint_star_add_self
+-/
 
 end AddCommMonoid
 
@@ -169,17 +189,23 @@ section Semigroup
 
 variable [Semigroup R] [StarSemigroup R]
 
+#print IsSelfAdjoint.conjugate /-
 theorem conjugate {x : R} (hx : IsSelfAdjoint x) (z : R) : IsSelfAdjoint (z * x * star z) := by
   simp only [isSelfAdjoint_iff, star_mul, star_star, mul_assoc, hx.star_eq]
 #align is_self_adjoint.conjugate IsSelfAdjoint.conjugate
+-/
 
+#print IsSelfAdjoint.conjugate' /-
 theorem conjugate' {x : R} (hx : IsSelfAdjoint x) (z : R) : IsSelfAdjoint (star z * x * z) := by
   simp only [isSelfAdjoint_iff, star_mul, star_star, mul_assoc, hx.star_eq]
 #align is_self_adjoint.conjugate' IsSelfAdjoint.conjugate'
+-/
 
+#print IsSelfAdjoint.isStarNormal /-
 theorem isStarNormal {x : R} (hx : IsSelfAdjoint x) : IsStarNormal x :=
   ⟨by simp only [hx.star_eq]⟩
 #align is_self_adjoint.is_star_normal IsSelfAdjoint.isStarNormal
+-/
 
 end Semigroup
 
@@ -189,9 +215,11 @@ variable [Monoid R] [StarSemigroup R]
 
 variable (R)
 
+#print isSelfAdjoint_one /-
 theorem isSelfAdjoint_one : IsSelfAdjoint (1 : R) :=
   star_one R
 #align is_self_adjoint_one isSelfAdjoint_one
+-/
 
 variable {R}
 
@@ -207,9 +235,11 @@ section Semiring
 
 variable [Semiring R] [StarRing R]
 
+#print IsSelfAdjoint.bit1 /-
 theorem bit1 {x : R} (hx : IsSelfAdjoint x) : IsSelfAdjoint (bit1 x) := by
   simp only [isSelfAdjoint_iff, star_bit1, hx.star_eq]
 #align is_self_adjoint.bit1 IsSelfAdjoint.bit1
+-/
 
 #print isSelfAdjoint_natCast /-
 @[simp]
@@ -224,9 +254,11 @@ section CommSemigroup
 
 variable [CommSemigroup R] [StarSemigroup R]
 
+#print IsSelfAdjoint.mul /-
 theorem mul {x y : R} (hx : IsSelfAdjoint x) (hy : IsSelfAdjoint y) : IsSelfAdjoint (x * y) := by
   simp only [isSelfAdjoint_iff, star_mul', hx.star_eq, hy.star_eq]
 #align is_self_adjoint.mul IsSelfAdjoint.mul
+-/
 
 end CommSemigroup
 
@@ -234,10 +266,12 @@ section Ring
 
 variable [Ring R] [StarRing R]
 
+#print isSelfAdjoint_intCast /-
 @[simp]
 theorem isSelfAdjoint_intCast (z : ℤ) : IsSelfAdjoint (z : R) :=
   star_intCast _
 #align is_self_adjoint_int_cast isSelfAdjoint_intCast
+-/
 
 end Ring
 
@@ -245,9 +279,11 @@ section DivisionSemiring
 
 variable [DivisionSemiring R] [StarRing R]
 
+#print IsSelfAdjoint.inv /-
 theorem inv {x : R} (hx : IsSelfAdjoint x) : IsSelfAdjoint x⁻¹ := by
   simp only [isSelfAdjoint_iff, star_inv', hx.star_eq]
 #align is_self_adjoint.inv IsSelfAdjoint.inv
+-/
 
 #print IsSelfAdjoint.zpow /-
 theorem zpow {x : R} (hx : IsSelfAdjoint x) (n : ℤ) : IsSelfAdjoint (x ^ n) := by
@@ -261,9 +297,11 @@ section DivisionRing
 
 variable [DivisionRing R] [StarRing R]
 
+#print isSelfAdjoint_ratCast /-
 theorem isSelfAdjoint_ratCast (x : ℚ) : IsSelfAdjoint (x : R) :=
   star_ratCast _
 #align is_self_adjoint_rat_cast isSelfAdjoint_ratCast
+-/
 
 end DivisionRing
 
@@ -271,9 +309,11 @@ section Semifield
 
 variable [Semifield R] [StarRing R]
 
+#print IsSelfAdjoint.div /-
 theorem div {x y : R} (hx : IsSelfAdjoint x) (hy : IsSelfAdjoint y) : IsSelfAdjoint (x / y) := by
   simp only [isSelfAdjoint_iff, star_div', hx.star_eq, hy.star_eq]
 #align is_self_adjoint.div IsSelfAdjoint.div
+-/
 
 end Semifield
 
@@ -281,9 +321,11 @@ section SMul
 
 variable [Star R] [AddMonoid A] [StarAddMonoid A] [SMul R A] [StarModule R A]
 
+#print IsSelfAdjoint.smul /-
 theorem smul {r : R} (hr : IsSelfAdjoint r) {x : A} (hx : IsSelfAdjoint x) :
     IsSelfAdjoint (r • x) := by simp only [isSelfAdjoint_iff, star_smul, hr.star_eq, hx.star_eq]
 #align is_self_adjoint.smul IsSelfAdjoint.smul
+-/
 
 end SMul
 
@@ -322,14 +364,18 @@ section AddGroup
 
 variable [AddGroup R] [StarAddMonoid R]
 
+#print selfAdjoint.mem_iff /-
 theorem mem_iff {x : R} : x ∈ selfAdjoint R ↔ star x = x := by rw [← AddSubgroup.mem_carrier];
   exact Iff.rfl
 #align self_adjoint.mem_iff selfAdjoint.mem_iff
+-/
 
+#print selfAdjoint.star_val_eq /-
 @[simp, norm_cast]
 theorem star_val_eq {x : selfAdjoint R} : star (x : R) = x :=
   x.Prop
 #align self_adjoint.star_coe_eq selfAdjoint.star_val_eq
+-/
 
 instance : Inhabited (selfAdjoint R) :=
   ⟨0⟩
@@ -362,10 +408,12 @@ instance : IntCast (selfAdjoint R) :=
 instance : Pow (selfAdjoint R) ℕ :=
   ⟨fun x n => ⟨(x : R) ^ n, x.Prop.pow n⟩⟩
 
+#print selfAdjoint.val_pow /-
 @[simp, norm_cast]
 theorem val_pow (x : selfAdjoint R) (n : ℕ) : ↑(x ^ n) = (x : R) ^ n :=
   rfl
 #align self_adjoint.coe_pow selfAdjoint.val_pow
+-/
 
 end Ring
 
@@ -376,10 +424,12 @@ variable [NonUnitalCommRing R] [StarRing R]
 instance : Mul (selfAdjoint R) :=
   ⟨fun x y => ⟨(x : R) * y, x.Prop.mul y.Prop⟩⟩
 
+#print selfAdjoint.val_mul /-
 @[simp, norm_cast]
 theorem val_mul (x y : selfAdjoint R) : ↑(x * y) = (x : R) * y :=
   rfl
 #align self_adjoint.coe_mul selfAdjoint.val_mul
+-/
 
 end NonUnitalCommRing
 
@@ -401,42 +451,54 @@ variable [Field R] [StarRing R]
 
 instance : Inv (selfAdjoint R) where inv x := ⟨x.val⁻¹, x.Prop.inv⟩
 
+#print selfAdjoint.val_inv /-
 @[simp, norm_cast]
 theorem val_inv (x : selfAdjoint R) : ↑x⁻¹ = (x : R)⁻¹ :=
   rfl
 #align self_adjoint.coe_inv selfAdjoint.val_inv
+-/
 
 instance : Div (selfAdjoint R) where div x y := ⟨x / y, x.Prop.div y.Prop⟩
 
+#print selfAdjoint.val_div /-
 @[simp, norm_cast]
 theorem val_div (x y : selfAdjoint R) : ↑(x / y) = (x / y : R) :=
   rfl
 #align self_adjoint.coe_div selfAdjoint.val_div
+-/
 
 instance : Pow (selfAdjoint R) ℤ where pow x z := ⟨x ^ z, x.Prop.zpow z⟩
 
+#print selfAdjoint.val_zpow /-
 @[simp, norm_cast]
 theorem val_zpow (x : selfAdjoint R) (z : ℤ) : ↑(x ^ z) = (x : R) ^ z :=
   rfl
 #align self_adjoint.coe_zpow selfAdjoint.val_zpow
+-/
 
 instance : HasRatCast (selfAdjoint R) :=
   ⟨fun n => ⟨n, isSelfAdjoint_ratCast n⟩⟩
 
+#print selfAdjoint.val_ratCast /-
 @[simp, norm_cast]
 theorem val_ratCast (x : ℚ) : ↑(x : selfAdjoint R) = (x : R) :=
   rfl
 #align self_adjoint.coe_rat_cast selfAdjoint.val_ratCast
+-/
 
+#print selfAdjoint.instQSMul /-
 instance instQSMul : SMul ℚ (selfAdjoint R) :=
   ⟨fun a x =>
     ⟨a • x, by rw [Rat.smul_def] <;> exact IsSelfAdjoint.mul (isSelfAdjoint_ratCast a) x.prop⟩⟩
 #align self_adjoint.has_qsmul selfAdjoint.instQSMul
+-/
 
+#print selfAdjoint.val_rat_smul /-
 @[simp, norm_cast]
 theorem val_rat_smul (x : selfAdjoint R) (a : ℚ) : ↑(a • x) = a • (x : R) :=
   rfl
 #align self_adjoint.coe_rat_smul selfAdjoint.val_rat_smul
+-/
 
 instance : Field (selfAdjoint R) :=
   Function.Injective.field _ Subtype.coe_injective (selfAdjoint R).val_zero val_one
@@ -453,10 +515,12 @@ variable [Star R] [TrivialStar R] [AddGroup A] [StarAddMonoid A]
 instance [SMul R A] [StarModule R A] : SMul R (selfAdjoint A) :=
   ⟨fun r x => ⟨r • x, (IsSelfAdjoint.all _).smul x.Prop⟩⟩
 
+#print selfAdjoint.val_smul /-
 @[simp, norm_cast]
 theorem val_smul [SMul R A] [StarModule R A] (r : R) (x : selfAdjoint A) : ↑(r • x) = r • (x : A) :=
   rfl
 #align self_adjoint.coe_smul selfAdjoint.val_smul
+-/
 
 instance [Monoid R] [MulAction R A] [StarModule R A] : MulAction R (selfAdjoint A) :=
   Function.Injective.mulAction coe Subtype.coe_injective val_smul
@@ -483,21 +547,27 @@ section AddGroup
 
 variable [AddCommGroup R] [StarAddMonoid R]
 
+#print skewAdjoint.mem_iff /-
 theorem mem_iff {x : R} : x ∈ skewAdjoint R ↔ star x = -x := by rw [← AddSubgroup.mem_carrier];
   exact Iff.rfl
 #align skew_adjoint.mem_iff skewAdjoint.mem_iff
+-/
 
+#print skewAdjoint.star_val_eq /-
 @[simp, norm_cast]
 theorem star_val_eq {x : skewAdjoint R} : star (x : R) = -x :=
   x.Prop
 #align skew_adjoint.star_coe_eq skewAdjoint.star_val_eq
+-/
 
 instance : Inhabited (skewAdjoint R) :=
   ⟨0⟩
 
+#print skewAdjoint.bit0_mem /-
 theorem bit0_mem {x : R} (hx : x ∈ skewAdjoint R) : bit0 x ∈ skewAdjoint R := by
   rw [mem_iff, star_bit0, mem_iff.mp hx, bit0, bit0, neg_add]
 #align skew_adjoint.bit0_mem skewAdjoint.bit0_mem
+-/
 
 end AddGroup
 
@@ -505,17 +575,23 @@ section Ring
 
 variable [Ring R] [StarRing R]
 
+#print skewAdjoint.conjugate /-
 theorem conjugate {x : R} (hx : x ∈ skewAdjoint R) (z : R) : z * x * star z ∈ skewAdjoint R := by
   simp only [mem_iff, star_mul, star_star, mem_iff.mp hx, neg_mul, mul_neg, mul_assoc]
 #align skew_adjoint.conjugate skewAdjoint.conjugate
+-/
 
+#print skewAdjoint.conjugate' /-
 theorem conjugate' {x : R} (hx : x ∈ skewAdjoint R) (z : R) : star z * x * z ∈ skewAdjoint R := by
   simp only [mem_iff, star_mul, star_star, mem_iff.mp hx, neg_mul, mul_neg, mul_assoc]
 #align skew_adjoint.conjugate' skewAdjoint.conjugate'
+-/
 
+#print skewAdjoint.isStarNormal_of_mem /-
 theorem isStarNormal_of_mem {x : R} (hx : x ∈ skewAdjoint R) : IsStarNormal x :=
   ⟨by simp only [mem_iff] at hx ; simp only [hx, Commute.neg_left]⟩
 #align skew_adjoint.is_star_normal_of_mem skewAdjoint.isStarNormal_of_mem
+-/
 
 instance (x : skewAdjoint R) : IsStarNormal (x : R) :=
   isStarNormal_of_mem (SetLike.coe_mem _)
@@ -526,19 +602,23 @@ section SMul
 
 variable [Star R] [TrivialStar R] [AddCommGroup A] [StarAddMonoid A]
 
+#print skewAdjoint.smul_mem /-
 theorem smul_mem [Monoid R] [DistribMulAction R A] [StarModule R A] (r : R) {x : A}
     (h : x ∈ skewAdjoint A) : r • x ∈ skewAdjoint A := by
   rw [mem_iff, star_smul, star_trivial, mem_iff.mp h, smul_neg r]
 #align skew_adjoint.smul_mem skewAdjoint.smul_mem
+-/
 
 instance [Monoid R] [DistribMulAction R A] [StarModule R A] : SMul R (skewAdjoint A) :=
   ⟨fun r x => ⟨r • x, smul_mem r x.Prop⟩⟩
 
+#print skewAdjoint.val_smul /-
 @[simp, norm_cast]
 theorem val_smul [Monoid R] [DistribMulAction R A] [StarModule R A] (r : R) (x : skewAdjoint A) :
     ↑(r • x) = r • (x : A) :=
   rfl
 #align skew_adjoint.coe_smul skewAdjoint.val_smul
+-/
 
 instance [Monoid R] [DistribMulAction R A] [StarModule R A] : DistribMulAction R (skewAdjoint A) :=
   Function.Injective.distribMulAction (skewAdjoint A).Subtype Subtype.coe_injective val_smul
@@ -550,6 +630,7 @@ end SMul
 
 end skewAdjoint
 
+#print IsSelfAdjoint.smul_mem_skewAdjoint /-
 /-- Scalar multiplication of a self-adjoint element by a skew-adjoint element produces a
 skew-adjoint element. -/
 theorem IsSelfAdjoint.smul_mem_skewAdjoint [Ring R] [AddCommGroup A] [Module R A] [StarAddMonoid R]
@@ -557,7 +638,9 @@ theorem IsSelfAdjoint.smul_mem_skewAdjoint [Ring R] [AddCommGroup A] [Module R A
     (ha : IsSelfAdjoint a) : r • a ∈ skewAdjoint A :=
   (star_smul _ _).trans <| (congr_arg₂ _ hr ha).trans <| neg_smul _ _
 #align is_self_adjoint.smul_mem_skew_adjoint IsSelfAdjoint.smul_mem_skewAdjoint
+-/
 
+#print isSelfAdjoint_smul_of_mem_skewAdjoint /-
 /-- Scalar multiplication of a skew-adjoint element by a skew-adjoint element produces a
 self-adjoint element. -/
 theorem isSelfAdjoint_smul_of_mem_skewAdjoint [Ring R] [AddCommGroup A] [Module R A]
@@ -565,29 +648,40 @@ theorem isSelfAdjoint_smul_of_mem_skewAdjoint [Ring R] [AddCommGroup A] [Module
     (ha : a ∈ skewAdjoint A) : IsSelfAdjoint (r • a) :=
   (star_smul _ _).trans <| (congr_arg₂ _ hr ha).trans <| neg_smul_neg _ _
 #align is_self_adjoint_smul_of_mem_skew_adjoint isSelfAdjoint_smul_of_mem_skewAdjoint
+-/
 
+#print isStarNormal_zero /-
 instance isStarNormal_zero [Semiring R] [StarRing R] : IsStarNormal (0 : R) :=
   ⟨by simp only [star_comm_self, star_zero]⟩
 #align is_star_normal_zero isStarNormal_zero
+-/
 
+#print isStarNormal_one /-
 instance isStarNormal_one [Monoid R] [StarSemigroup R] : IsStarNormal (1 : R) :=
   ⟨by simp only [star_comm_self, star_one]⟩
 #align is_star_normal_one isStarNormal_one
+-/
 
+#print isStarNormal_star_self /-
 instance isStarNormal_star_self [Monoid R] [StarSemigroup R] {x : R} [IsStarNormal x] :
     IsStarNormal (star x) :=
   ⟨show star (star x) * star x = star x * star (star x) by rw [star_star, star_comm_self']⟩
 #align is_star_normal_star_self isStarNormal_star_self
+-/
 
+#print TrivialStar.isStarNormal /-
 -- see Note [lower instance priority]
 instance (priority := 100) TrivialStar.isStarNormal [Monoid R] [StarSemigroup R] [TrivialStar R]
     {x : R} : IsStarNormal x :=
   ⟨by rw [star_trivial]⟩
 #align has_trivial_star.is_star_normal TrivialStar.isStarNormal
+-/
 
+#print CommMonoid.isStarNormal /-
 -- see Note [lower instance priority]
 instance (priority := 100) CommMonoid.isStarNormal [CommMonoid R] [StarSemigroup R] {x : R} :
     IsStarNormal x :=
   ⟨mul_comm _ _⟩
 #align comm_monoid.is_star_normal CommMonoid.isStarNormal
+-/

a6ece354

bump to nightly-2023-06-04-18

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

3fb4268b

Diff

@@ -295,7 +295,7 @@ variable (R)
 /-- The self-adjoint elements of a star additive group, as an additive subgroup. -/
 def selfAdjoint [AddGroup R] [StarAddMonoid R] : AddSubgroup R
     where
-  carrier := { x | IsSelfAdjoint x }
+  carrier := {x | IsSelfAdjoint x}
   zero_mem' := star_zero R
   add_mem' _ _ hx := hx.add
   neg_mem' _ hx := hx.neg
@@ -306,7 +306,7 @@ def selfAdjoint [AddGroup R] [StarAddMonoid R] : AddSubgroup R
 /-- The skew-adjoint elements of a star additive group, as an additive subgroup. -/
 def skewAdjoint [AddCommGroup R] [StarAddMonoid R] : AddSubgroup R
     where
-  carrier := { x | star x = -x }
+  carrier := {x | star x = -x}
   zero_mem' := show star (0 : R) = -0 by simp only [star_zero, neg_zero]
   add_mem' x y (hx : star x = -x) (hy : star y = -y) :=
     show star (x + y) = -(x + y) by rw [star_add x y, hx, hy, neg_add]

a6ece354

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -514,7 +514,7 @@ theorem conjugate' {x : R} (hx : x ∈ skewAdjoint R) (z : R) : star z * x * z 
 #align skew_adjoint.conjugate' skewAdjoint.conjugate'
 
 theorem isStarNormal_of_mem {x : R} (hx : x ∈ skewAdjoint R) : IsStarNormal x :=
-  ⟨by simp only [mem_iff] at hx; simp only [hx, Commute.neg_left]⟩
+  ⟨by simp only [mem_iff] at hx ; simp only [hx, Commute.neg_left]⟩
 #align skew_adjoint.is_star_normal_of_mem skewAdjoint.isStarNormal_of_mem
 
 instance (x : skewAdjoint R) : IsStarNormal (x : R) :=

a6ece354

bump to nightly-2023-06-01-04

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

4d9eaa85

Diff

@@ -389,7 +389,7 @@ variable [CommRing R] [StarRing R]
 
 instance : CommRing (selfAdjoint R) :=
   Function.Injective.commRing _ Subtype.coe_injective (selfAdjoint R).val_zero val_one
-    (selfAdjoint R).val_add val_mul (selfAdjoint R).coe_neg (selfAdjoint R).val_neg_eq_neg_val
+    (selfAdjoint R).val_add val_mul (selfAdjoint R).coeNeg (selfAdjoint R).val_neg_eq_neg_val
     (selfAdjoint R).val_nsmul_eq_nsmul_val (selfAdjoint R).val_zsmul_eq_zsmul_val val_pow
     (fun _ => rfl) fun _ => rfl
 
@@ -440,7 +440,7 @@ theorem val_rat_smul (x : selfAdjoint R) (a : ℚ) : ↑(a • x) = a • (x : R
 
 instance : Field (selfAdjoint R) :=
   Function.Injective.field _ Subtype.coe_injective (selfAdjoint R).val_zero val_one
-    (selfAdjoint R).val_add val_mul (selfAdjoint R).coe_neg (selfAdjoint R).val_neg_eq_neg_val
+    (selfAdjoint R).val_add val_mul (selfAdjoint R).coeNeg (selfAdjoint R).val_neg_eq_neg_val
     val_inv val_div (selfAdjoint R).val_nsmul_eq_nsmul_val (selfAdjoint R).val_zsmul_eq_zsmul_val
     val_rat_smul val_pow val_zpow (fun _ => rfl) (fun _ => rfl) val_ratCast

a6ece354

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -99,34 +99,16 @@ theorem star_iff [InvolutiveStar R] {x : R} : IsSelfAdjoint (star x) ↔ IsSelfA
 #align is_self_adjoint.star_iff IsSelfAdjoint.star_iff
 -/
 
-/- warning: is_self_adjoint.star_mul_self -> IsSelfAdjoint.star_mul_self is a dubious translation:
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-  forall {R : Type.{u1}} [_inst_1 : Semigroup.{u1} R] [_inst_2 : StarSemigroup.{u1} R _inst_1] (x : R), IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarSemigroup.toHasInvolutiveStar.{u1} R _inst_1 _inst_2)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Semigroup.toHasMul.{u1} R _inst_1)) (Star.star.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarSemigroup.toHasInvolutiveStar.{u1} R _inst_1 _inst_2)) x) x)
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semigroup.{u1} R] [_inst_2 : StarSemigroup.{u1} R _inst_1] (x : R), IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarSemigroup.toInvolutiveStar.{u1} R _inst_1 _inst_2)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Semigroup.toMul.{u1} R _inst_1)) (Star.star.{u1} R (InvolutiveStar.toStar.{u1} R (StarSemigroup.toInvolutiveStar.{u1} R _inst_1 _inst_2)) x) x)
-Case conversion may be inaccurate. Consider using '#align is_self_adjoint.star_mul_self IsSelfAdjoint.star_mul_selfₓ'. -/
 @[simp]
 theorem star_mul_self [Semigroup R] [StarSemigroup R] (x : R) : IsSelfAdjoint (star x * x) := by
   simp only [IsSelfAdjoint, star_mul, star_star]
 #align is_self_adjoint.star_mul_self IsSelfAdjoint.star_mul_self
 
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-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semigroup.{u1} R] [_inst_2 : StarSemigroup.{u1} R _inst_1] (x : R), IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarSemigroup.toInvolutiveStar.{u1} R _inst_1 _inst_2)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Semigroup.toMul.{u1} R _inst_1)) x (Star.star.{u1} R (InvolutiveStar.toStar.{u1} R (StarSemigroup.toInvolutiveStar.{u1} R _inst_1 _inst_2)) x))
-Case conversion may be inaccurate. Consider using '#align is_self_adjoint.mul_star_self IsSelfAdjoint.mul_star_selfₓ'. -/
 @[simp]
 theorem mul_star_self [Semigroup R] [StarSemigroup R] (x : R) : IsSelfAdjoint (x * star x) := by
   simpa only [star_star] using star_mul_self (star x)
 #align is_self_adjoint.mul_star_self IsSelfAdjoint.mul_star_self
 
-/- warning: is_self_adjoint.star_hom_apply -> IsSelfAdjoint.starHom_apply is a dubious translation:
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-but is expected to have type
-  forall {F : Type.{u3}} {R : Type.{u2}} {S : Type.{u1}} [_inst_1 : Star.{u2} R] [_inst_2 : Star.{u1} S] [_inst_3 : StarHomClass.{u3, u2, u1} F R S _inst_1 _inst_2] {x : R}, (IsSelfAdjoint.{u2} R _inst_1 x) -> (forall (f : F), IsSelfAdjoint.{u1} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3328 : R) => S) x) _inst_2 (FunLike.coe.{succ u3, succ u2, succ u1} F R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3328 : R) => S) _x) (StarHomClass.toFunLike.{u3, u2, u1} F R S _inst_1 _inst_2 _inst_3) f x))
-Case conversion may be inaccurate. Consider using '#align is_self_adjoint.star_hom_apply IsSelfAdjoint.starHom_applyₓ'. -/
 /-- Functions in a `star_hom_class` preserve self-adjoint elements. -/
 theorem starHom_apply {F R S : Type _} [Star R] [Star S] [StarHomClass F R S] {x : R}
     (hx : IsSelfAdjoint x) (f : F) : IsSelfAdjoint (f x) :=
@@ -139,34 +121,16 @@ variable [AddMonoid R] [StarAddMonoid R]
 
 variable (R)
 
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-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 is_self_adjoint_zero isSelfAdjoint_zeroₓ'. -/
 theorem isSelfAdjoint_zero : IsSelfAdjoint (0 : R) :=
   star_zero R
 #align is_self_adjoint_zero isSelfAdjoint_zero
 
 variable {R}
 
-/- warning: is_self_adjoint.add -> IsSelfAdjoint.add is a dubious translation:
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-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : AddMonoid.{u1} R] [_inst_2 : StarAddMonoid.{u1} R _inst_1] {x : R} {y : R}, (IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R _inst_1 _inst_2)) x) -> (IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R _inst_1 _inst_2)) y) -> (IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R _inst_1 _inst_2)) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (AddZeroClass.toAdd.{u1} R (AddMonoid.toAddZeroClass.{u1} R _inst_1))) x y))
-Case conversion may be inaccurate. Consider using '#align is_self_adjoint.add IsSelfAdjoint.addₓ'. -/
 theorem add {x y : R} (hx : IsSelfAdjoint x) (hy : IsSelfAdjoint y) : IsSelfAdjoint (x + y) := by
   simp only [isSelfAdjoint_iff, star_add, hx.star_eq, hy.star_eq]
 #align is_self_adjoint.add IsSelfAdjoint.add
 
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-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : AddMonoid.{u1} R] [_inst_2 : StarAddMonoid.{u1} R _inst_1] {x : R}, (IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R _inst_1 _inst_2)) x) -> (IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R _inst_1 _inst_2)) (bit0.{u1} R (AddZeroClass.toAdd.{u1} R (AddMonoid.toAddZeroClass.{u1} R _inst_1)) x))
-Case conversion may be inaccurate. Consider using '#align is_self_adjoint.bit0 IsSelfAdjoint.bit0ₓ'. -/
 theorem bit0 {x : R} (hx : IsSelfAdjoint x) : IsSelfAdjoint (bit0 x) := by
   simp only [isSelfAdjoint_iff, star_bit0, hx.star_eq]
 #align is_self_adjoint.bit0 IsSelfAdjoint.bit0
@@ -177,22 +141,10 @@ section AddGroup
 
 variable [AddGroup R] [StarAddMonoid R]
 
-/- warning: is_self_adjoint.neg -> IsSelfAdjoint.neg is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : AddGroup.{u1} R] [_inst_2 : StarAddMonoid.{u1} R (SubNegMonoid.toAddMonoid.{u1} R (AddGroup.toSubNegMonoid.{u1} R _inst_1))] {x : R}, (IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (SubNegMonoid.toAddMonoid.{u1} R (AddGroup.toSubNegMonoid.{u1} R _inst_1)) _inst_2)) x) -> (IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (SubNegMonoid.toAddMonoid.{u1} R (AddGroup.toSubNegMonoid.{u1} R _inst_1)) _inst_2)) (Neg.neg.{u1} R (NegZeroClass.toNeg.{u1} R (SubNegZeroMonoid.toNegZeroClass.{u1} R (SubtractionMonoid.toSubNegZeroMonoid.{u1} R (AddGroup.toSubtractionMonoid.{u1} R _inst_1)))) x))
-Case conversion may be inaccurate. Consider using '#align is_self_adjoint.neg IsSelfAdjoint.negₓ'. -/
 theorem neg {x : R} (hx : IsSelfAdjoint x) : IsSelfAdjoint (-x) := by
   simp only [isSelfAdjoint_iff, star_neg, hx.star_eq]
 #align is_self_adjoint.neg IsSelfAdjoint.neg
 
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-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : AddGroup.{u1} R] [_inst_2 : StarAddMonoid.{u1} R (SubNegMonoid.toAddMonoid.{u1} R (AddGroup.toSubNegMonoid.{u1} R _inst_1))] {x : R} {y : R}, (IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (SubNegMonoid.toAddMonoid.{u1} R (AddGroup.toSubNegMonoid.{u1} R _inst_1)) _inst_2)) x) -> (IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (SubNegMonoid.toAddMonoid.{u1} R (AddGroup.toSubNegMonoid.{u1} R _inst_1)) _inst_2)) y) -> (IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (SubNegMonoid.toAddMonoid.{u1} R (AddGroup.toSubNegMonoid.{u1} R _inst_1)) _inst_2)) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R _inst_1))) x y))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : AddGroup.{u1} R] [_inst_2 : StarAddMonoid.{u1} R (SubNegMonoid.toAddMonoid.{u1} R (AddGroup.toSubNegMonoid.{u1} R _inst_1))] {x : R} {y : R}, (IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (SubNegMonoid.toAddMonoid.{u1} R (AddGroup.toSubNegMonoid.{u1} R _inst_1)) _inst_2)) x) -> (IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (SubNegMonoid.toAddMonoid.{u1} R (AddGroup.toSubNegMonoid.{u1} R _inst_1)) _inst_2)) y) -> (IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (SubNegMonoid.toAddMonoid.{u1} R (AddGroup.toSubNegMonoid.{u1} R _inst_1)) _inst_2)) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R _inst_1))) x y))
-Case conversion may be inaccurate. Consider using '#align is_self_adjoint.sub IsSelfAdjoint.subₓ'. -/
 theorem sub {x y : R} (hx : IsSelfAdjoint x) (hy : IsSelfAdjoint y) : IsSelfAdjoint (x - y) := by
   simp only [isSelfAdjoint_iff, star_sub, hx.star_eq, hy.star_eq]
 #align is_self_adjoint.sub IsSelfAdjoint.sub
@@ -203,22 +155,10 @@ section AddCommMonoid
 
 variable [AddCommMonoid R] [StarAddMonoid R]
 
-/- warning: is_self_adjoint_add_star_self -> isSelfAdjoint_add_star_self is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : AddCommMonoid.{u1} R] [_inst_2 : StarAddMonoid.{u1} R (AddCommMonoid.toAddMonoid.{u1} R _inst_1)] (x : R), IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R _inst_1) _inst_2)) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (AddZeroClass.toHasAdd.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R _inst_1)))) x (Star.star.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R _inst_1) _inst_2)) x))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : AddCommMonoid.{u1} R] [_inst_2 : StarAddMonoid.{u1} R (AddCommMonoid.toAddMonoid.{u1} R _inst_1)] (x : R), IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R _inst_1) _inst_2)) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (AddZeroClass.toAdd.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R _inst_1)))) x (Star.star.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R _inst_1) _inst_2)) x))
-Case conversion may be inaccurate. Consider using '#align is_self_adjoint_add_star_self isSelfAdjoint_add_star_selfₓ'. -/
 theorem isSelfAdjoint_add_star_self (x : R) : IsSelfAdjoint (x + star x) := by
   simp only [isSelfAdjoint_iff, add_comm, star_add, star_star]
 #align is_self_adjoint_add_star_self isSelfAdjoint_add_star_self
 
-/- warning: is_self_adjoint_star_add_self -> isSelfAdjoint_star_add_self is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : AddCommMonoid.{u1} R] [_inst_2 : StarAddMonoid.{u1} R (AddCommMonoid.toAddMonoid.{u1} R _inst_1)] (x : R), IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R _inst_1) _inst_2)) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (AddZeroClass.toAdd.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R _inst_1)))) (Star.star.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R _inst_1) _inst_2)) x) x)
-Case conversion may be inaccurate. Consider using '#align is_self_adjoint_star_add_self isSelfAdjoint_star_add_selfₓ'. -/
 theorem isSelfAdjoint_star_add_self (x : R) : IsSelfAdjoint (star x + x) := by
   simp only [isSelfAdjoint_iff, add_comm, star_add, star_star]
 #align is_self_adjoint_star_add_self isSelfAdjoint_star_add_self
@@ -229,32 +169,14 @@ section Semigroup
 
 variable [Semigroup R] [StarSemigroup R]
 
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-  forall {R : Type.{u1}} [_inst_1 : Semigroup.{u1} R] [_inst_2 : StarSemigroup.{u1} R _inst_1] {x : R}, (IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarSemigroup.toHasInvolutiveStar.{u1} R _inst_1 _inst_2)) x) -> (forall (z : R), IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarSemigroup.toHasInvolutiveStar.{u1} R _inst_1 _inst_2)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Semigroup.toHasMul.{u1} R _inst_1)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Semigroup.toHasMul.{u1} R _inst_1)) z x) (Star.star.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarSemigroup.toHasInvolutiveStar.{u1} R _inst_1 _inst_2)) z)))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semigroup.{u1} R] [_inst_2 : StarSemigroup.{u1} R _inst_1] {x : R}, (IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarSemigroup.toInvolutiveStar.{u1} R _inst_1 _inst_2)) x) -> (forall (z : R), IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarSemigroup.toInvolutiveStar.{u1} R _inst_1 _inst_2)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Semigroup.toMul.{u1} R _inst_1)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Semigroup.toMul.{u1} R _inst_1)) z x) (Star.star.{u1} R (InvolutiveStar.toStar.{u1} R (StarSemigroup.toInvolutiveStar.{u1} R _inst_1 _inst_2)) z)))
-Case conversion may be inaccurate. Consider using '#align is_self_adjoint.conjugate IsSelfAdjoint.conjugateₓ'. -/
 theorem conjugate {x : R} (hx : IsSelfAdjoint x) (z : R) : IsSelfAdjoint (z * x * star z) := by
   simp only [isSelfAdjoint_iff, star_mul, star_star, mul_assoc, hx.star_eq]
 #align is_self_adjoint.conjugate IsSelfAdjoint.conjugate
 
-/- warning: is_self_adjoint.conjugate' -> IsSelfAdjoint.conjugate' is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : Semigroup.{u1} R] [_inst_2 : StarSemigroup.{u1} R _inst_1] {x : R}, (IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarSemigroup.toHasInvolutiveStar.{u1} R _inst_1 _inst_2)) x) -> (forall (z : R), IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarSemigroup.toHasInvolutiveStar.{u1} R _inst_1 _inst_2)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Semigroup.toHasMul.{u1} R _inst_1)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Semigroup.toHasMul.{u1} R _inst_1)) (Star.star.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarSemigroup.toHasInvolutiveStar.{u1} R _inst_1 _inst_2)) z) x) z))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semigroup.{u1} R] [_inst_2 : StarSemigroup.{u1} R _inst_1] {x : R}, (IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarSemigroup.toInvolutiveStar.{u1} R _inst_1 _inst_2)) x) -> (forall (z : R), IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarSemigroup.toInvolutiveStar.{u1} R _inst_1 _inst_2)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Semigroup.toMul.{u1} R _inst_1)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Semigroup.toMul.{u1} R _inst_1)) (Star.star.{u1} R (InvolutiveStar.toStar.{u1} R (StarSemigroup.toInvolutiveStar.{u1} R _inst_1 _inst_2)) z) x) z))
-Case conversion may be inaccurate. Consider using '#align is_self_adjoint.conjugate' IsSelfAdjoint.conjugate'ₓ'. -/
 theorem conjugate' {x : R} (hx : IsSelfAdjoint x) (z : R) : IsSelfAdjoint (star z * x * z) := by
   simp only [isSelfAdjoint_iff, star_mul, star_star, mul_assoc, hx.star_eq]
 #align is_self_adjoint.conjugate' IsSelfAdjoint.conjugate'
 
-/- warning: is_self_adjoint.is_star_normal -> IsSelfAdjoint.isStarNormal is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : Semigroup.{u1} R] [_inst_2 : StarSemigroup.{u1} R _inst_1] {x : R}, (IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarSemigroup.toHasInvolutiveStar.{u1} R _inst_1 _inst_2)) x) -> (IsStarNormal.{u1} R (Semigroup.toHasMul.{u1} R _inst_1) (InvolutiveStar.toHasStar.{u1} R (StarSemigroup.toHasInvolutiveStar.{u1} R _inst_1 _inst_2)) x)
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semigroup.{u1} R] [_inst_2 : StarSemigroup.{u1} R _inst_1] {x : R}, (IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarSemigroup.toInvolutiveStar.{u1} R _inst_1 _inst_2)) x) -> (IsStarNormal.{u1} R (Semigroup.toMul.{u1} R _inst_1) (InvolutiveStar.toStar.{u1} R (StarSemigroup.toInvolutiveStar.{u1} R _inst_1 _inst_2)) x)
-Case conversion may be inaccurate. Consider using '#align is_self_adjoint.is_star_normal IsSelfAdjoint.isStarNormalₓ'. -/
 theorem isStarNormal {x : R} (hx : IsSelfAdjoint x) : IsStarNormal x :=
   ⟨by simp only [hx.star_eq]⟩
 #align is_self_adjoint.is_star_normal IsSelfAdjoint.isStarNormal
@@ -267,12 +189,6 @@ variable [Monoid R] [StarSemigroup R]
 
 variable (R)
 
-/- warning: is_self_adjoint_one -> isSelfAdjoint_one is a dubious translation:
-lean 3 declaration is
-  forall (R : Type.{u1}) [_inst_1 : Monoid.{u1} R] [_inst_2 : StarSemigroup.{u1} R (Monoid.toSemigroup.{u1} R _inst_1)], IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarSemigroup.toHasInvolutiveStar.{u1} R (Monoid.toSemigroup.{u1} R _inst_1) _inst_2)) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (MulOneClass.toHasOne.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)))))
-but is expected to have type
-  forall (R : Type.{u1}) [_inst_1 : Monoid.{u1} R] [_inst_2 : StarSemigroup.{u1} R (Monoid.toSemigroup.{u1} R _inst_1)], IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarSemigroup.toInvolutiveStar.{u1} R (Monoid.toSemigroup.{u1} R _inst_1) _inst_2)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Monoid.toOne.{u1} R _inst_1)))
-Case conversion may be inaccurate. Consider using '#align is_self_adjoint_one isSelfAdjoint_oneₓ'. -/
 theorem isSelfAdjoint_one : IsSelfAdjoint (1 : R) :=
   star_one R
 #align is_self_adjoint_one isSelfAdjoint_one
@@ -291,12 +207,6 @@ section Semiring
 
 variable [Semiring R] [StarRing R]
 
-/- warning: is_self_adjoint.bit1 -> IsSelfAdjoint.bit1 is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_2 : StarRing.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_1)] {x : R}, (IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_1) _inst_2))) x) -> (IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_1) _inst_2))) (bit1.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Distrib.toHasAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) x))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_2 : StarRing.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_1)] {x : R}, (IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_1) _inst_2))) x) -> (IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_1) _inst_2))) (bit1.{u1} R (Semiring.toOne.{u1} R _inst_1) (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) x))
-Case conversion may be inaccurate. Consider using '#align is_self_adjoint.bit1 IsSelfAdjoint.bit1ₓ'. -/
 theorem bit1 {x : R} (hx : IsSelfAdjoint x) : IsSelfAdjoint (bit1 x) := by
   simp only [isSelfAdjoint_iff, star_bit1, hx.star_eq]
 #align is_self_adjoint.bit1 IsSelfAdjoint.bit1
@@ -314,12 +224,6 @@ section CommSemigroup
 
 variable [CommSemigroup R] [StarSemigroup R]
 
-/- warning: is_self_adjoint.mul -> IsSelfAdjoint.mul is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemigroup.{u1} R] [_inst_2 : StarSemigroup.{u1} R (CommSemigroup.toSemigroup.{u1} R _inst_1)] {x : R} {y : R}, (IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarSemigroup.toHasInvolutiveStar.{u1} R (CommSemigroup.toSemigroup.{u1} R _inst_1) _inst_2)) x) -> (IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarSemigroup.toHasInvolutiveStar.{u1} R (CommSemigroup.toSemigroup.{u1} R _inst_1) _inst_2)) y) -> (IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarSemigroup.toHasInvolutiveStar.{u1} R (CommSemigroup.toSemigroup.{u1} R _inst_1) _inst_2)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Semigroup.toHasMul.{u1} R (CommSemigroup.toSemigroup.{u1} R _inst_1))) x y))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemigroup.{u1} R] [_inst_2 : StarSemigroup.{u1} R (CommSemigroup.toSemigroup.{u1} R _inst_1)] {x : R} {y : R}, (IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarSemigroup.toInvolutiveStar.{u1} R (CommSemigroup.toSemigroup.{u1} R _inst_1) _inst_2)) x) -> (IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarSemigroup.toInvolutiveStar.{u1} R (CommSemigroup.toSemigroup.{u1} R _inst_1) _inst_2)) y) -> (IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarSemigroup.toInvolutiveStar.{u1} R (CommSemigroup.toSemigroup.{u1} R _inst_1) _inst_2)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Semigroup.toMul.{u1} R (CommSemigroup.toSemigroup.{u1} R _inst_1))) x y))
-Case conversion may be inaccurate. Consider using '#align is_self_adjoint.mul IsSelfAdjoint.mulₓ'. -/
 theorem mul {x y : R} (hx : IsSelfAdjoint x) (hy : IsSelfAdjoint y) : IsSelfAdjoint (x * y) := by
   simp only [isSelfAdjoint_iff, star_mul', hx.star_eq, hy.star_eq]
 #align is_self_adjoint.mul IsSelfAdjoint.mul
@@ -330,12 +234,6 @@ section Ring
 
 variable [Ring R] [StarRing R]
 
-/- warning: is_self_adjoint_int_cast -> isSelfAdjoint_intCast is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1))] (z : Int), IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1)) _inst_2))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int R (HasLiftT.mk.{1, succ u1} Int R (CoeTCₓ.coe.{1, succ u1} Int R (Int.castCoe.{u1} R (AddGroupWithOne.toHasIntCast.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1)))))) z)
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] [_inst_2 : StarRing.{u1} R (Semiring.toNonUnitalSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))] (z : Int), IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1))) (StarRing.toStarAddMonoid.{u1} R (Semiring.toNonUnitalSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) _inst_2))) (Int.cast.{u1} R (Ring.toIntCast.{u1} R _inst_1) z)
-Case conversion may be inaccurate. Consider using '#align is_self_adjoint_int_cast isSelfAdjoint_intCastₓ'. -/
 @[simp]
 theorem isSelfAdjoint_intCast (z : ℤ) : IsSelfAdjoint (z : R) :=
   star_intCast _
@@ -347,12 +245,6 @@ section DivisionSemiring
 
 variable [DivisionSemiring R] [StarRing R]
 
-/- warning: is_self_adjoint.inv -> IsSelfAdjoint.inv is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : DivisionSemiring.{u1} R] [_inst_2 : StarRing.{u1} R (Semiring.toNonUnitalSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R _inst_1))] {x : R}, (IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonUnitalSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (Semiring.toNonUnitalSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R _inst_1)) _inst_2))) x) -> (IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonUnitalSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (Semiring.toNonUnitalSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R _inst_1)) _inst_2))) (Inv.inv.{u1} R (DivInvMonoid.toHasInv.{u1} R (GroupWithZero.toDivInvMonoid.{u1} R (DivisionSemiring.toGroupWithZero.{u1} R _inst_1))) x))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : DivisionSemiring.{u1} R] [_inst_2 : StarRing.{u1} R (Semiring.toNonUnitalSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R _inst_1))] {x : R}, (IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (Semiring.toNonUnitalSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R _inst_1)) _inst_2))) x) -> (IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (Semiring.toNonUnitalSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R _inst_1)) _inst_2))) (Inv.inv.{u1} R (DivisionSemiring.toInv.{u1} R _inst_1) x))
-Case conversion may be inaccurate. Consider using '#align is_self_adjoint.inv IsSelfAdjoint.invₓ'. -/
 theorem inv {x : R} (hx : IsSelfAdjoint x) : IsSelfAdjoint x⁻¹ := by
   simp only [isSelfAdjoint_iff, star_inv', hx.star_eq]
 #align is_self_adjoint.inv IsSelfAdjoint.inv
@@ -369,12 +261,6 @@ section DivisionRing
 
 variable [DivisionRing R] [StarRing R]
 
-/- warning: is_self_adjoint_rat_cast -> isSelfAdjoint_ratCast is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : DivisionRing.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))] (x : Rat), IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) _inst_2))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Rat R (HasLiftT.mk.{1, succ u1} Rat R (CoeTCₓ.coe.{1, succ u1} Rat R (Rat.castCoe.{u1} R (DivisionRing.toHasRatCast.{u1} R _inst_1)))) x)
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : DivisionRing.{u1} R] [_inst_2 : StarRing.{u1} R (Semiring.toNonUnitalSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1)))] (x : Rat), IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (Semiring.toNonUnitalSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) _inst_2))) (Rat.cast.{u1} R (DivisionRing.toRatCast.{u1} R _inst_1) x)
-Case conversion may be inaccurate. Consider using '#align is_self_adjoint_rat_cast isSelfAdjoint_ratCastₓ'. -/
 theorem isSelfAdjoint_ratCast (x : ℚ) : IsSelfAdjoint (x : R) :=
   star_ratCast _
 #align is_self_adjoint_rat_cast isSelfAdjoint_ratCast
@@ -385,12 +271,6 @@ section Semifield
 
 variable [Semifield R] [StarRing R]
 
-/- warning: is_self_adjoint.div -> IsSelfAdjoint.div is a dubious translation:
-lean 3 declaration is
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 theorem div {x y : R} (hx : IsSelfAdjoint x) (hy : IsSelfAdjoint y) : IsSelfAdjoint (x / y) := by
   simp only [isSelfAdjoint_iff, star_div', hx.star_eq, hy.star_eq]
 #align is_self_adjoint.div IsSelfAdjoint.div
@@ -401,12 +281,6 @@ section SMul
 
 variable [Star R] [AddMonoid A] [StarAddMonoid A] [SMul R A] [StarModule R A]
 
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 theorem smul {r : R} (hr : IsSelfAdjoint r) {x : A} (hx : IsSelfAdjoint x) :
     IsSelfAdjoint (r • x) := by simp only [isSelfAdjoint_iff, star_smul, hr.star_eq, hx.star_eq]
 #align is_self_adjoint.smul IsSelfAdjoint.smul
@@ -448,22 +322,10 @@ section AddGroup
 
 variable [AddGroup R] [StarAddMonoid R]
 
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 theorem mem_iff {x : R} : x ∈ selfAdjoint R ↔ star x = x := by rw [← AddSubgroup.mem_carrier];
   exact Iff.rfl
 #align self_adjoint.mem_iff selfAdjoint.mem_iff
 
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 @[simp, norm_cast]
 theorem star_val_eq {x : selfAdjoint R} : star (x : R) = x :=
   x.Prop
@@ -500,9 +362,6 @@ instance : IntCast (selfAdjoint R) :=
 instance : Pow (selfAdjoint R) ℕ :=
   ⟨fun x n => ⟨(x : R) ^ n, x.Prop.pow n⟩⟩
 
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 @[simp, norm_cast]
 theorem val_pow (x : selfAdjoint R) (n : ℕ) : ↑(x ^ n) = (x : R) ^ n :=
   rfl
@@ -517,9 +376,6 @@ variable [NonUnitalCommRing R] [StarRing R]
 instance : Mul (selfAdjoint R) :=
   ⟨fun x y => ⟨(x : R) * y, x.Prop.mul y.Prop⟩⟩
 
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 @[simp, norm_cast]
 theorem val_mul (x y : selfAdjoint R) : ↑(x * y) = (x : R) * y :=
   rfl
@@ -545,9 +401,6 @@ variable [Field R] [StarRing R]
 
 instance : Inv (selfAdjoint R) where inv x := ⟨x.val⁻¹, x.Prop.inv⟩
 
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 @[simp, norm_cast]
 theorem val_inv (x : selfAdjoint R) : ↑x⁻¹ = (x : R)⁻¹ :=
   rfl
@@ -555,9 +408,6 @@ theorem val_inv (x : selfAdjoint R) : ↑x⁻¹ = (x : R)⁻¹ :=
 
 instance : Div (selfAdjoint R) where div x y := ⟨x / y, x.Prop.div y.Prop⟩
 
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 @[simp, norm_cast]
 theorem val_div (x y : selfAdjoint R) : ↑(x / y) = (x / y : R) :=
   rfl
@@ -565,9 +415,6 @@ theorem val_div (x y : selfAdjoint R) : ↑(x / y) = (x / y : R) :=
 
 instance : Pow (selfAdjoint R) ℤ where pow x z := ⟨x ^ z, x.Prop.zpow z⟩
 
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 @[simp, norm_cast]
 theorem val_zpow (x : selfAdjoint R) (z : ℤ) : ↑(x ^ z) = (x : R) ^ z :=
   rfl
@@ -576,28 +423,16 @@ theorem val_zpow (x : selfAdjoint R) (z : ℤ) : ↑(x ^ z) = (x : R) ^ z :=
 instance : HasRatCast (selfAdjoint R) :=
   ⟨fun n => ⟨n, isSelfAdjoint_ratCast n⟩⟩
 
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 @[simp, norm_cast]
 theorem val_ratCast (x : ℚ) : ↑(x : selfAdjoint R) = (x : R) :=
   rfl
 #align self_adjoint.coe_rat_cast selfAdjoint.val_ratCast
 
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 instance instQSMul : SMul ℚ (selfAdjoint R) :=
   ⟨fun a x =>
     ⟨a • x, by rw [Rat.smul_def] <;> exact IsSelfAdjoint.mul (isSelfAdjoint_ratCast a) x.prop⟩⟩
 #align self_adjoint.has_qsmul selfAdjoint.instQSMul
 
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 @[simp, norm_cast]
 theorem val_rat_smul (x : selfAdjoint R) (a : ℚ) : ↑(a • x) = a • (x : R) :=
   rfl
@@ -618,12 +453,6 @@ variable [Star R] [TrivialStar R] [AddGroup A] [StarAddMonoid A]
 instance [SMul R A] [StarModule R A] : SMul R (selfAdjoint A) :=
   ⟨fun r x => ⟨r • x, (IsSelfAdjoint.all _).smul x.Prop⟩⟩
 
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 @[simp, norm_cast]
 theorem val_smul [SMul R A] [StarModule R A] (r : R) (x : selfAdjoint A) : ↑(r • x) = r • (x : A) :=
   rfl
@@ -654,22 +483,10 @@ section AddGroup
 
 variable [AddCommGroup R] [StarAddMonoid R]
 
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 theorem mem_iff {x : R} : x ∈ skewAdjoint R ↔ star x = -x := by rw [← AddSubgroup.mem_carrier];
   exact Iff.rfl
 #align skew_adjoint.mem_iff skewAdjoint.mem_iff
 
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 @[simp, norm_cast]
 theorem star_val_eq {x : skewAdjoint R} : star (x : R) = -x :=
   x.Prop
@@ -678,12 +495,6 @@ theorem star_val_eq {x : skewAdjoint R} : star (x : R) = -x :=
 instance : Inhabited (skewAdjoint R) :=
   ⟨0⟩
 
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-Case conversion may be inaccurate. Consider using '#align skew_adjoint.bit0_mem skewAdjoint.bit0_memₓ'. -/
 theorem bit0_mem {x : R} (hx : x ∈ skewAdjoint R) : bit0 x ∈ skewAdjoint R := by
   rw [mem_iff, star_bit0, mem_iff.mp hx, bit0, bit0, neg_add]
 #align skew_adjoint.bit0_mem skewAdjoint.bit0_mem
@@ -694,32 +505,14 @@ section Ring
 
 variable [Ring R] [StarRing R]
 
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-Case conversion may be inaccurate. Consider using '#align skew_adjoint.conjugate skewAdjoint.conjugateₓ'. -/
 theorem conjugate {x : R} (hx : x ∈ skewAdjoint R) (z : R) : z * x * star z ∈ skewAdjoint R := by
   simp only [mem_iff, star_mul, star_star, mem_iff.mp hx, neg_mul, mul_neg, mul_assoc]
 #align skew_adjoint.conjugate skewAdjoint.conjugate
 
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 theorem conjugate' {x : R} (hx : x ∈ skewAdjoint R) (z : R) : star z * x * z ∈ skewAdjoint R := by
   simp only [mem_iff, star_mul, star_star, mem_iff.mp hx, neg_mul, mul_neg, mul_assoc]
 #align skew_adjoint.conjugate' skewAdjoint.conjugate'
 
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-Case conversion may be inaccurate. Consider using '#align skew_adjoint.is_star_normal_of_mem skewAdjoint.isStarNormal_of_memₓ'. -/
 theorem isStarNormal_of_mem {x : R} (hx : x ∈ skewAdjoint R) : IsStarNormal x :=
   ⟨by simp only [mem_iff] at hx; simp only [hx, Commute.neg_left]⟩
 #align skew_adjoint.is_star_normal_of_mem skewAdjoint.isStarNormal_of_mem
@@ -733,12 +526,6 @@ section SMul
 
 variable [Star R] [TrivialStar R] [AddCommGroup A] [StarAddMonoid A]
 
-/- warning: skew_adjoint.smul_mem -> skewAdjoint.smul_mem is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : Star.{u1} R] [_inst_2 : TrivialStar.{u1} R _inst_1] [_inst_3 : AddCommGroup.{u2} A] [_inst_4 : StarAddMonoid.{u2} A (SubNegMonoid.toAddMonoid.{u2} A (AddGroup.toSubNegMonoid.{u2} A (AddCommGroup.toAddGroup.{u2} A _inst_3)))] [_inst_5 : Monoid.{u1} R] [_inst_6 : DistribMulAction.{u1, u2} R A _inst_5 (SubNegMonoid.toAddMonoid.{u2} A (AddGroup.toSubNegMonoid.{u2} A (AddCommGroup.toAddGroup.{u2} A _inst_3)))] [_inst_7 : StarModule.{u1, u2} R A _inst_1 (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (SubNegMonoid.toAddMonoid.{u2} A (AddGroup.toSubNegMonoid.{u2} A (AddCommGroup.toAddGroup.{u2} A _inst_3))) _inst_4)) (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (SubNegMonoid.toAddMonoid.{u2} A (AddGroup.toSubNegMonoid.{u2} A (AddCommGroup.toAddGroup.{u2} A _inst_3))))) (DistribSMul.toSmulZeroClass.{u1, u2} R A (AddMonoid.toAddZeroClass.{u2} A (SubNegMonoid.toAddMonoid.{u2} A (AddGroup.toSubNegMonoid.{u2} A (AddCommGroup.toAddGroup.{u2} A _inst_3)))) (DistribMulAction.toDistribSMul.{u1, u2} R A _inst_5 (SubNegMonoid.toAddMonoid.{u2} A (AddGroup.toSubNegMonoid.{u2} A (AddCommGroup.toAddGroup.{u2} A _inst_3))) _inst_6)))] (r : R) {x : A}, (Membership.Mem.{u2, u2} A (AddSubgroup.{u2} A (AddCommGroup.toAddGroup.{u2} A _inst_3)) (SetLike.hasMem.{u2, u2} (AddSubgroup.{u2} A (AddCommGroup.toAddGroup.{u2} A _inst_3)) A (AddSubgroup.setLike.{u2} A (AddCommGroup.toAddGroup.{u2} A _inst_3))) x (skewAdjoint.{u2} A _inst_3 _inst_4)) -> (Membership.Mem.{u2, u2} A (AddSubgroup.{u2} A (AddCommGroup.toAddGroup.{u2} A _inst_3)) (SetLike.hasMem.{u2, u2} (AddSubgroup.{u2} A (AddCommGroup.toAddGroup.{u2} A _inst_3)) A (AddSubgroup.setLike.{u2} A (AddCommGroup.toAddGroup.{u2} A _inst_3))) (SMul.smul.{u1, u2} R A (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (SubNegMonoid.toAddMonoid.{u2} A (AddGroup.toSubNegMonoid.{u2} A (AddCommGroup.toAddGroup.{u2} A _inst_3))))) (DistribSMul.toSmulZeroClass.{u1, u2} R A (AddMonoid.toAddZeroClass.{u2} A (SubNegMonoid.toAddMonoid.{u2} A (AddGroup.toSubNegMonoid.{u2} A (AddCommGroup.toAddGroup.{u2} A _inst_3)))) (DistribMulAction.toDistribSMul.{u1, u2} R A _inst_5 (SubNegMonoid.toAddMonoid.{u2} A (AddGroup.toSubNegMonoid.{u2} A (AddCommGroup.toAddGroup.{u2} A _inst_3))) _inst_6))) r x) (skewAdjoint.{u2} A _inst_3 _inst_4))
-but is expected to have type
-  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : Star.{u2} R] [_inst_2 : TrivialStar.{u2} R _inst_1] [_inst_3 : AddCommGroup.{u1} A] [_inst_4 : StarAddMonoid.{u1} A (SubNegMonoid.toAddMonoid.{u1} A (AddGroup.toSubNegMonoid.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_3)))] [_inst_5 : Monoid.{u2} R] [_inst_6 : DistribMulAction.{u2, u1} R A _inst_5 (SubNegMonoid.toAddMonoid.{u1} A (AddGroup.toSubNegMonoid.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_3)))] [_inst_7 : StarModule.{u2, u1} R A _inst_1 (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (SubNegMonoid.toAddMonoid.{u1} A (AddGroup.toSubNegMonoid.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_3))) _inst_4)) (SMulZeroClass.toSMul.{u2, u1} R A (NegZeroClass.toZero.{u1} A (SubNegZeroMonoid.toNegZeroClass.{u1} A (SubtractionMonoid.toSubNegZeroMonoid.{u1} A (SubtractionCommMonoid.toSubtractionMonoid.{u1} A (AddCommGroup.toDivisionAddCommMonoid.{u1} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u2, u1} R A (AddMonoid.toAddZeroClass.{u1} A (SubNegMonoid.toAddMonoid.{u1} A (AddGroup.toSubNegMonoid.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_3)))) (DistribMulAction.toDistribSMul.{u2, u1} R A _inst_5 (SubNegMonoid.toAddMonoid.{u1} A (AddGroup.toSubNegMonoid.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_3))) _inst_6)))] (r : R) {x : A}, (Membership.mem.{u1, u1} A (AddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_3)) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_3)) A (AddSubgroup.instSetLikeAddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_3))) x (skewAdjoint.{u1} A _inst_3 _inst_4)) -> (Membership.mem.{u1, u1} A (AddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_3)) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_3)) A (AddSubgroup.instSetLikeAddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_3))) (HSMul.hSMul.{u2, u1, u1} R A A (instHSMul.{u2, u1} R A (SMulZeroClass.toSMul.{u2, u1} R A (NegZeroClass.toZero.{u1} A (SubNegZeroMonoid.toNegZeroClass.{u1} A (SubtractionMonoid.toSubNegZeroMonoid.{u1} A (SubtractionCommMonoid.toSubtractionMonoid.{u1} A (AddCommGroup.toDivisionAddCommMonoid.{u1} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u2, u1} R A (AddMonoid.toAddZeroClass.{u1} A (SubNegMonoid.toAddMonoid.{u1} A (AddGroup.toSubNegMonoid.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_3)))) (DistribMulAction.toDistribSMul.{u2, u1} R A _inst_5 (SubNegMonoid.toAddMonoid.{u1} A (AddGroup.toSubNegMonoid.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_3))) _inst_6)))) r x) (skewAdjoint.{u1} A _inst_3 _inst_4))
-Case conversion may be inaccurate. Consider using '#align skew_adjoint.smul_mem skewAdjoint.smul_memₓ'. -/
 theorem smul_mem [Monoid R] [DistribMulAction R A] [StarModule R A] (r : R) {x : A}
     (h : x ∈ skewAdjoint A) : r • x ∈ skewAdjoint A := by
   rw [mem_iff, star_smul, star_trivial, mem_iff.mp h, smul_neg r]
@@ -747,9 +534,6 @@ theorem smul_mem [Monoid R] [DistribMulAction R A] [StarModule R A] (r : R) {x :
 instance [Monoid R] [DistribMulAction R A] [StarModule R A] : SMul R (skewAdjoint A) :=
   ⟨fun r x => ⟨r • x, smul_mem r x.Prop⟩⟩
 
-/- warning: skew_adjoint.coe_smul -> skewAdjoint.val_smul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align skew_adjoint.coe_smul skewAdjoint.val_smulₓ'. -/
 @[simp, norm_cast]
 theorem val_smul [Monoid R] [DistribMulAction R A] [StarModule R A] (r : R) (x : skewAdjoint A) :
     ↑(r • x) = r • (x : A) :=
@@ -766,12 +550,6 @@ end SMul
 
 end skewAdjoint
 
-/- warning: is_self_adjoint.smul_mem_skew_adjoint -> IsSelfAdjoint.smul_mem_skewAdjoint is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} A] [_inst_3 : Module.{u1, u2} R A (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} A _inst_2)] [_inst_4 : StarAddMonoid.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1))))] [_inst_5 : StarAddMonoid.{u2} A (SubNegMonoid.toAddMonoid.{u2} A (AddGroup.toSubNegMonoid.{u2} A (AddCommGroup.toAddGroup.{u2} A _inst_2)))] [_inst_6 : StarModule.{u1, u2} R A (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1)))) _inst_4)) (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (SubNegMonoid.toAddMonoid.{u2} A (AddGroup.toSubNegMonoid.{u2} A (AddCommGroup.toAddGroup.{u2} A _inst_2))) _inst_5)) (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (AddCommGroup.toAddCommMonoid.{u2} A _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (AddCommGroup.toAddCommMonoid.{u2} A _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (AddCommGroup.toAddCommMonoid.{u2} A _inst_2)))) (Module.toMulActionWithZero.{u1, u2} R A (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} A _inst_2) _inst_3))))] {r : R}, (Membership.Mem.{u1, u1} R (AddSubgroup.{u1} R (AddCommGroup.toAddGroup.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))) (SetLike.hasMem.{u1, u1} (AddSubgroup.{u1} R (AddCommGroup.toAddGroup.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))) R (AddSubgroup.setLike.{u1} R (AddCommGroup.toAddGroup.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))))) r (skewAdjoint.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) _inst_4)) -> (forall {a : A}, (IsSelfAdjoint.{u2} A (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (SubNegMonoid.toAddMonoid.{u2} A (AddGroup.toSubNegMonoid.{u2} A (AddCommGroup.toAddGroup.{u2} A _inst_2))) _inst_5)) a) -> (Membership.Mem.{u2, u2} A (AddSubgroup.{u2} A (AddCommGroup.toAddGroup.{u2} A _inst_2)) (SetLike.hasMem.{u2, u2} (AddSubgroup.{u2} A (AddCommGroup.toAddGroup.{u2} A _inst_2)) A (AddSubgroup.setLike.{u2} A (AddCommGroup.toAddGroup.{u2} A _inst_2))) (SMul.smul.{u1, u2} R A (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (AddCommGroup.toAddCommMonoid.{u2} A _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (AddCommGroup.toAddCommMonoid.{u2} A _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (AddCommGroup.toAddCommMonoid.{u2} A _inst_2)))) (Module.toMulActionWithZero.{u1, u2} R A (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} A _inst_2) _inst_3)))) r a) (skewAdjoint.{u2} A _inst_2 _inst_5)))
-but is expected to have type
-  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} A] [_inst_3 : Module.{u2, u1} R A (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} A _inst_2)] [_inst_4 : StarAddMonoid.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (Ring.toAddGroupWithOne.{u2} R _inst_1)))] [_inst_5 : StarAddMonoid.{u1} A (SubNegMonoid.toAddMonoid.{u1} A (AddGroup.toSubNegMonoid.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_2)))] [_inst_6 : StarModule.{u2, u1} R A (InvolutiveStar.toStar.{u2} R (StarAddMonoid.toInvolutiveStar.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (Ring.toAddGroupWithOne.{u2} R _inst_1))) _inst_4)) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (SubNegMonoid.toAddMonoid.{u1} A (AddGroup.toSubNegMonoid.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_2))) _inst_5)) (SMulZeroClass.toSMul.{u2, u1} R A (NegZeroClass.toZero.{u1} A (SubNegZeroMonoid.toNegZeroClass.{u1} A (SubtractionMonoid.toSubNegZeroMonoid.{u1} A (SubtractionCommMonoid.toSubtractionMonoid.{u1} A (AddCommGroup.toDivisionAddCommMonoid.{u1} A _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} R A (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (NegZeroClass.toZero.{u1} A (SubNegZeroMonoid.toNegZeroClass.{u1} A (SubtractionMonoid.toSubNegZeroMonoid.{u1} A (SubtractionCommMonoid.toSubtractionMonoid.{u1} A (AddCommGroup.toDivisionAddCommMonoid.{u1} A _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} R A (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (NegZeroClass.toZero.{u1} A (SubNegZeroMonoid.toNegZeroClass.{u1} A (SubtractionMonoid.toSubNegZeroMonoid.{u1} A (SubtractionCommMonoid.toSubtractionMonoid.{u1} A (AddCommGroup.toDivisionAddCommMonoid.{u1} A _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R A (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} A _inst_2) _inst_3))))] {r : R}, (Membership.mem.{u2, u2} R (AddSubgroup.{u2} R (AddCommGroup.toAddGroup.{u2} R (Ring.toAddCommGroup.{u2} R _inst_1))) (SetLike.instMembership.{u2, u2} (AddSubgroup.{u2} R (AddCommGroup.toAddGroup.{u2} R (Ring.toAddCommGroup.{u2} R _inst_1))) R (AddSubgroup.instSetLikeAddSubgroup.{u2} R (AddCommGroup.toAddGroup.{u2} R (Ring.toAddCommGroup.{u2} R _inst_1)))) r (skewAdjoint.{u2} R (Ring.toAddCommGroup.{u2} R _inst_1) _inst_4)) -> (forall {a : A}, (IsSelfAdjoint.{u1} A (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (SubNegMonoid.toAddMonoid.{u1} A (AddGroup.toSubNegMonoid.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_2))) _inst_5)) a) -> (Membership.mem.{u1, u1} A (AddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_2)) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_2)) A (AddSubgroup.instSetLikeAddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_2))) (HSMul.hSMul.{u2, u1, u1} R A A (instHSMul.{u2, u1} R A (SMulZeroClass.toSMul.{u2, u1} R A (NegZeroClass.toZero.{u1} A (SubNegZeroMonoid.toNegZeroClass.{u1} A (SubtractionMonoid.toSubNegZeroMonoid.{u1} A (SubtractionCommMonoid.toSubtractionMonoid.{u1} A (AddCommGroup.toDivisionAddCommMonoid.{u1} A _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} R A (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (NegZeroClass.toZero.{u1} A (SubNegZeroMonoid.toNegZeroClass.{u1} A (SubtractionMonoid.toSubNegZeroMonoid.{u1} A (SubtractionCommMonoid.toSubtractionMonoid.{u1} A (AddCommGroup.toDivisionAddCommMonoid.{u1} A _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} R A (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (NegZeroClass.toZero.{u1} A (SubNegZeroMonoid.toNegZeroClass.{u1} A (SubtractionMonoid.toSubNegZeroMonoid.{u1} A (SubtractionCommMonoid.toSubtractionMonoid.{u1} A (AddCommGroup.toDivisionAddCommMonoid.{u1} A _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R A (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} A _inst_2) _inst_3))))) r a) (skewAdjoint.{u1} A _inst_2 _inst_5)))
-Case conversion may be inaccurate. Consider using '#align is_self_adjoint.smul_mem_skew_adjoint IsSelfAdjoint.smul_mem_skewAdjointₓ'. -/
 /-- Scalar multiplication of a self-adjoint element by a skew-adjoint element produces a
 skew-adjoint element. -/
 theorem IsSelfAdjoint.smul_mem_skewAdjoint [Ring R] [AddCommGroup A] [Module R A] [StarAddMonoid R]
@@ -780,12 +558,6 @@ theorem IsSelfAdjoint.smul_mem_skewAdjoint [Ring R] [AddCommGroup A] [Module R A
   (star_smul _ _).trans <| (congr_arg₂ _ hr ha).trans <| neg_smul _ _
 #align is_self_adjoint.smul_mem_skew_adjoint IsSelfAdjoint.smul_mem_skewAdjoint
 
-/- warning: is_self_adjoint_smul_of_mem_skew_adjoint -> isSelfAdjoint_smul_of_mem_skewAdjoint is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} A] [_inst_3 : Module.{u1, u2} R A (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} A _inst_2)] [_inst_4 : StarAddMonoid.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1))))] [_inst_5 : StarAddMonoid.{u2} A (SubNegMonoid.toAddMonoid.{u2} A (AddGroup.toSubNegMonoid.{u2} A (AddCommGroup.toAddGroup.{u2} A _inst_2)))] [_inst_6 : StarModule.{u1, u2} R A (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1)))) _inst_4)) (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (SubNegMonoid.toAddMonoid.{u2} A (AddGroup.toSubNegMonoid.{u2} A (AddCommGroup.toAddGroup.{u2} A _inst_2))) _inst_5)) (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (AddCommGroup.toAddCommMonoid.{u2} A _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (AddCommGroup.toAddCommMonoid.{u2} A _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (AddCommGroup.toAddCommMonoid.{u2} A _inst_2)))) (Module.toMulActionWithZero.{u1, u2} R A (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} A _inst_2) _inst_3))))] {r : R}, (Membership.Mem.{u1, u1} R (AddSubgroup.{u1} R (AddCommGroup.toAddGroup.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))) (SetLike.hasMem.{u1, u1} (AddSubgroup.{u1} R (AddCommGroup.toAddGroup.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))) R (AddSubgroup.setLike.{u1} R (AddCommGroup.toAddGroup.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))))) r (skewAdjoint.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) _inst_4)) -> (forall {a : A}, (Membership.Mem.{u2, u2} A (AddSubgroup.{u2} A (AddCommGroup.toAddGroup.{u2} A _inst_2)) (SetLike.hasMem.{u2, u2} (AddSubgroup.{u2} A (AddCommGroup.toAddGroup.{u2} A _inst_2)) A (AddSubgroup.setLike.{u2} A (AddCommGroup.toAddGroup.{u2} A _inst_2))) a (skewAdjoint.{u2} A _inst_2 _inst_5)) -> (IsSelfAdjoint.{u2} A (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (SubNegMonoid.toAddMonoid.{u2} A (AddGroup.toSubNegMonoid.{u2} A (AddCommGroup.toAddGroup.{u2} A _inst_2))) _inst_5)) (SMul.smul.{u1, u2} R A (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (AddCommGroup.toAddCommMonoid.{u2} A _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (AddCommGroup.toAddCommMonoid.{u2} A _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (AddCommGroup.toAddCommMonoid.{u2} A _inst_2)))) (Module.toMulActionWithZero.{u1, u2} R A (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} A _inst_2) _inst_3)))) r a)))
-but is expected to have type
-  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} A] [_inst_3 : Module.{u2, u1} R A (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} A _inst_2)] [_inst_4 : StarAddMonoid.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (Ring.toAddGroupWithOne.{u2} R _inst_1)))] [_inst_5 : StarAddMonoid.{u1} A (SubNegMonoid.toAddMonoid.{u1} A (AddGroup.toSubNegMonoid.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_2)))] [_inst_6 : StarModule.{u2, u1} R A (InvolutiveStar.toStar.{u2} R (StarAddMonoid.toInvolutiveStar.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (Ring.toAddGroupWithOne.{u2} R _inst_1))) _inst_4)) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (SubNegMonoid.toAddMonoid.{u1} A (AddGroup.toSubNegMonoid.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_2))) _inst_5)) (SMulZeroClass.toSMul.{u2, u1} R A (NegZeroClass.toZero.{u1} A (SubNegZeroMonoid.toNegZeroClass.{u1} A (SubtractionMonoid.toSubNegZeroMonoid.{u1} A (SubtractionCommMonoid.toSubtractionMonoid.{u1} A (AddCommGroup.toDivisionAddCommMonoid.{u1} A _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} R A (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (NegZeroClass.toZero.{u1} A (SubNegZeroMonoid.toNegZeroClass.{u1} A (SubtractionMonoid.toSubNegZeroMonoid.{u1} A (SubtractionCommMonoid.toSubtractionMonoid.{u1} A (AddCommGroup.toDivisionAddCommMonoid.{u1} A _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} R A (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (NegZeroClass.toZero.{u1} A (SubNegZeroMonoid.toNegZeroClass.{u1} A (SubtractionMonoid.toSubNegZeroMonoid.{u1} A (SubtractionCommMonoid.toSubtractionMonoid.{u1} A (AddCommGroup.toDivisionAddCommMonoid.{u1} A _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R A (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} A _inst_2) _inst_3))))] {r : R}, (Membership.mem.{u2, u2} R (AddSubgroup.{u2} R (AddCommGroup.toAddGroup.{u2} R (Ring.toAddCommGroup.{u2} R _inst_1))) (SetLike.instMembership.{u2, u2} (AddSubgroup.{u2} R (AddCommGroup.toAddGroup.{u2} R (Ring.toAddCommGroup.{u2} R _inst_1))) R (AddSubgroup.instSetLikeAddSubgroup.{u2} R (AddCommGroup.toAddGroup.{u2} R (Ring.toAddCommGroup.{u2} R _inst_1)))) r (skewAdjoint.{u2} R (Ring.toAddCommGroup.{u2} R _inst_1) _inst_4)) -> (forall {a : A}, (Membership.mem.{u1, u1} A (AddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_2)) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_2)) A (AddSubgroup.instSetLikeAddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_2))) a (skewAdjoint.{u1} A _inst_2 _inst_5)) -> (IsSelfAdjoint.{u1} A (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (SubNegMonoid.toAddMonoid.{u1} A (AddGroup.toSubNegMonoid.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_2))) _inst_5)) (HSMul.hSMul.{u2, u1, u1} R A A (instHSMul.{u2, u1} R A (SMulZeroClass.toSMul.{u2, u1} R A (NegZeroClass.toZero.{u1} A (SubNegZeroMonoid.toNegZeroClass.{u1} A (SubtractionMonoid.toSubNegZeroMonoid.{u1} A (SubtractionCommMonoid.toSubtractionMonoid.{u1} A (AddCommGroup.toDivisionAddCommMonoid.{u1} A _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} R A (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (NegZeroClass.toZero.{u1} A (SubNegZeroMonoid.toNegZeroClass.{u1} A (SubtractionMonoid.toSubNegZeroMonoid.{u1} A (SubtractionCommMonoid.toSubtractionMonoid.{u1} A (AddCommGroup.toDivisionAddCommMonoid.{u1} A _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} R A (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (NegZeroClass.toZero.{u1} A (SubNegZeroMonoid.toNegZeroClass.{u1} A (SubtractionMonoid.toSubNegZeroMonoid.{u1} A (SubtractionCommMonoid.toSubtractionMonoid.{u1} A (AddCommGroup.toDivisionAddCommMonoid.{u1} A _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R A (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} A _inst_2) _inst_3))))) r a)))
-Case conversion may be inaccurate. Consider using '#align is_self_adjoint_smul_of_mem_skew_adjoint isSelfAdjoint_smul_of_mem_skewAdjointₓ'. -/
 /-- Scalar multiplication of a skew-adjoint element by a skew-adjoint element produces a
 self-adjoint element. -/
 theorem isSelfAdjoint_smul_of_mem_skewAdjoint [Ring R] [AddCommGroup A] [Module R A]
@@ -794,55 +566,25 @@ theorem isSelfAdjoint_smul_of_mem_skewAdjoint [Ring R] [AddCommGroup A] [Module
   (star_smul _ _).trans <| (congr_arg₂ _ hr ha).trans <| neg_smul_neg _ _
 #align is_self_adjoint_smul_of_mem_skew_adjoint isSelfAdjoint_smul_of_mem_skewAdjoint
 
-/- warning: is_star_normal_zero -> isStarNormal_zero is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_2 : StarRing.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_1)], IsStarNormal.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_1) _inst_2))) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_2 : StarRing.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_1)], IsStarNormal.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_1) _inst_2))) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))
-Case conversion may be inaccurate. Consider using '#align is_star_normal_zero isStarNormal_zeroₓ'. -/
 instance isStarNormal_zero [Semiring R] [StarRing R] : IsStarNormal (0 : R) :=
   ⟨by simp only [star_comm_self, star_zero]⟩
 #align is_star_normal_zero isStarNormal_zero
 
-/- warning: is_star_normal_one -> isStarNormal_one is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : Monoid.{u1} R] [_inst_2 : StarSemigroup.{u1} R (Monoid.toSemigroup.{u1} R _inst_1)], IsStarNormal.{u1} R (MulOneClass.toHasMul.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (InvolutiveStar.toHasStar.{u1} R (StarSemigroup.toHasInvolutiveStar.{u1} R (Monoid.toSemigroup.{u1} R _inst_1) _inst_2)) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (MulOneClass.toHasOne.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)))))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Monoid.{u1} R] [_inst_2 : StarSemigroup.{u1} R (Monoid.toSemigroup.{u1} R _inst_1)], IsStarNormal.{u1} R (MulOneClass.toMul.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (InvolutiveStar.toStar.{u1} R (StarSemigroup.toInvolutiveStar.{u1} R (Monoid.toSemigroup.{u1} R _inst_1) _inst_2)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Monoid.toOne.{u1} R _inst_1)))
-Case conversion may be inaccurate. Consider using '#align is_star_normal_one isStarNormal_oneₓ'. -/
 instance isStarNormal_one [Monoid R] [StarSemigroup R] : IsStarNormal (1 : R) :=
   ⟨by simp only [star_comm_self, star_one]⟩
 #align is_star_normal_one isStarNormal_one
 
-/- warning: is_star_normal_star_self -> isStarNormal_star_self is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : Monoid.{u1} R] [_inst_2 : StarSemigroup.{u1} R (Monoid.toSemigroup.{u1} R _inst_1)] {x : R} [_inst_3 : IsStarNormal.{u1} R (MulOneClass.toHasMul.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (InvolutiveStar.toHasStar.{u1} R (StarSemigroup.toHasInvolutiveStar.{u1} R (Monoid.toSemigroup.{u1} R _inst_1) _inst_2)) x], IsStarNormal.{u1} R (MulOneClass.toHasMul.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (InvolutiveStar.toHasStar.{u1} R (StarSemigroup.toHasInvolutiveStar.{u1} R (Monoid.toSemigroup.{u1} R _inst_1) _inst_2)) (Star.star.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarSemigroup.toHasInvolutiveStar.{u1} R (Monoid.toSemigroup.{u1} R _inst_1) _inst_2)) x)
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Monoid.{u1} R] [_inst_2 : StarSemigroup.{u1} R (Monoid.toSemigroup.{u1} R _inst_1)] {x : R} [_inst_3 : IsStarNormal.{u1} R (MulOneClass.toMul.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (InvolutiveStar.toStar.{u1} R (StarSemigroup.toInvolutiveStar.{u1} R (Monoid.toSemigroup.{u1} R _inst_1) _inst_2)) x], IsStarNormal.{u1} R (MulOneClass.toMul.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (InvolutiveStar.toStar.{u1} R (StarSemigroup.toInvolutiveStar.{u1} R (Monoid.toSemigroup.{u1} R _inst_1) _inst_2)) (Star.star.{u1} R (InvolutiveStar.toStar.{u1} R (StarSemigroup.toInvolutiveStar.{u1} R (Monoid.toSemigroup.{u1} R _inst_1) _inst_2)) x)
-Case conversion may be inaccurate. Consider using '#align is_star_normal_star_self isStarNormal_star_selfₓ'. -/
 instance isStarNormal_star_self [Monoid R] [StarSemigroup R] {x : R} [IsStarNormal x] :
     IsStarNormal (star x) :=
   ⟨show star (star x) * star x = star x * star (star x) by rw [star_star, star_comm_self']⟩
 #align is_star_normal_star_self isStarNormal_star_self
 
-/- warning: has_trivial_star.is_star_normal -> TrivialStar.isStarNormal is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : Monoid.{u1} R] [_inst_2 : StarSemigroup.{u1} R (Monoid.toSemigroup.{u1} R _inst_1)] [_inst_3 : TrivialStar.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarSemigroup.toHasInvolutiveStar.{u1} R (Monoid.toSemigroup.{u1} R _inst_1) _inst_2))] {x : R}, IsStarNormal.{u1} R (MulOneClass.toHasMul.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (InvolutiveStar.toHasStar.{u1} R (StarSemigroup.toHasInvolutiveStar.{u1} R (Monoid.toSemigroup.{u1} R _inst_1) _inst_2)) x
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Monoid.{u1} R] [_inst_2 : StarSemigroup.{u1} R (Monoid.toSemigroup.{u1} R _inst_1)] [_inst_3 : TrivialStar.{u1} R (InvolutiveStar.toStar.{u1} R (StarSemigroup.toInvolutiveStar.{u1} R (Monoid.toSemigroup.{u1} R _inst_1) _inst_2))] {x : R}, IsStarNormal.{u1} R (MulOneClass.toMul.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)) (InvolutiveStar.toStar.{u1} R (StarSemigroup.toInvolutiveStar.{u1} R (Monoid.toSemigroup.{u1} R _inst_1) _inst_2)) x
-Case conversion may be inaccurate. Consider using '#align has_trivial_star.is_star_normal TrivialStar.isStarNormalₓ'. -/
 -- see Note [lower instance priority]
 instance (priority := 100) TrivialStar.isStarNormal [Monoid R] [StarSemigroup R] [TrivialStar R]
     {x : R} : IsStarNormal x :=
   ⟨by rw [star_trivial]⟩
 #align has_trivial_star.is_star_normal TrivialStar.isStarNormal
 
-/- warning: comm_monoid.is_star_normal -> CommMonoid.isStarNormal is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommMonoid.{u1} R] [_inst_2 : StarSemigroup.{u1} R (Monoid.toSemigroup.{u1} R (CommMonoid.toMonoid.{u1} R _inst_1))] {x : R}, IsStarNormal.{u1} R (MulOneClass.toHasMul.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R _inst_1))) (InvolutiveStar.toHasStar.{u1} R (StarSemigroup.toHasInvolutiveStar.{u1} R (Monoid.toSemigroup.{u1} R (CommMonoid.toMonoid.{u1} R _inst_1)) _inst_2)) x
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommMonoid.{u1} R] [_inst_2 : StarSemigroup.{u1} R (Monoid.toSemigroup.{u1} R (CommMonoid.toMonoid.{u1} R _inst_1))] {x : R}, IsStarNormal.{u1} R (MulOneClass.toMul.{u1} R (Monoid.toMulOneClass.{u1} R (CommMonoid.toMonoid.{u1} R _inst_1))) (InvolutiveStar.toStar.{u1} R (StarSemigroup.toInvolutiveStar.{u1} R (Monoid.toSemigroup.{u1} R (CommMonoid.toMonoid.{u1} R _inst_1)) _inst_2)) x
-Case conversion may be inaccurate. Consider using '#align comm_monoid.is_star_normal CommMonoid.isStarNormalₓ'. -/
 -- see Note [lower instance priority]
 instance (priority := 100) CommMonoid.isStarNormal [CommMonoid R] [StarSemigroup R] {x : R} :
     IsStarNormal x :=

a6ece354

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -454,9 +454,7 @@ lean 3 declaration is
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : AddGroup.{u1} R] [_inst_2 : StarAddMonoid.{u1} R (SubNegMonoid.toAddMonoid.{u1} R (AddGroup.toSubNegMonoid.{u1} R _inst_1))] {x : R}, Iff (Membership.mem.{u1, u1} R (AddSubgroup.{u1} R _inst_1) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} R _inst_1) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R _inst_1)) x (selfAdjoint.{u1} R _inst_1 _inst_2)) (Eq.{succ u1} R (Star.star.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (SubNegMonoid.toAddMonoid.{u1} R (AddGroup.toSubNegMonoid.{u1} R _inst_1)) _inst_2)) x) x)
 Case conversion may be inaccurate. Consider using '#align self_adjoint.mem_iff selfAdjoint.mem_iffₓ'. -/
-theorem mem_iff {x : R} : x ∈ selfAdjoint R ↔ star x = x :=
-  by
-  rw [← AddSubgroup.mem_carrier]
+theorem mem_iff {x : R} : x ∈ selfAdjoint R ↔ star x = x := by rw [← AddSubgroup.mem_carrier];
   exact Iff.rfl
 #align self_adjoint.mem_iff selfAdjoint.mem_iff
 
@@ -662,9 +660,7 @@ lean 3 declaration is
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : AddCommGroup.{u1} R] [_inst_2 : StarAddMonoid.{u1} R (SubNegMonoid.toAddMonoid.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddCommGroup.toAddGroup.{u1} R _inst_1)))] {x : R}, Iff (Membership.mem.{u1, u1} R (AddSubgroup.{u1} R (AddCommGroup.toAddGroup.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} R (AddCommGroup.toAddGroup.{u1} R _inst_1)) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddCommGroup.toAddGroup.{u1} R _inst_1))) x (skewAdjoint.{u1} R _inst_1 _inst_2)) (Eq.{succ u1} R (Star.star.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (SubNegMonoid.toAddMonoid.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddCommGroup.toAddGroup.{u1} R _inst_1))) _inst_2)) x) (Neg.neg.{u1} R (NegZeroClass.toNeg.{u1} R (SubNegZeroMonoid.toNegZeroClass.{u1} R (SubtractionMonoid.toSubNegZeroMonoid.{u1} R (SubtractionCommMonoid.toSubtractionMonoid.{u1} R (AddCommGroup.toDivisionAddCommMonoid.{u1} R _inst_1))))) x))
 Case conversion may be inaccurate. Consider using '#align skew_adjoint.mem_iff skewAdjoint.mem_iffₓ'. -/
-theorem mem_iff {x : R} : x ∈ skewAdjoint R ↔ star x = -x :=
-  by
-  rw [← AddSubgroup.mem_carrier]
+theorem mem_iff {x : R} : x ∈ skewAdjoint R ↔ star x = -x := by rw [← AddSubgroup.mem_carrier];
   exact Iff.rfl
 #align skew_adjoint.mem_iff skewAdjoint.mem_iff
 
@@ -725,9 +721,7 @@ but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] [_inst_2 : StarRing.{u1} R (Semiring.toNonUnitalSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))] {x : R}, (Membership.mem.{u1, u1} R (AddSubgroup.{u1} R (AddCommGroup.toAddGroup.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} R (AddCommGroup.toAddGroup.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddCommGroup.toAddGroup.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)))) x (skewAdjoint.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1) (StarRing.toStarAddMonoid.{u1} R (Semiring.toNonUnitalSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) _inst_2))) -> (IsStarNormal.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1))) (StarRing.toStarAddMonoid.{u1} R (Semiring.toNonUnitalSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) _inst_2))) x)
 Case conversion may be inaccurate. Consider using '#align skew_adjoint.is_star_normal_of_mem skewAdjoint.isStarNormal_of_memₓ'. -/
 theorem isStarNormal_of_mem {x : R} (hx : x ∈ skewAdjoint R) : IsStarNormal x :=
-  ⟨by
-    simp only [mem_iff] at hx
-    simp only [hx, Commute.neg_left]⟩
+  ⟨by simp only [mem_iff] at hx; simp only [hx, Commute.neg_left]⟩
 #align skew_adjoint.is_star_normal_of_mem skewAdjoint.isStarNormal_of_mem
 
 instance (x : skewAdjoint R) : IsStarNormal (x : R) :=

a6ece354

bump to nightly-2023-05-28-03

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

6c6011cf

Diff

@@ -503,10 +503,7 @@ instance : Pow (selfAdjoint R) ℕ :=
   ⟨fun x n => ⟨(x : R) ^ n, x.Prop.pow n⟩⟩
 
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 Case conversion may be inaccurate. Consider using '#align self_adjoint.coe_pow selfAdjoint.val_powₓ'. -/
 @[simp, norm_cast]
 theorem val_pow (x : selfAdjoint R) (n : ℕ) : ↑(x ^ n) = (x : R) ^ n :=
@@ -523,10 +520,7 @@ instance : Mul (selfAdjoint R) :=
   ⟨fun x y => ⟨(x : R) * y, x.Prop.mul y.Prop⟩⟩
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align self_adjoint.coe_mul selfAdjoint.val_mulₓ'. -/
 @[simp, norm_cast]
 theorem val_mul (x y : selfAdjoint R) : ↑(x * y) = (x : R) * y :=
@@ -554,10 +548,7 @@ variable [Field R] [StarRing R]
 instance : Inv (selfAdjoint R) where inv x := ⟨x.val⁻¹, x.Prop.inv⟩
 
 /- warning: self_adjoint.coe_inv -> selfAdjoint.val_inv is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align self_adjoint.coe_inv selfAdjoint.val_invₓ'. -/
 @[simp, norm_cast]
 theorem val_inv (x : selfAdjoint R) : ↑x⁻¹ = (x : R)⁻¹ :=
@@ -567,10 +558,7 @@ theorem val_inv (x : selfAdjoint R) : ↑x⁻¹ = (x : R)⁻¹ :=
 instance : Div (selfAdjoint R) where div x y := ⟨x / y, x.Prop.div y.Prop⟩
 
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 Case conversion may be inaccurate. Consider using '#align self_adjoint.coe_div selfAdjoint.val_divₓ'. -/
 @[simp, norm_cast]
 theorem val_div (x y : selfAdjoint R) : ↑(x / y) = (x / y : R) :=
@@ -580,10 +568,7 @@ theorem val_div (x y : selfAdjoint R) : ↑(x / y) = (x / y : R) :=
 instance : Pow (selfAdjoint R) ℤ where pow x z := ⟨x ^ z, x.Prop.zpow z⟩
 
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 Case conversion may be inaccurate. Consider using '#align self_adjoint.coe_zpow selfAdjoint.val_zpowₓ'. -/
 @[simp, norm_cast]
 theorem val_zpow (x : selfAdjoint R) (z : ℤ) : ↑(x ^ z) = (x : R) ^ z :=
@@ -594,10 +579,7 @@ instance : HasRatCast (selfAdjoint R) :=
   ⟨fun n => ⟨n, isSelfAdjoint_ratCast n⟩⟩
 
 /- warning: self_adjoint.coe_rat_cast -> selfAdjoint.val_ratCast is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align self_adjoint.coe_rat_cast selfAdjoint.val_ratCastₓ'. -/
 @[simp, norm_cast]
 theorem val_ratCast (x : ℚ) : ↑(x : selfAdjoint R) = (x : R) :=
@@ -616,10 +598,7 @@ instance instQSMul : SMul ℚ (selfAdjoint R) :=
 #align self_adjoint.has_qsmul selfAdjoint.instQSMul
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align self_adjoint.coe_rat_smul selfAdjoint.val_rat_smulₓ'. -/
 @[simp, norm_cast]
 theorem val_rat_smul (x : selfAdjoint R) (a : ℚ) : ↑(a • x) = a • (x : R) :=
@@ -775,10 +754,7 @@ instance [Monoid R] [DistribMulAction R A] [StarModule R A] : SMul R (skewAdjoin
   ⟨fun r x => ⟨r • x, smul_mem r x.Prop⟩⟩
 
 /- warning: skew_adjoint.coe_smul -> skewAdjoint.val_smul is a dubious translation:
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-but is expected to have type
-  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : Star.{u2} R] [_inst_2 : TrivialStar.{u2} R _inst_1] [_inst_3 : AddCommGroup.{u1} A] [_inst_4 : StarAddMonoid.{u1} A (SubNegMonoid.toAddMonoid.{u1} A (AddGroup.toSubNegMonoid.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_3)))] [_inst_5 : Monoid.{u2} R] [_inst_6 : DistribMulAction.{u2, u1} R A _inst_5 (SubNegMonoid.toAddMonoid.{u1} A (AddGroup.toSubNegMonoid.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_3)))] [_inst_7 : StarModule.{u2, u1} R A _inst_1 (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (SubNegMonoid.toAddMonoid.{u1} A (AddGroup.toSubNegMonoid.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_3))) _inst_4)) (SMulZeroClass.toSMul.{u2, u1} R A (NegZeroClass.toZero.{u1} A (SubNegZeroMonoid.toNegZeroClass.{u1} A (SubtractionMonoid.toSubNegZeroMonoid.{u1} A (SubtractionCommMonoid.toSubtractionMonoid.{u1} A (AddCommGroup.toDivisionAddCommMonoid.{u1} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u2, u1} R A (AddMonoid.toAddZeroClass.{u1} A (SubNegMonoid.toAddMonoid.{u1} A (AddGroup.toSubNegMonoid.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_3)))) (DistribMulAction.toDistribSMul.{u2, u1} R A _inst_5 (SubNegMonoid.toAddMonoid.{u1} A (AddGroup.toSubNegMonoid.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_3))) _inst_6)))] (r : R) (x : Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (AddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_3)) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_3)) A (AddSubgroup.instSetLikeAddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_3))) x (skewAdjoint.{u1} A _inst_3 _inst_4))), Eq.{succ u1} A (Subtype.val.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Set.{u1} A) (Set.instMembershipSet.{u1} A) x (SetLike.coe.{u1, u1} (AddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_3)) A (AddSubgroup.instSetLikeAddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_3)) (skewAdjoint.{u1} A _inst_3 _inst_4))) (HSMul.hSMul.{u2, u1, u1} R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (AddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_3)) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_3)) A (AddSubgroup.instSetLikeAddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_3))) x (skewAdjoint.{u1} A _inst_3 _inst_4))) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (AddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_3)) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_3)) A (AddSubgroup.instSetLikeAddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_3))) x (skewAdjoint.{u1} A _inst_3 _inst_4))) (instHSMul.{u2, u1} R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (AddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_3)) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_3)) A (AddSubgroup.instSetLikeAddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_3))) x (skewAdjoint.{u1} A _inst_3 _inst_4))) (skewAdjoint.instSMulSubtypeMemAddSubgroupToAddGroupInstMembershipInstSetLikeAddSubgroupSkewAdjoint.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7)) r x)) (HSMul.hSMul.{u2, u1, u1} R A A (instHSMul.{u2, u1} R A (SMulZeroClass.toSMul.{u2, u1} R A (NegZeroClass.toZero.{u1} A (SubNegZeroMonoid.toNegZeroClass.{u1} A (SubtractionMonoid.toSubNegZeroMonoid.{u1} A (SubtractionCommMonoid.toSubtractionMonoid.{u1} A (AddCommGroup.toDivisionAddCommMonoid.{u1} A _inst_3))))) (DistribSMul.toSMulZeroClass.{u2, u1} R A (AddMonoid.toAddZeroClass.{u1} A (SubNegMonoid.toAddMonoid.{u1} A (AddGroup.toSubNegMonoid.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_3)))) (DistribMulAction.toDistribSMul.{u2, u1} R A _inst_5 (SubNegMonoid.toAddMonoid.{u1} A (AddGroup.toSubNegMonoid.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_3))) _inst_6)))) r (Subtype.val.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Set.{u1} A) (Set.instMembershipSet.{u1} A) x (SetLike.coe.{u1, u1} (AddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_3)) A (AddSubgroup.instSetLikeAddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_3)) (skewAdjoint.{u1} A _inst_3 _inst_4))) x))
+<too large>
 Case conversion may be inaccurate. Consider using '#align skew_adjoint.coe_smul skewAdjoint.val_smulₓ'. -/
 @[simp, norm_cast]
 theorem val_smul [Monoid R] [DistribMulAction R A] [StarModule R A] (r : R) (x : skewAdjoint A) :

a6ece354

bump to nightly-2023-05-24-06

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

fbc7b476

Diff

@@ -125,7 +125,7 @@ theorem mul_star_self [Semigroup R] [StarSemigroup R] (x : R) : IsSelfAdjoint (x
 lean 3 declaration is
   forall {F : Type.{u1}} {R : Type.{u2}} {S : Type.{u3}} [_inst_1 : Star.{u2} R] [_inst_2 : Star.{u3} S] [_inst_3 : StarHomClass.{u1, u2, u3} F R S _inst_1 _inst_2] {x : R}, (IsSelfAdjoint.{u2} R _inst_1 x) -> (forall (f : F), IsSelfAdjoint.{u3} S _inst_2 (coeFn.{succ u1, max (succ u2) (succ u3)} F (fun (_x : F) => R -> S) (FunLike.hasCoeToFun.{succ u1, succ u2, succ u3} F R (fun (_x : R) => S) (StarHomClass.toFunLike.{u1, u2, u3} F R S _inst_1 _inst_2 _inst_3)) f x))
 but is expected to have type
-  forall {F : Type.{u3}} {R : Type.{u2}} {S : Type.{u1}} [_inst_1 : Star.{u2} R] [_inst_2 : Star.{u1} S] [_inst_3 : StarHomClass.{u3, u2, u1} F R S _inst_1 _inst_2] {x : R}, (IsSelfAdjoint.{u2} R _inst_1 x) -> (forall (f : F), IsSelfAdjoint.{u1} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3326 : R) => S) x) _inst_2 (FunLike.coe.{succ u3, succ u2, succ u1} F R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3326 : R) => S) _x) (StarHomClass.toFunLike.{u3, u2, u1} F R S _inst_1 _inst_2 _inst_3) f x))
+  forall {F : Type.{u3}} {R : Type.{u2}} {S : Type.{u1}} [_inst_1 : Star.{u2} R] [_inst_2 : Star.{u1} S] [_inst_3 : StarHomClass.{u3, u2, u1} F R S _inst_1 _inst_2] {x : R}, (IsSelfAdjoint.{u2} R _inst_1 x) -> (forall (f : F), IsSelfAdjoint.{u1} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3328 : R) => S) x) _inst_2 (FunLike.coe.{succ u3, succ u2, succ u1} F R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3328 : R) => S) _x) (StarHomClass.toFunLike.{u3, u2, u1} F R S _inst_1 _inst_2 _inst_3) f x))
 Case conversion may be inaccurate. Consider using '#align is_self_adjoint.star_hom_apply IsSelfAdjoint.starHom_applyₓ'. -/
 /-- Functions in a `star_hom_class` preserve self-adjoint elements. -/
 theorem starHom_apply {F R S : Type _} [Star R] [Star S] [StarHomClass F R S] {x : R}

a6ece354

bump to nightly-2023-05-16-14

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

b356e20f

Diff

@@ -125,7 +125,7 @@ theorem mul_star_self [Semigroup R] [StarSemigroup R] (x : R) : IsSelfAdjoint (x
 lean 3 declaration is
   forall {F : Type.{u1}} {R : Type.{u2}} {S : Type.{u3}} [_inst_1 : Star.{u2} R] [_inst_2 : Star.{u3} S] [_inst_3 : StarHomClass.{u1, u2, u3} F R S _inst_1 _inst_2] {x : R}, (IsSelfAdjoint.{u2} R _inst_1 x) -> (forall (f : F), IsSelfAdjoint.{u3} S _inst_2 (coeFn.{succ u1, max (succ u2) (succ u3)} F (fun (_x : F) => R -> S) (FunLike.hasCoeToFun.{succ u1, succ u2, succ u3} F R (fun (_x : R) => S) (StarHomClass.toFunLike.{u1, u2, u3} F R S _inst_1 _inst_2 _inst_3)) f x))
 but is expected to have type
-  forall {F : Type.{u3}} {R : Type.{u2}} {S : Type.{u1}} [_inst_1 : Star.{u2} R] [_inst_2 : Star.{u1} S] [_inst_3 : StarHomClass.{u3, u2, u1} F R S _inst_1 _inst_2] {x : R}, (IsSelfAdjoint.{u2} R _inst_1 x) -> (forall (f : F), IsSelfAdjoint.{u1} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3333 : R) => S) x) _inst_2 (FunLike.coe.{succ u3, succ u2, succ u1} F R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3333 : R) => S) _x) (StarHomClass.toFunLike.{u3, u2, u1} F R S _inst_1 _inst_2 _inst_3) f x))
+  forall {F : Type.{u3}} {R : Type.{u2}} {S : Type.{u1}} [_inst_1 : Star.{u2} R] [_inst_2 : Star.{u1} S] [_inst_3 : StarHomClass.{u3, u2, u1} F R S _inst_1 _inst_2] {x : R}, (IsSelfAdjoint.{u2} R _inst_1 x) -> (forall (f : F), IsSelfAdjoint.{u1} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3326 : R) => S) x) _inst_2 (FunLike.coe.{succ u3, succ u2, succ u1} F R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3326 : R) => S) _x) (StarHomClass.toFunLike.{u3, u2, u1} F R S _inst_1 _inst_2 _inst_3) f x))
 Case conversion may be inaccurate. Consider using '#align is_self_adjoint.star_hom_apply IsSelfAdjoint.starHom_applyₓ'. -/
 /-- Functions in a `star_hom_class` preserve self-adjoint elements. -/
 theorem starHom_apply {F R S : Type _} [Star R] [Star S] [StarHomClass F R S] {x : R}

a6ece354

bump to nightly-2023-05-08-22

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

63e712c6

Diff

@@ -125,7 +125,7 @@ theorem mul_star_self [Semigroup R] [StarSemigroup R] (x : R) : IsSelfAdjoint (x
 lean 3 declaration is
   forall {F : Type.{u1}} {R : Type.{u2}} {S : Type.{u3}} [_inst_1 : Star.{u2} R] [_inst_2 : Star.{u3} S] [_inst_3 : StarHomClass.{u1, u2, u3} F R S _inst_1 _inst_2] {x : R}, (IsSelfAdjoint.{u2} R _inst_1 x) -> (forall (f : F), IsSelfAdjoint.{u3} S _inst_2 (coeFn.{succ u1, max (succ u2) (succ u3)} F (fun (_x : F) => R -> S) (FunLike.hasCoeToFun.{succ u1, succ u2, succ u3} F R (fun (_x : R) => S) (StarHomClass.toFunLike.{u1, u2, u3} F R S _inst_1 _inst_2 _inst_3)) f x))
 but is expected to have type
-  forall {F : Type.{u3}} {R : Type.{u2}} {S : Type.{u1}} [_inst_1 : Star.{u2} R] [_inst_2 : Star.{u1} S] [_inst_3 : StarHomClass.{u3, u2, u1} F R S _inst_1 _inst_2] {x : R}, (IsSelfAdjoint.{u2} R _inst_1 x) -> (forall (f : F), IsSelfAdjoint.{u1} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3327 : R) => S) x) _inst_2 (FunLike.coe.{succ u3, succ u2, succ u1} F R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3327 : R) => S) _x) (StarHomClass.toFunLike.{u3, u2, u1} F R S _inst_1 _inst_2 _inst_3) f x))
+  forall {F : Type.{u3}} {R : Type.{u2}} {S : Type.{u1}} [_inst_1 : Star.{u2} R] [_inst_2 : Star.{u1} S] [_inst_3 : StarHomClass.{u3, u2, u1} F R S _inst_1 _inst_2] {x : R}, (IsSelfAdjoint.{u2} R _inst_1 x) -> (forall (f : F), IsSelfAdjoint.{u1} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3333 : R) => S) x) _inst_2 (FunLike.coe.{succ u3, succ u2, succ u1} F R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3333 : R) => S) _x) (StarHomClass.toFunLike.{u3, u2, u1} F R S _inst_1 _inst_2 _inst_3) f x))
 Case conversion may be inaccurate. Consider using '#align is_self_adjoint.star_hom_apply IsSelfAdjoint.starHom_applyₓ'. -/
 /-- Functions in a `star_hom_class` preserve self-adjoint elements. -/
 theorem starHom_apply {F R S : Type _} [Star R] [Star S] [StarHomClass F R S] {x : R}
@@ -334,7 +334,7 @@ variable [Ring R] [StarRing R]
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1))] (z : Int), IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1)) _inst_2))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int R (HasLiftT.mk.{1, succ u1} Int R (CoeTCₓ.coe.{1, succ u1} Int R (Int.castCoe.{u1} R (AddGroupWithOne.toHasIntCast.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1)))))) z)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1))] (z : Int), IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1)) _inst_2))) (Int.cast.{u1} R (Ring.toIntCast.{u1} R _inst_1) z)
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] [_inst_2 : StarRing.{u1} R (Semiring.toNonUnitalSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))] (z : Int), IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1))) (StarRing.toStarAddMonoid.{u1} R (Semiring.toNonUnitalSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) _inst_2))) (Int.cast.{u1} R (Ring.toIntCast.{u1} R _inst_1) z)
 Case conversion may be inaccurate. Consider using '#align is_self_adjoint_int_cast isSelfAdjoint_intCastₓ'. -/
 @[simp]
 theorem isSelfAdjoint_intCast (z : ℤ) : IsSelfAdjoint (z : R) :=
@@ -373,7 +373,7 @@ variable [DivisionRing R] [StarRing R]
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : DivisionRing.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))] (x : Rat), IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) _inst_2))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Rat R (HasLiftT.mk.{1, succ u1} Rat R (CoeTCₓ.coe.{1, succ u1} Rat R (Rat.castCoe.{u1} R (DivisionRing.toHasRatCast.{u1} R _inst_1)))) x)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : DivisionRing.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))] (x : Rat), IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) _inst_2))) (Rat.cast.{u1} R (DivisionRing.toRatCast.{u1} R _inst_1) x)
+  forall {R : Type.{u1}} [_inst_1 : DivisionRing.{u1} R] [_inst_2 : StarRing.{u1} R (Semiring.toNonUnitalSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1)))] (x : Rat), IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (Semiring.toNonUnitalSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (DivisionRing.toDivisionSemiring.{u1} R _inst_1))) _inst_2))) (Rat.cast.{u1} R (DivisionRing.toRatCast.{u1} R _inst_1) x)
 Case conversion may be inaccurate. Consider using '#align is_self_adjoint_rat_cast isSelfAdjoint_ratCastₓ'. -/
 theorem isSelfAdjoint_ratCast (x : ℚ) : IsSelfAdjoint (x : R) :=
   star_ratCast _
@@ -506,7 +506,7 @@ instance : Pow (selfAdjoint R) ℕ :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1))] (x : coeSort.{succ u1, succ (succ u1)} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1)))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1)))) R (AddSubgroup.setLike.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1))))) (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1)) _inst_2))) (n : Nat), Eq.{succ u1} R ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1)))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1)))) R (AddSubgroup.setLike.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1))))) (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1)) _inst_2))) R (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1)))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1)))) R (AddSubgroup.setLike.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1))))) (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1)) _inst_2))) R (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1)))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1)))) R (AddSubgroup.setLike.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1))))) (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1)) _inst_2))) R (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1)))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1)))) R (AddSubgroup.setLike.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1))))) (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1)) _inst_2))) R (coeSubtype.{succ u1} R (fun (x : R) => Membership.Mem.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1)))) (SetLike.hasMem.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1)))) R (AddSubgroup.setLike.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1))))) x (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1)) _inst_2))))))) (HPow.hPow.{u1, 0, u1} (coeSort.{succ u1, succ (succ u1)} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1)))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1)))) R (AddSubgroup.setLike.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1))))) (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1)) _inst_2))) Nat (coeSort.{succ u1, succ (succ u1)} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1)))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1)))) R (AddSubgroup.setLike.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1))))) (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1)) _inst_2))) (instHPow.{u1, 0} (coeSort.{succ u1, succ (succ u1)} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1)))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1)))) R (AddSubgroup.setLike.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1))))) (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1)) _inst_2))) Nat (selfAdjoint.Nat.hasPow.{u1} R _inst_1 _inst_2)) x n)) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R _inst_1))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => 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(AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1)) _inst_2))))))) x) n)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1))] (x : Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1)))) x (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1)) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1)) _inst_2)))) (n : Nat), Eq.{succ u1} R (Subtype.val.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x (SetLike.coe.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1))) (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1)) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1)) _inst_2)))) (HPow.hPow.{u1, 0, u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1)))) x (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1)) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1)) _inst_2)))) Nat (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1)))) x (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1)) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1)) _inst_2)))) (instHPow.{u1, 0} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1)))) x (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1)) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1)) _inst_2)))) Nat (selfAdjoint.instPowSubtypeMemAddSubgroupToAddGroupToAddGroupWithOneInstMembershipInstSetLikeAddSubgroupSelfAdjointToStarAddMonoidToNonUnitalSemiringToNonUnitalRingNat.{u1} R _inst_1 _inst_2)) x n)) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (Subtype.val.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x (SetLike.coe.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1))) (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1)) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1)) _inst_2)))) x) n)
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] [_inst_2 : StarRing.{u1} R (Semiring.toNonUnitalSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))] (x : Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1)))) x (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1)) (StarRing.toStarAddMonoid.{u1} R (Semiring.toNonUnitalSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) _inst_2)))) (n : Nat), Eq.{succ u1} R (Subtype.val.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x (SetLike.coe.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1))) (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1)) (StarRing.toStarAddMonoid.{u1} R (Semiring.toNonUnitalSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) _inst_2)))) (HPow.hPow.{u1, 0, u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1)))) x (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1)) (StarRing.toStarAddMonoid.{u1} R (Semiring.toNonUnitalSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) _inst_2)))) Nat (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1)))) x (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1)) (StarRing.toStarAddMonoid.{u1} R (Semiring.toNonUnitalSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) _inst_2)))) (instHPow.{u1, 0} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1)))) x (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1)) (StarRing.toStarAddMonoid.{u1} R (Semiring.toNonUnitalSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) _inst_2)))) Nat (selfAdjoint.instPowSubtypeMemAddSubgroupToAddGroupToAddGroupWithOneInstMembershipInstSetLikeAddSubgroupSelfAdjointToStarAddMonoidToNonUnitalSemiringToSemiringNat.{u1} R _inst_1 _inst_2)) x n)) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (Subtype.val.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x (SetLike.coe.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1))) (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1)) (StarRing.toStarAddMonoid.{u1} R (Semiring.toNonUnitalSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) _inst_2)))) x) n)
 Case conversion may be inaccurate. Consider using '#align self_adjoint.coe_pow selfAdjoint.val_powₓ'. -/
 @[simp, norm_cast]
 theorem val_pow (x : selfAdjoint R) (n : ℕ) : ↑(x ^ n) = (x : R) ^ n :=
@@ -526,7 +526,7 @@ instance : Mul (selfAdjoint R) :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : NonUnitalCommRing.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R _inst_1))] (x : coeSort.{succ u1, succ (succ u1)} (AddSubgroup.{u1} R (AddCommGroup.toAddGroup.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R _inst_1))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (AddSubgroup.{u1} R (AddCommGroup.toAddGroup.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R _inst_1))))) R (AddSubgroup.setLike.{u1} R (AddCommGroup.toAddGroup.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R _inst_1)))))) (selfAdjoint.{u1} R (AddCommGroup.toAddGroup.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R _inst_1)) _inst_2))) (y : coeSort.{succ u1, succ (succ u1)} (AddSubgroup.{u1} R (AddCommGroup.toAddGroup.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R _inst_1))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (AddSubgroup.{u1} R (AddCommGroup.toAddGroup.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R _inst_1))))) R (AddSubgroup.setLike.{u1} R (AddCommGroup.toAddGroup.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R _inst_1)))))) (selfAdjoint.{u1} R (AddCommGroup.toAddGroup.{u1} R 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 but is expected to have type
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+  forall {R : Type.{u1}} [_inst_1 : NonUnitalCommRing.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R _inst_1))] (x : Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (AddSubgroup.{u1} R (AddCommGroup.toAddGroup.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R _inst_1))))) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} R (AddCommGroup.toAddGroup.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R _inst_1))))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddCommGroup.toAddGroup.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R _inst_1)))))) x (selfAdjoint.{u1} R (AddCommGroup.toAddGroup.{u1} R 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(instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R _inst_1)))) (Subtype.val.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x (SetLike.coe.{u1, u1} (AddSubgroup.{u1} R (AddCommGroup.toAddGroup.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R _inst_1))))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddCommGroup.toAddGroup.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R _inst_1))))) (selfAdjoint.{u1} R (AddCommGroup.toAddGroup.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R _inst_1)) _inst_2)))) x) (Subtype.val.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x (SetLike.coe.{u1, u1} (AddSubgroup.{u1} R (AddCommGroup.toAddGroup.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R _inst_1))))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddCommGroup.toAddGroup.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R _inst_1))))) (selfAdjoint.{u1} R (AddCommGroup.toAddGroup.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R _inst_1)) _inst_2)))) y))
 Case conversion may be inaccurate. Consider using '#align self_adjoint.coe_mul selfAdjoint.val_mulₓ'. -/
 @[simp, norm_cast]
 theorem val_mul (x y : selfAdjoint R) : ↑(x * y) = (x : R) * y :=
@@ -557,7 +557,7 @@ instance : Inv (selfAdjoint R) where inv x := ⟨x.val⁻¹, x.Prop.inv⟩
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1))))] (x : coeSort.{succ u1, succ (succ u1)} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) R (AddSubgroup.setLike.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))))) (selfAdjoint.{u1} R 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(NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2))) R (coeSubtype.{succ u1} R (fun (x : R) => Membership.Mem.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (SetLike.hasMem.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) R (AddSubgroup.setLike.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))))) x (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R 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(Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) R (AddSubgroup.setLike.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))))) (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2))) R (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) R (AddSubgroup.setLike.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))))) (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2))) R (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) R (AddSubgroup.setLike.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))))) (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2))) R (coeSubtype.{succ u1} R (fun (x : R) => Membership.Mem.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (SetLike.hasMem.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) R (AddSubgroup.setLike.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))))) x (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2))))))) x))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1))))] (x : Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) x (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2)))), Eq.{succ u1} R (Subtype.val.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x (SetLike.coe.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2)))) (Inv.inv.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) x (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2)))) (selfAdjoint.instInvSubtypeMemAddSubgroupToAddGroupToAddGroupWithOneToRingToDivisionRingInstMembershipInstSetLikeAddSubgroupSelfAdjointToStarAddMonoidToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingToCommRing.{u1} R _inst_1 _inst_2) x)) (Inv.inv.{u1} R (Field.toInv.{u1} R _inst_1) (Subtype.val.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x (SetLike.coe.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2)))) x))
+  forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1))))] (x : Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) x (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2)))), Eq.{succ u1} R (Subtype.val.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x (SetLike.coe.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2)))) (Inv.inv.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) x (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2)))) (selfAdjoint.instInvSubtypeMemAddSubgroupToAddGroupToAddGroupWithOneToRingToDivisionRingInstMembershipInstSetLikeAddSubgroupSelfAdjointToStarAddMonoidToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingToCommRing.{u1} R _inst_1 _inst_2) x)) (Inv.inv.{u1} R (Field.toInv.{u1} R _inst_1) (Subtype.val.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x (SetLike.coe.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2)))) x))
 Case conversion may be inaccurate. Consider using '#align self_adjoint.coe_inv selfAdjoint.val_invₓ'. -/
 @[simp, norm_cast]
 theorem val_inv (x : selfAdjoint R) : ↑x⁻¹ = (x : R)⁻¹ :=
@@ -570,7 +570,7 @@ instance : Div (selfAdjoint R) where div x y := ⟨x / y, x.Prop.div y.Prop⟩
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1))))] (x : coeSort.{succ u1, succ (succ u1)} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) R (AddSubgroup.setLike.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))))) (selfAdjoint.{u1} R 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(Field.toCommRing.{u1} R _inst_1)))) _inst_2))))))) x) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) R (AddSubgroup.setLike.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))))) (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R 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 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1))))] (x : Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) x (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2)))) (y : Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) x (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2)))), Eq.{succ u1} R (Subtype.val.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x (SetLike.coe.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2)))) (HDiv.hDiv.{u1, u1, u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) x (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2)))) (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) x (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2)))) (Subtype.{succ u1} R (fun (x : R) => 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(AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) x (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2)))) (selfAdjoint.instDivSubtypeMemAddSubgroupToAddGroupToAddGroupWithOneToRingToDivisionRingInstMembershipInstSetLikeAddSubgroupSelfAdjointToStarAddMonoidToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingToCommRing.{u1} R _inst_1 _inst_2)) x y)) (HDiv.hDiv.{u1, u1, u1} R R R (instHDiv.{u1} R (Field.toDiv.{u1} R _inst_1)) (Subtype.val.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x (SetLike.coe.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2)))) x) (Subtype.val.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x (SetLike.coe.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2)))) y))
+  forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1))))] (x : Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) x (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2)))) (y : Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) x (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2)))), Eq.{succ u1} R (Subtype.val.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x (SetLike.coe.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2)))) (HDiv.hDiv.{u1, u1, u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) x (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R 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R (Field.toCommRing.{u1} R _inst_1)))) _inst_2)))) (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) x (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2)))) (instHDiv.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) x (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2)))) (selfAdjoint.instDivSubtypeMemAddSubgroupToAddGroupToAddGroupWithOneToRingToDivisionRingInstMembershipInstSetLikeAddSubgroupSelfAdjointToStarAddMonoidToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingToCommRing.{u1} R _inst_1 _inst_2)) x y)) (HDiv.hDiv.{u1, u1, u1} R R R (instHDiv.{u1} R (Field.toDiv.{u1} R _inst_1)) (Subtype.val.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x (SetLike.coe.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2)))) x) (Subtype.val.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x (SetLike.coe.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2)))) y))
 Case conversion may be inaccurate. Consider using '#align self_adjoint.coe_div selfAdjoint.val_divₓ'. -/
 @[simp, norm_cast]
 theorem val_div (x y : selfAdjoint R) : ↑(x / y) = (x / y : R) :=
@@ -583,7 +583,7 @@ instance : Pow (selfAdjoint R) ℤ where pow x z := ⟨x ^ z, x.Prop.zpow z⟩
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1))))] (x : coeSort.{succ u1, succ (succ u1)} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) R (AddSubgroup.setLike.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))))) (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2))) (z : Int), Eq.{succ u1} R ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) R (AddSubgroup.setLike.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))))) (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2))) R (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) R (AddSubgroup.setLike.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))))) (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2))) R (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R 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R (AddSubgroup.setLike.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))))) (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2))) R (coeSubtype.{succ u1} R (fun (x : R) => Membership.Mem.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (SetLike.hasMem.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R 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 but is expected to have type
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(StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2)))) (z : Int), Eq.{succ u1} R (Subtype.val.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x (SetLike.coe.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2)))) (HPow.hPow.{u1, 0, u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) x (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2)))) Int (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) x (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2)))) (instHPow.{u1, 0} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) x (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2)))) Int (selfAdjoint.instPowSubtypeMemAddSubgroupToAddGroupToAddGroupWithOneToRingToDivisionRingInstMembershipInstSetLikeAddSubgroupSelfAdjointToStarAddMonoidToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingToCommRingInt.{u1} R _inst_1 _inst_2)) x z)) (HPow.hPow.{u1, 0, u1} R Int R (instHPow.{u1, 0} R Int (DivInvMonoid.Pow.{u1} R (DivisionRing.toDivInvMonoid.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Subtype.val.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x (SetLike.coe.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2)))) x) z)
+  forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1))))] (x : Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) x (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2)))) (z : Int), Eq.{succ u1} R (Subtype.val.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x (SetLike.coe.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2)))) (HPow.hPow.{u1, 0, u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) x (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2)))) Int (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) x (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2)))) (instHPow.{u1, 0} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) x (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2)))) Int (selfAdjoint.instPowSubtypeMemAddSubgroupToAddGroupToAddGroupWithOneToRingToDivisionRingInstMembershipInstSetLikeAddSubgroupSelfAdjointToStarAddMonoidToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingToCommRingInt.{u1} R _inst_1 _inst_2)) x z)) (HPow.hPow.{u1, 0, u1} R Int R (instHPow.{u1, 0} R Int (DivInvMonoid.Pow.{u1} R (DivisionRing.toDivInvMonoid.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Subtype.val.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x (SetLike.coe.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2)))) x) z)
 Case conversion may be inaccurate. Consider using '#align self_adjoint.coe_zpow selfAdjoint.val_zpowₓ'. -/
 @[simp, norm_cast]
 theorem val_zpow (x : selfAdjoint R) (z : ℤ) : ↑(x ^ z) = (x : R) ^ z :=
@@ -597,7 +597,7 @@ instance : HasRatCast (selfAdjoint R) :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1))))] (x : Rat), Eq.{succ u1} R ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) R (AddSubgroup.setLike.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))))) (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2))) R (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) R (AddSubgroup.setLike.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))))) (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2))) R (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) R (AddSubgroup.setLike.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))))) (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2))) R (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) R (AddSubgroup.setLike.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))))) (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2))) R (coeSubtype.{succ u1} R (fun (x : R) => Membership.Mem.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (SetLike.hasMem.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) R (AddSubgroup.setLike.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))))) x (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2))))))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Rat (coeSort.{succ u1, succ (succ u1)} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) R (AddSubgroup.setLike.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))))) (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2))) (HasLiftT.mk.{1, succ u1} Rat (coeSort.{succ u1, succ (succ u1)} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) R (AddSubgroup.setLike.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))))) (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2))) (CoeTCₓ.coe.{1, succ u1} Rat (coeSort.{succ u1, succ (succ u1)} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) R (AddSubgroup.setLike.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))))) (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2))) (Rat.castCoe.{u1} (coeSort.{succ u1, succ (succ u1)} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) R (AddSubgroup.setLike.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))))) (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2))) (selfAdjoint.hasRatCast.{u1} R _inst_1 _inst_2)))) x)) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Rat R (HasLiftT.mk.{1, succ u1} Rat R (CoeTCₓ.coe.{1, succ u1} Rat R (Rat.castCoe.{u1} R (DivisionRing.toHasRatCast.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) x)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1))))] (x : Rat), Eq.{succ u1} R (Subtype.val.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x (SetLike.coe.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2)))) (Rat.cast.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) x (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2)))) (selfAdjoint.instRatCastSubtypeMemAddSubgroupToAddGroupToAddGroupWithOneToRingToDivisionRingInstMembershipInstSetLikeAddSubgroupSelfAdjointToStarAddMonoidToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingToCommRing.{u1} R _inst_1 _inst_2) x)) (Rat.cast.{u1} R (Field.toRatCast.{u1} R _inst_1) x)
+  forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1))))] (x : Rat), Eq.{succ u1} R (Subtype.val.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x (SetLike.coe.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2)))) (Rat.cast.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) x (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2)))) (selfAdjoint.instRatCastSubtypeMemAddSubgroupToAddGroupToAddGroupWithOneToRingToDivisionRingInstMembershipInstSetLikeAddSubgroupSelfAdjointToStarAddMonoidToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingToCommRing.{u1} R _inst_1 _inst_2) x)) (Rat.cast.{u1} R (Field.toRatCast.{u1} R _inst_1) x)
 Case conversion may be inaccurate. Consider using '#align self_adjoint.coe_rat_cast selfAdjoint.val_ratCastₓ'. -/
 @[simp, norm_cast]
 theorem val_ratCast (x : ℚ) : ↑(x : selfAdjoint R) = (x : R) :=
@@ -608,7 +608,7 @@ theorem val_ratCast (x : ℚ) : ↑(x : selfAdjoint R) = (x : R) :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1))))], SMul.{0, u1} Rat (coeSort.{succ u1, succ (succ u1)} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) R (AddSubgroup.setLike.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))))) (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2)))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1))))], SMul.{0, u1} Rat (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) x (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2))))
+  forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1))))], SMul.{0, u1} Rat (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) x (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2))))
 Case conversion may be inaccurate. Consider using '#align self_adjoint.has_qsmul selfAdjoint.instQSMulₓ'. -/
 instance instQSMul : SMul ℚ (selfAdjoint R) :=
   ⟨fun a x =>
@@ -619,7 +619,7 @@ instance instQSMul : SMul ℚ (selfAdjoint R) :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1))))] (x : coeSort.{succ u1, succ (succ u1)} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) R (AddSubgroup.setLike.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))))) (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2))) (a : Rat), Eq.{succ u1} R ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) R (AddSubgroup.setLike.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))))) (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2))) R (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) R (AddSubgroup.setLike.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))))) (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2))) R (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) R (AddSubgroup.setLike.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))))) (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2))) R (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) R (AddSubgroup.setLike.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))))) (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2))) R (coeSubtype.{succ u1} R (fun (x : R) => Membership.Mem.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (SetLike.hasMem.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) R (AddSubgroup.setLike.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))))) x (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2))))))) (SMul.smul.{0, u1} Rat (coeSort.{succ u1, succ (succ u1)} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) R (AddSubgroup.setLike.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))))) (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2))) (selfAdjoint.instQSMul.{u1} R _inst_1 _inst_2) a x)) (SMul.smul.{0, u1} Rat R (SMulZeroClass.toHasSmul.{0, u1} Rat R (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))))) (DistribSMul.toSmulZeroClass.{0, u1} Rat R (AddMonoid.toAddZeroClass.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R 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 but is expected to have type
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(StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2)))) (a : Rat), Eq.{succ u1} R (Subtype.val.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x (SetLike.coe.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R 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_inst_1)))) _inst_2)))) (selfAdjoint.instQSMul.{u1} R _inst_1 _inst_2)) a x)) (HSMul.hSMul.{0, u1, u1} Rat R R (instHSMul.{0, u1} Rat R (SMulZeroClass.toSMul.{0, u1} Rat R (CommMonoidWithZero.toZero.{u1} R (CommGroupWithZero.toCommMonoidWithZero.{u1} R (Semifield.toCommGroupWithZero.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (DistribSMul.toSMulZeroClass.{0, u1} Rat R (AddMonoid.toAddZeroClass.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (Rat.distribSMul.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) a (Subtype.val.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x (SetLike.coe.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2)))) x))
+  forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1))))] (x : Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) x (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2)))) (a : Rat), Eq.{succ u1} R (Subtype.val.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x (SetLike.coe.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2)))) (HSMul.hSMul.{0, u1, u1} Rat (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) x (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2)))) (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) x (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2)))) (instHSMul.{0, u1} Rat (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) x (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2)))) (selfAdjoint.instQSMul.{u1} R _inst_1 _inst_2)) a x)) (HSMul.hSMul.{0, u1, u1} Rat R R (instHSMul.{0, u1} Rat R (SMulZeroClass.toSMul.{0, u1} Rat R (CommMonoidWithZero.toZero.{u1} R (CommGroupWithZero.toCommMonoidWithZero.{u1} R (Semifield.toCommGroupWithZero.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (DistribSMul.toSMulZeroClass.{0, u1} Rat R (AddMonoid.toAddZeroClass.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (Rat.distribSMul.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) a (Subtype.val.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x (SetLike.coe.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2)))) x))
 Case conversion may be inaccurate. Consider using '#align self_adjoint.coe_rat_smul selfAdjoint.val_rat_smulₓ'. -/
 @[simp, norm_cast]
 theorem val_rat_smul (x : selfAdjoint R) (a : ℚ) : ↑(a • x) = a • (x : R) :=
@@ -723,7 +723,7 @@ variable [Ring R] [StarRing R]
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1))] {x : R}, (Membership.Mem.{u1, u1} R (AddSubgroup.{u1} R (AddCommGroup.toAddGroup.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))) (SetLike.hasMem.{u1, u1} (AddSubgroup.{u1} R (AddCommGroup.toAddGroup.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))) R (AddSubgroup.setLike.{u1} R (AddCommGroup.toAddGroup.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))))) x (skewAdjoint.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1)) _inst_2))) -> (forall (z : R), Membership.Mem.{u1, u1} R (AddSubgroup.{u1} R (AddCommGroup.toAddGroup.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))) (SetLike.hasMem.{u1, u1} (AddSubgroup.{u1} R (AddCommGroup.toAddGroup.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))) R (AddSubgroup.setLike.{u1} R (AddCommGroup.toAddGroup.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R _inst_1))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R _inst_1))) z x) (Star.star.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1)) _inst_2))) z)) (skewAdjoint.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1)) _inst_2)))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1))] {x : R}, (Membership.mem.{u1, u1} R (AddSubgroup.{u1} R (AddCommGroup.toAddGroup.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} R (AddCommGroup.toAddGroup.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddCommGroup.toAddGroup.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)))) x (skewAdjoint.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1)) _inst_2))) -> (forall (z : R), Membership.mem.{u1, u1} R (AddSubgroup.{u1} R (AddCommGroup.toAddGroup.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} R (AddCommGroup.toAddGroup.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddCommGroup.toAddGroup.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) z x) (Star.star.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1)) _inst_2))) z)) (skewAdjoint.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1)) _inst_2)))
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] [_inst_2 : StarRing.{u1} R (Semiring.toNonUnitalSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))] {x : R}, (Membership.mem.{u1, u1} R (AddSubgroup.{u1} R (AddCommGroup.toAddGroup.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} R (AddCommGroup.toAddGroup.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddCommGroup.toAddGroup.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)))) x (skewAdjoint.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1) (StarRing.toStarAddMonoid.{u1} R (Semiring.toNonUnitalSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) _inst_2))) -> (forall (z : R), Membership.mem.{u1, u1} R (AddSubgroup.{u1} R (AddCommGroup.toAddGroup.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} R (AddCommGroup.toAddGroup.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddCommGroup.toAddGroup.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) z x) (Star.star.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1))) (StarRing.toStarAddMonoid.{u1} R (Semiring.toNonUnitalSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) _inst_2))) z)) (skewAdjoint.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1) (StarRing.toStarAddMonoid.{u1} R (Semiring.toNonUnitalSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) _inst_2)))
 Case conversion may be inaccurate. Consider using '#align skew_adjoint.conjugate skewAdjoint.conjugateₓ'. -/
 theorem conjugate {x : R} (hx : x ∈ skewAdjoint R) (z : R) : z * x * star z ∈ skewAdjoint R := by
   simp only [mem_iff, star_mul, star_star, mem_iff.mp hx, neg_mul, mul_neg, mul_assoc]
@@ -733,7 +733,7 @@ theorem conjugate {x : R} (hx : x ∈ skewAdjoint R) (z : R) : z * x * star z 
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1))] {x : R}, (Membership.Mem.{u1, u1} R (AddSubgroup.{u1} R (AddCommGroup.toAddGroup.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))) (SetLike.hasMem.{u1, u1} (AddSubgroup.{u1} R (AddCommGroup.toAddGroup.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))) R (AddSubgroup.setLike.{u1} R (AddCommGroup.toAddGroup.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))))) x (skewAdjoint.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1)) _inst_2))) -> (forall (z : R), Membership.Mem.{u1, u1} R (AddSubgroup.{u1} R (AddCommGroup.toAddGroup.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))) (SetLike.hasMem.{u1, u1} (AddSubgroup.{u1} R (AddCommGroup.toAddGroup.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))) R (AddSubgroup.setLike.{u1} R (AddCommGroup.toAddGroup.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R _inst_1))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R _inst_1))) (Star.star.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1)) _inst_2))) z) x) z) (skewAdjoint.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1)) _inst_2)))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1))] {x : R}, (Membership.mem.{u1, u1} R (AddSubgroup.{u1} R (AddCommGroup.toAddGroup.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} R (AddCommGroup.toAddGroup.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddCommGroup.toAddGroup.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)))) x (skewAdjoint.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1)) _inst_2))) -> (forall (z : R), Membership.mem.{u1, u1} R (AddSubgroup.{u1} R (AddCommGroup.toAddGroup.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} R (AddCommGroup.toAddGroup.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddCommGroup.toAddGroup.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Star.star.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1)) _inst_2))) z) x) z) (skewAdjoint.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1)) _inst_2)))
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] [_inst_2 : StarRing.{u1} R (Semiring.toNonUnitalSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))] {x : R}, (Membership.mem.{u1, u1} R (AddSubgroup.{u1} R (AddCommGroup.toAddGroup.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} R (AddCommGroup.toAddGroup.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddCommGroup.toAddGroup.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)))) x (skewAdjoint.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1) (StarRing.toStarAddMonoid.{u1} R (Semiring.toNonUnitalSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) _inst_2))) -> (forall (z : R), Membership.mem.{u1, u1} R (AddSubgroup.{u1} R (AddCommGroup.toAddGroup.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} R (AddCommGroup.toAddGroup.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddCommGroup.toAddGroup.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Star.star.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1))) (StarRing.toStarAddMonoid.{u1} R (Semiring.toNonUnitalSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) _inst_2))) z) x) z) (skewAdjoint.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1) (StarRing.toStarAddMonoid.{u1} R (Semiring.toNonUnitalSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) _inst_2)))
 Case conversion may be inaccurate. Consider using '#align skew_adjoint.conjugate' skewAdjoint.conjugate'ₓ'. -/
 theorem conjugate' {x : R} (hx : x ∈ skewAdjoint R) (z : R) : star z * x * z ∈ skewAdjoint R := by
   simp only [mem_iff, star_mul, star_star, mem_iff.mp hx, neg_mul, mul_neg, mul_assoc]
@@ -743,7 +743,7 @@ theorem conjugate' {x : R} (hx : x ∈ skewAdjoint R) (z : R) : star z * x * z 
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1))] {x : R}, (Membership.Mem.{u1, u1} R (AddSubgroup.{u1} R (AddCommGroup.toAddGroup.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))) (SetLike.hasMem.{u1, u1} (AddSubgroup.{u1} R (AddCommGroup.toAddGroup.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))) R (AddSubgroup.setLike.{u1} R (AddCommGroup.toAddGroup.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))))) x (skewAdjoint.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1)) _inst_2))) -> (IsStarNormal.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R _inst_1)) (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1)) _inst_2))) x)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1))] {x : R}, (Membership.mem.{u1, u1} R (AddSubgroup.{u1} R (AddCommGroup.toAddGroup.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} R (AddCommGroup.toAddGroup.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddCommGroup.toAddGroup.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)))) x (skewAdjoint.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1)) _inst_2))) -> (IsStarNormal.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1)) _inst_2))) x)
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] [_inst_2 : StarRing.{u1} R (Semiring.toNonUnitalSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))] {x : R}, (Membership.mem.{u1, u1} R (AddSubgroup.{u1} R (AddCommGroup.toAddGroup.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} R (AddCommGroup.toAddGroup.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddCommGroup.toAddGroup.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1)))) x (skewAdjoint.{u1} R (Ring.toAddCommGroup.{u1} R _inst_1) (StarRing.toStarAddMonoid.{u1} R (Semiring.toNonUnitalSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) _inst_2))) -> (IsStarNormal.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1))) (StarRing.toStarAddMonoid.{u1} R (Semiring.toNonUnitalSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) _inst_2))) x)
 Case conversion may be inaccurate. Consider using '#align skew_adjoint.is_star_normal_of_mem skewAdjoint.isStarNormal_of_memₓ'. -/
 theorem isStarNormal_of_mem {x : R} (hx : x ∈ skewAdjoint R) : IsStarNormal x :=
   ⟨by

a6ece354

bump to nightly-2023-05-03-22

mathlib commit https://github.com/leanprover-community/mathlib/commit/36b8aa61ea7c05727161f96a0532897bd72aedab

aa7b8e08

Diff

@@ -125,7 +125,7 @@ theorem mul_star_self [Semigroup R] [StarSemigroup R] (x : R) : IsSelfAdjoint (x
 lean 3 declaration is
   forall {F : Type.{u1}} {R : Type.{u2}} {S : Type.{u3}} [_inst_1 : Star.{u2} R] [_inst_2 : Star.{u3} S] [_inst_3 : StarHomClass.{u1, u2, u3} F R S _inst_1 _inst_2] {x : R}, (IsSelfAdjoint.{u2} R _inst_1 x) -> (forall (f : F), IsSelfAdjoint.{u3} S _inst_2 (coeFn.{succ u1, max (succ u2) (succ u3)} F (fun (_x : F) => R -> S) (FunLike.hasCoeToFun.{succ u1, succ u2, succ u3} F R (fun (_x : R) => S) (StarHomClass.toFunLike.{u1, u2, u3} F R S _inst_1 _inst_2 _inst_3)) f x))
 but is expected to have type
-  forall {F : Type.{u3}} {R : Type.{u2}} {S : Type.{u1}} [_inst_1 : Star.{u2} R] [_inst_2 : Star.{u1} S] [_inst_3 : StarHomClass.{u3, u2, u1} F R S _inst_1 _inst_2] {x : R}, (IsSelfAdjoint.{u2} R _inst_1 x) -> (forall (f : F), IsSelfAdjoint.{u1} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3329 : R) => S) x) _inst_2 (FunLike.coe.{succ u3, succ u2, succ u1} F R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3329 : R) => S) _x) (StarHomClass.toFunLike.{u3, u2, u1} F R S _inst_1 _inst_2 _inst_3) f x))
+  forall {F : Type.{u3}} {R : Type.{u2}} {S : Type.{u1}} [_inst_1 : Star.{u2} R] [_inst_2 : Star.{u1} S] [_inst_3 : StarHomClass.{u3, u2, u1} F R S _inst_1 _inst_2] {x : R}, (IsSelfAdjoint.{u2} R _inst_1 x) -> (forall (f : F), IsSelfAdjoint.{u1} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3327 : R) => S) x) _inst_2 (FunLike.coe.{succ u3, succ u2, succ u1} F R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3327 : R) => S) _x) (StarHomClass.toFunLike.{u3, u2, u1} F R S _inst_1 _inst_2 _inst_3) f x))
 Case conversion may be inaccurate. Consider using '#align is_self_adjoint.star_hom_apply IsSelfAdjoint.starHom_applyₓ'. -/
 /-- Functions in a `star_hom_class` preserve self-adjoint elements. -/
 theorem starHom_apply {F R S : Type _} [Star R] [Star S] [StarHomClass F R S] {x : R}

a6ece354

bump to nightly-2023-04-28-10

mathlib commit https://github.com/leanprover-community/mathlib/commit/fa78268d4d77cb2b2fbc89f0527e2e7807763780

7fdaed52

Diff

@@ -125,7 +125,7 @@ theorem mul_star_self [Semigroup R] [StarSemigroup R] (x : R) : IsSelfAdjoint (x
 lean 3 declaration is
   forall {F : Type.{u1}} {R : Type.{u2}} {S : Type.{u3}} [_inst_1 : Star.{u2} R] [_inst_2 : Star.{u3} S] [_inst_3 : StarHomClass.{u1, u2, u3} F R S _inst_1 _inst_2] {x : R}, (IsSelfAdjoint.{u2} R _inst_1 x) -> (forall (f : F), IsSelfAdjoint.{u3} S _inst_2 (coeFn.{succ u1, max (succ u2) (succ u3)} F (fun (_x : F) => R -> S) (FunLike.hasCoeToFun.{succ u1, succ u2, succ u3} F R (fun (_x : R) => S) (StarHomClass.toFunLike.{u1, u2, u3} F R S _inst_1 _inst_2 _inst_3)) f x))
 but is expected to have type
-  forall {F : Type.{u3}} {R : Type.{u2}} {S : Type.{u1}} [_inst_1 : Star.{u2} R] [_inst_2 : Star.{u1} S] [_inst_3 : StarHomClass.{u3, u2, u1} F R S _inst_1 _inst_2] {x : R}, (IsSelfAdjoint.{u2} R _inst_1 x) -> (forall (f : F), IsSelfAdjoint.{u1} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3050 : R) => S) x) _inst_2 (FunLike.coe.{succ u3, succ u2, succ u1} F R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3050 : R) => S) _x) (StarHomClass.toFunLike.{u3, u2, u1} F R S _inst_1 _inst_2 _inst_3) f x))
+  forall {F : Type.{u3}} {R : Type.{u2}} {S : Type.{u1}} [_inst_1 : Star.{u2} R] [_inst_2 : Star.{u1} S] [_inst_3 : StarHomClass.{u3, u2, u1} F R S _inst_1 _inst_2] {x : R}, (IsSelfAdjoint.{u2} R _inst_1 x) -> (forall (f : F), IsSelfAdjoint.{u1} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3329 : R) => S) x) _inst_2 (FunLike.coe.{succ u3, succ u2, succ u1} F R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3329 : R) => S) _x) (StarHomClass.toFunLike.{u3, u2, u1} F R S _inst_1 _inst_2 _inst_3) f x))
 Case conversion may be inaccurate. Consider using '#align is_self_adjoint.star_hom_apply IsSelfAdjoint.starHom_applyₓ'. -/
 /-- Functions in a `star_hom_class` preserve self-adjoint elements. -/
 theorem starHom_apply {F R S : Type _} [Star R] [Star S] [StarHomClass F R S] {x : R}

a6ece354

bump to nightly-2023-03-31-02

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

c3ffa91f

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Frédéric Dupuis
 
 ! This file was ported from Lean 3 source module algebra.star.self_adjoint
-! leanprover-community/mathlib commit 9abfa6f0727d5adc99067e325e15d1a9de17fd8e
+! leanprover-community/mathlib commit a6ece35404f60597c651689c1b46ead86de5ac1b
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -381,13 +381,13 @@ theorem isSelfAdjoint_ratCast (x : ℚ) : IsSelfAdjoint (x : R) :=
 
 end DivisionRing
 
-section Field
+section Semifield
 
-variable [Field R] [StarRing R]
+variable [Semifield R] [StarRing R]
 
 /- warning: is_self_adjoint.div -> IsSelfAdjoint.div is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1))))] {x : R} {y : R}, (IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1))))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2))) x) -> (IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1))))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2))) y) -> (IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1))))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2))) (HDiv.hDiv.{u1, u1, u1} R R R (instHDiv.{u1} R (DivInvMonoid.toHasDiv.{u1} R (DivisionRing.toDivInvMonoid.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) x y))
+  forall {R : Type.{u1}} [_inst_1 : Semifield.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R (Semifield.toCommSemiring.{u1} R _inst_1)))] {x : R} {y : R}, (IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R (Semifield.toCommSemiring.{u1} R _inst_1)))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R (Semifield.toCommSemiring.{u1} R _inst_1))) _inst_2))) x) -> (IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R (Semifield.toCommSemiring.{u1} R _inst_1)))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R (Semifield.toCommSemiring.{u1} R _inst_1))) _inst_2))) y) -> (IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R (Semifield.toCommSemiring.{u1} R _inst_1)))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R (Semifield.toCommSemiring.{u1} R _inst_1))) _inst_2))) (HDiv.hDiv.{u1, u1, u1} R R R (instHDiv.{u1} R (DivInvMonoid.toHasDiv.{u1} R (GroupWithZero.toDivInvMonoid.{u1} R (DivisionSemiring.toGroupWithZero.{u1} R (Semifield.toDivisionSemiring.{u1} R _inst_1))))) x y))
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : Semifield.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R (Semifield.toCommSemiring.{u1} R _inst_1)))] {x : R} {y : R}, (IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R _inst_1)))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R (Semifield.toCommSemiring.{u1} R _inst_1))) _inst_2))) x) -> (IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R _inst_1)))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R (Semifield.toCommSemiring.{u1} R _inst_1))) _inst_2))) y) -> (IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R _inst_1)))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R (Semifield.toCommSemiring.{u1} R _inst_1))) _inst_2))) (HDiv.hDiv.{u1, u1, u1} R R R (instHDiv.{u1} R (Semifield.toDiv.{u1} R _inst_1)) x y))
 Case conversion may be inaccurate. Consider using '#align is_self_adjoint.div IsSelfAdjoint.divₓ'. -/
@@ -395,7 +395,7 @@ theorem div {x y : R} (hx : IsSelfAdjoint x) (hy : IsSelfAdjoint y) : IsSelfAdjo
   simp only [isSelfAdjoint_iff, star_div', hx.star_eq, hy.star_eq]
 #align is_self_adjoint.div IsSelfAdjoint.div
 
-end Field
+end Semifield
 
 section SMul

9abfa6f0

bump to nightly-2023-03-29-08

mathlib commit https://github.com/leanprover-community/mathlib/commit/0148d455199ed64bf8eb2f493a1e7eb9211ce170

fbc8cdc2

Diff

@@ -72,11 +72,13 @@ theorem star_comm_self' [Mul R] [Star R] (x : R) [IsStarNormal x] : star x * x =
 
 namespace IsSelfAdjoint
 
+#print IsSelfAdjoint.all /-
 -- named to match `commute.all`
 /-- All elements are self-adjoint when `star` is trivial. -/
 theorem all [Star R] [TrivialStar R] (r : R) : IsSelfAdjoint r :=
   star_trivial _
 #align is_self_adjoint.all IsSelfAdjoint.all
+-/
 
 #print IsSelfAdjoint.star_eq /-
 theorem star_eq [Star R] {x : R} (hx : IsSelfAdjoint x) : star x = x :=
@@ -141,7 +143,7 @@ variable (R)
 lean 3 declaration is
   forall (R : Type.{u1}) [_inst_1 : AddMonoid.{u1} R] [_inst_2 : StarAddMonoid.{u1} R _inst_1], IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R _inst_1 _inst_2)) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R _inst_1)))))
 but is expected to have type
-  forall (R : Type.{u1}) [_inst_1 : AddGroup.{u1} R] [_inst_2 : StarAddMonoid.{u1} R (SubNegMonoid.toAddMonoid.{u1} R (AddGroup.toSubNegMonoid.{u1} R _inst_1))], IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (SubNegMonoid.toAddMonoid.{u1} R (AddGroup.toSubNegMonoid.{u1} R _inst_1)) _inst_2)) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (NegZeroClass.toZero.{u1} R (SubNegZeroMonoid.toNegZeroClass.{u1} R (SubtractionMonoid.toSubNegZeroMonoid.{u1} R (AddGroup.toSubtractionMonoid.{u1} R _inst_1))))))
+  forall (R : Type.{u1}) [_inst_1 : AddMonoid.{u1} R] [_inst_2 : StarAddMonoid.{u1} R _inst_1], IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R _inst_1 _inst_2)) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (AddMonoid.toZero.{u1} R _inst_1)))
 Case conversion may be inaccurate. Consider using '#align is_self_adjoint_zero isSelfAdjoint_zeroₓ'. -/
 theorem isSelfAdjoint_zero : IsSelfAdjoint (0 : R) :=
   star_zero R
@@ -153,7 +155,7 @@ variable {R}
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : AddMonoid.{u1} R] [_inst_2 : StarAddMonoid.{u1} R _inst_1] {x : R} {y : R}, (IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R _inst_1 _inst_2)) x) -> (IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R _inst_1 _inst_2)) y) -> (IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R _inst_1 _inst_2)) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (AddZeroClass.toHasAdd.{u1} R (AddMonoid.toAddZeroClass.{u1} R _inst_1))) x y))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : AddGroup.{u1} R] [_inst_2 : StarAddMonoid.{u1} R (SubNegMonoid.toAddMonoid.{u1} R (AddGroup.toSubNegMonoid.{u1} R _inst_1))] {x : R} {y : R}, (IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (SubNegMonoid.toAddMonoid.{u1} R (AddGroup.toSubNegMonoid.{u1} R _inst_1)) _inst_2)) x) -> (IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (SubNegMonoid.toAddMonoid.{u1} R (AddGroup.toSubNegMonoid.{u1} R _inst_1)) _inst_2)) y) -> (IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (SubNegMonoid.toAddMonoid.{u1} R (AddGroup.toSubNegMonoid.{u1} R _inst_1)) _inst_2)) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (AddZeroClass.toAdd.{u1} R (AddMonoid.toAddZeroClass.{u1} R (SubNegMonoid.toAddMonoid.{u1} R (AddGroup.toSubNegMonoid.{u1} R _inst_1))))) x y))
+  forall {R : Type.{u1}} [_inst_1 : AddMonoid.{u1} R] [_inst_2 : StarAddMonoid.{u1} R _inst_1] {x : R} {y : R}, (IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R _inst_1 _inst_2)) x) -> (IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R _inst_1 _inst_2)) y) -> (IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R _inst_1 _inst_2)) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (AddZeroClass.toAdd.{u1} R (AddMonoid.toAddZeroClass.{u1} R _inst_1))) x y))
 Case conversion may be inaccurate. Consider using '#align is_self_adjoint.add IsSelfAdjoint.addₓ'. -/
 theorem add {x y : R} (hx : IsSelfAdjoint x) (hy : IsSelfAdjoint y) : IsSelfAdjoint (x + y) := by
   simp only [isSelfAdjoint_iff, star_add, hx.star_eq, hy.star_eq]
@@ -163,7 +165,7 @@ theorem add {x y : R} (hx : IsSelfAdjoint x) (hy : IsSelfAdjoint y) : IsSelfAdjo
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : AddMonoid.{u1} R] [_inst_2 : StarAddMonoid.{u1} R _inst_1] {x : R}, (IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R _inst_1 _inst_2)) x) -> (IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R _inst_1 _inst_2)) (bit0.{u1} R (AddZeroClass.toHasAdd.{u1} R (AddMonoid.toAddZeroClass.{u1} R _inst_1)) x))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : AddGroup.{u1} R] [_inst_2 : StarAddMonoid.{u1} R (SubNegMonoid.toAddMonoid.{u1} R (AddGroup.toSubNegMonoid.{u1} R _inst_1))] {x : R}, (IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (SubNegMonoid.toAddMonoid.{u1} R (AddGroup.toSubNegMonoid.{u1} R _inst_1)) _inst_2)) x) -> (IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (SubNegMonoid.toAddMonoid.{u1} R (AddGroup.toSubNegMonoid.{u1} R _inst_1)) _inst_2)) (bit0.{u1} R (AddZeroClass.toAdd.{u1} R (AddMonoid.toAddZeroClass.{u1} R (SubNegMonoid.toAddMonoid.{u1} R (AddGroup.toSubNegMonoid.{u1} R _inst_1)))) x))
+  forall {R : Type.{u1}} [_inst_1 : AddMonoid.{u1} R] [_inst_2 : StarAddMonoid.{u1} R _inst_1] {x : R}, (IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R _inst_1 _inst_2)) x) -> (IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R _inst_1 _inst_2)) (bit0.{u1} R (AddZeroClass.toAdd.{u1} R (AddMonoid.toAddZeroClass.{u1} R _inst_1)) x))
 Case conversion may be inaccurate. Consider using '#align is_self_adjoint.bit0 IsSelfAdjoint.bit0ₓ'. -/
 theorem bit0 {x : R} (hx : IsSelfAdjoint x) : IsSelfAdjoint (bit0 x) := by
   simp only [isSelfAdjoint_iff, star_bit0, hx.star_eq]
@@ -201,10 +203,22 @@ section AddCommMonoid
 
 variable [AddCommMonoid R] [StarAddMonoid R]
 
+/- warning: is_self_adjoint_add_star_self -> isSelfAdjoint_add_star_self is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : AddCommMonoid.{u1} R] [_inst_2 : StarAddMonoid.{u1} R (AddCommMonoid.toAddMonoid.{u1} R _inst_1)] (x : R), IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R _inst_1) _inst_2)) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (AddZeroClass.toHasAdd.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R _inst_1)))) x (Star.star.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R _inst_1) _inst_2)) x))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : AddCommMonoid.{u1} R] [_inst_2 : StarAddMonoid.{u1} R (AddCommMonoid.toAddMonoid.{u1} R _inst_1)] (x : R), IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R _inst_1) _inst_2)) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (AddZeroClass.toAdd.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R _inst_1)))) x (Star.star.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R _inst_1) _inst_2)) x))
+Case conversion may be inaccurate. Consider using '#align is_self_adjoint_add_star_self isSelfAdjoint_add_star_selfₓ'. -/
 theorem isSelfAdjoint_add_star_self (x : R) : IsSelfAdjoint (x + star x) := by
   simp only [isSelfAdjoint_iff, add_comm, star_add, star_star]
 #align is_self_adjoint_add_star_self isSelfAdjoint_add_star_self
 
+/- warning: is_self_adjoint_star_add_self -> isSelfAdjoint_star_add_self is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : AddCommMonoid.{u1} R] [_inst_2 : StarAddMonoid.{u1} R (AddCommMonoid.toAddMonoid.{u1} R _inst_1)] (x : R), IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R _inst_1) _inst_2)) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (AddZeroClass.toHasAdd.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R _inst_1)))) (Star.star.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R _inst_1) _inst_2)) x) x)
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : AddCommMonoid.{u1} R] [_inst_2 : StarAddMonoid.{u1} R (AddCommMonoid.toAddMonoid.{u1} R _inst_1)] (x : R), IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R _inst_1) _inst_2)) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (AddZeroClass.toAdd.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R _inst_1)))) (Star.star.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R _inst_1) _inst_2)) x) x)
+Case conversion may be inaccurate. Consider using '#align is_self_adjoint_star_add_self isSelfAdjoint_star_add_selfₓ'. -/
 theorem isSelfAdjoint_star_add_self (x : R) : IsSelfAdjoint (star x + x) := by
   simp only [isSelfAdjoint_iff, add_comm, star_add, star_star]
 #align is_self_adjoint_star_add_self isSelfAdjoint_star_add_self
@@ -219,7 +233,7 @@ variable [Semigroup R] [StarSemigroup R]
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semigroup.{u1} R] [_inst_2 : StarSemigroup.{u1} R _inst_1] {x : R}, (IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarSemigroup.toHasInvolutiveStar.{u1} R _inst_1 _inst_2)) x) -> (forall (z : R), IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarSemigroup.toHasInvolutiveStar.{u1} R _inst_1 _inst_2)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Semigroup.toHasMul.{u1} R _inst_1)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Semigroup.toHasMul.{u1} R _inst_1)) z x) (Star.star.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarSemigroup.toHasInvolutiveStar.{u1} R _inst_1 _inst_2)) z)))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : NonUnitalSemiring.{u1} R] [_inst_2 : StarRing.{u1} R _inst_1] {x : R}, (IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_1))) (StarRing.toStarAddMonoid.{u1} R _inst_1 _inst_2))) x) -> (forall (z : R), IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_1))) (StarRing.toStarAddMonoid.{u1} R _inst_1 _inst_2))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_1))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_1))) z x) (Star.star.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_1))) (StarRing.toStarAddMonoid.{u1} R _inst_1 _inst_2))) z)))
+  forall {R : Type.{u1}} [_inst_1 : Semigroup.{u1} R] [_inst_2 : StarSemigroup.{u1} R _inst_1] {x : R}, (IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarSemigroup.toInvolutiveStar.{u1} R _inst_1 _inst_2)) x) -> (forall (z : R), IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarSemigroup.toInvolutiveStar.{u1} R _inst_1 _inst_2)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Semigroup.toMul.{u1} R _inst_1)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Semigroup.toMul.{u1} R _inst_1)) z x) (Star.star.{u1} R (InvolutiveStar.toStar.{u1} R (StarSemigroup.toInvolutiveStar.{u1} R _inst_1 _inst_2)) z)))
 Case conversion may be inaccurate. Consider using '#align is_self_adjoint.conjugate IsSelfAdjoint.conjugateₓ'. -/
 theorem conjugate {x : R} (hx : IsSelfAdjoint x) (z : R) : IsSelfAdjoint (z * x * star z) := by
   simp only [isSelfAdjoint_iff, star_mul, star_star, mul_assoc, hx.star_eq]
@@ -229,7 +243,7 @@ theorem conjugate {x : R} (hx : IsSelfAdjoint x) (z : R) : IsSelfAdjoint (z * x
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semigroup.{u1} R] [_inst_2 : StarSemigroup.{u1} R _inst_1] {x : R}, (IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarSemigroup.toHasInvolutiveStar.{u1} R _inst_1 _inst_2)) x) -> (forall (z : R), IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarSemigroup.toHasInvolutiveStar.{u1} R _inst_1 _inst_2)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Semigroup.toHasMul.{u1} R _inst_1)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Semigroup.toHasMul.{u1} R _inst_1)) (Star.star.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarSemigroup.toHasInvolutiveStar.{u1} R _inst_1 _inst_2)) z) x) z))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : NonUnitalSemiring.{u1} R] [_inst_2 : StarRing.{u1} R _inst_1] {x : R}, (IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_1))) (StarRing.toStarAddMonoid.{u1} R _inst_1 _inst_2))) x) -> (forall (z : R), IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_1))) (StarRing.toStarAddMonoid.{u1} R _inst_1 _inst_2))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_1))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_1))) (Star.star.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_1))) (StarRing.toStarAddMonoid.{u1} R _inst_1 _inst_2))) z) x) z))
+  forall {R : Type.{u1}} [_inst_1 : Semigroup.{u1} R] [_inst_2 : StarSemigroup.{u1} R _inst_1] {x : R}, (IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarSemigroup.toInvolutiveStar.{u1} R _inst_1 _inst_2)) x) -> (forall (z : R), IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarSemigroup.toInvolutiveStar.{u1} R _inst_1 _inst_2)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Semigroup.toMul.{u1} R _inst_1)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Semigroup.toMul.{u1} R _inst_1)) (Star.star.{u1} R (InvolutiveStar.toStar.{u1} R (StarSemigroup.toInvolutiveStar.{u1} R _inst_1 _inst_2)) z) x) z))
 Case conversion may be inaccurate. Consider using '#align is_self_adjoint.conjugate' IsSelfAdjoint.conjugate'ₓ'. -/
 theorem conjugate' {x : R} (hx : IsSelfAdjoint x) (z : R) : IsSelfAdjoint (star z * x * z) := by
   simp only [isSelfAdjoint_iff, star_mul, star_star, mul_assoc, hx.star_eq]
@@ -239,7 +253,7 @@ theorem conjugate' {x : R} (hx : IsSelfAdjoint x) (z : R) : IsSelfAdjoint (star
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semigroup.{u1} R] [_inst_2 : StarSemigroup.{u1} R _inst_1] {x : R}, (IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarSemigroup.toHasInvolutiveStar.{u1} R _inst_1 _inst_2)) x) -> (IsStarNormal.{u1} R (Semigroup.toHasMul.{u1} R _inst_1) (InvolutiveStar.toHasStar.{u1} R (StarSemigroup.toHasInvolutiveStar.{u1} R _inst_1 _inst_2)) x)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : NonUnitalSemiring.{u1} R] [_inst_2 : StarRing.{u1} R _inst_1] {x : R}, (IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_1))) (StarRing.toStarAddMonoid.{u1} R _inst_1 _inst_2))) x) -> (IsStarNormal.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_1)) (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_1))) (StarRing.toStarAddMonoid.{u1} R _inst_1 _inst_2))) x)
+  forall {R : Type.{u1}} [_inst_1 : Semigroup.{u1} R] [_inst_2 : StarSemigroup.{u1} R _inst_1] {x : R}, (IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarSemigroup.toInvolutiveStar.{u1} R _inst_1 _inst_2)) x) -> (IsStarNormal.{u1} R (Semigroup.toMul.{u1} R _inst_1) (InvolutiveStar.toStar.{u1} R (StarSemigroup.toInvolutiveStar.{u1} R _inst_1 _inst_2)) x)
 Case conversion may be inaccurate. Consider using '#align is_self_adjoint.is_star_normal IsSelfAdjoint.isStarNormalₓ'. -/
 theorem isStarNormal {x : R} (hx : IsSelfAdjoint x) : IsStarNormal x :=
   ⟨by simp only [hx.star_eq]⟩
@@ -257,7 +271,7 @@ variable (R)
 lean 3 declaration is
   forall (R : Type.{u1}) [_inst_1 : Monoid.{u1} R] [_inst_2 : StarSemigroup.{u1} R (Monoid.toSemigroup.{u1} R _inst_1)], IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarSemigroup.toHasInvolutiveStar.{u1} R (Monoid.toSemigroup.{u1} R _inst_1) _inst_2)) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (MulOneClass.toHasOne.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)))))
 but is expected to have type
-  forall (R : Type.{u1}) [_inst_1 : Ring.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1))], IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1)) _inst_2))) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (NonAssocRing.toOne.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))
+  forall (R : Type.{u1}) [_inst_1 : Monoid.{u1} R] [_inst_2 : StarSemigroup.{u1} R (Monoid.toSemigroup.{u1} R _inst_1)], IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarSemigroup.toInvolutiveStar.{u1} R (Monoid.toSemigroup.{u1} R _inst_1) _inst_2)) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Monoid.toOne.{u1} R _inst_1)))
 Case conversion may be inaccurate. Consider using '#align is_self_adjoint_one isSelfAdjoint_oneₓ'. -/
 theorem isSelfAdjoint_one : IsSelfAdjoint (1 : R) :=
   star_one R
@@ -265,15 +279,11 @@ theorem isSelfAdjoint_one : IsSelfAdjoint (1 : R) :=
 
 variable {R}
 
-/- warning: is_self_adjoint.pow -> IsSelfAdjoint.pow is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : Monoid.{u1} R] [_inst_2 : StarSemigroup.{u1} R (Monoid.toSemigroup.{u1} R _inst_1)] {x : R}, (IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarSemigroup.toHasInvolutiveStar.{u1} R (Monoid.toSemigroup.{u1} R _inst_1) _inst_2)) x) -> (forall (n : Nat), IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarSemigroup.toHasInvolutiveStar.{u1} R (Monoid.toSemigroup.{u1} R _inst_1) _inst_2)) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R _inst_1)) x n))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1))] {x : R}, (IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1)) _inst_2))) x) -> (forall (n : Nat), IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1)) _inst_2))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) x n))
-Case conversion may be inaccurate. Consider using '#align is_self_adjoint.pow IsSelfAdjoint.powₓ'. -/
+#print IsSelfAdjoint.pow /-
 theorem pow {x : R} (hx : IsSelfAdjoint x) (n : ℕ) : IsSelfAdjoint (x ^ n) := by
   simp only [isSelfAdjoint_iff, star_pow, hx.star_eq]
 #align is_self_adjoint.pow IsSelfAdjoint.pow
+-/
 
 end Monoid
 
@@ -285,16 +295,18 @@ variable [Semiring R] [StarRing R]
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_2 : StarRing.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_1)] {x : R}, (IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_1) _inst_2))) x) -> (IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_1) _inst_2))) (bit1.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Distrib.toHasAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) x))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1))] {x : R}, (IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1)) _inst_2))) x) -> (IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1)) _inst_2))) (bit1.{u1} R (NonAssocRing.toOne.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))) x))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_2 : StarRing.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_1)] {x : R}, (IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_1) _inst_2))) x) -> (IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_1) _inst_2))) (bit1.{u1} R (Semiring.toOne.{u1} R _inst_1) (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) x))
 Case conversion may be inaccurate. Consider using '#align is_self_adjoint.bit1 IsSelfAdjoint.bit1ₓ'. -/
 theorem bit1 {x : R} (hx : IsSelfAdjoint x) : IsSelfAdjoint (bit1 x) := by
   simp only [isSelfAdjoint_iff, star_bit1, hx.star_eq]
 #align is_self_adjoint.bit1 IsSelfAdjoint.bit1
 
+#print isSelfAdjoint_natCast /-
 @[simp]
-theorem isSelfAdjoint_nat_cast (n : ℕ) : IsSelfAdjoint (n : R) :=
+theorem isSelfAdjoint_natCast (n : ℕ) : IsSelfAdjoint (n : R) :=
   star_natCast _
-#align is_self_adjoint_nat_cast isSelfAdjoint_nat_cast
+#align is_self_adjoint_nat_cast isSelfAdjoint_natCast
+-/
 
 end Semiring
 
@@ -306,7 +318,7 @@ variable [CommSemigroup R] [StarSemigroup R]
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemigroup.{u1} R] [_inst_2 : StarSemigroup.{u1} R (CommSemigroup.toSemigroup.{u1} R _inst_1)] {x : R} {y : R}, (IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarSemigroup.toHasInvolutiveStar.{u1} R (CommSemigroup.toSemigroup.{u1} R _inst_1) _inst_2)) x) -> (IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarSemigroup.toHasInvolutiveStar.{u1} R (CommSemigroup.toSemigroup.{u1} R _inst_1) _inst_2)) y) -> (IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarSemigroup.toHasInvolutiveStar.{u1} R (CommSemigroup.toSemigroup.{u1} R _inst_1) _inst_2)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Semigroup.toHasMul.{u1} R (CommSemigroup.toSemigroup.{u1} R _inst_1))) x y))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : NonUnitalCommRing.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R _inst_1))] {x : R} {y : R}, (IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (SubNegMonoid.toAddMonoid.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddCommGroup.toAddGroup.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R _inst_1)))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R _inst_1)) _inst_2))) x) -> (IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (SubNegMonoid.toAddMonoid.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddCommGroup.toAddGroup.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R _inst_1)))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R _inst_1)) _inst_2))) y) -> (IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (SubNegMonoid.toAddMonoid.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddCommGroup.toAddGroup.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R _inst_1)))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R _inst_1)) _inst_2))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R _inst_1)))) x y))
+  forall {R : Type.{u1}} [_inst_1 : CommSemigroup.{u1} R] [_inst_2 : StarSemigroup.{u1} R (CommSemigroup.toSemigroup.{u1} R _inst_1)] {x : R} {y : R}, (IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarSemigroup.toInvolutiveStar.{u1} R (CommSemigroup.toSemigroup.{u1} R _inst_1) _inst_2)) x) -> (IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarSemigroup.toInvolutiveStar.{u1} R (CommSemigroup.toSemigroup.{u1} R _inst_1) _inst_2)) y) -> (IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarSemigroup.toInvolutiveStar.{u1} R (CommSemigroup.toSemigroup.{u1} R _inst_1) _inst_2)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Semigroup.toMul.{u1} R (CommSemigroup.toSemigroup.{u1} R _inst_1))) x y))
 Case conversion may be inaccurate. Consider using '#align is_self_adjoint.mul IsSelfAdjoint.mulₓ'. -/
 theorem mul {x y : R} (hx : IsSelfAdjoint x) (hy : IsSelfAdjoint y) : IsSelfAdjoint (x * y) := by
   simp only [isSelfAdjoint_iff, star_mul', hx.star_eq, hy.star_eq]
@@ -318,10 +330,16 @@ section Ring
 
 variable [Ring R] [StarRing R]
 
+/- warning: is_self_adjoint_int_cast -> isSelfAdjoint_intCast is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1))] (z : Int), IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1)) _inst_2))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int R (HasLiftT.mk.{1, succ u1} Int R (CoeTCₓ.coe.{1, succ u1} Int R (Int.castCoe.{u1} R (AddGroupWithOne.toHasIntCast.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1)))))) z)
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1))] (z : Int), IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1)) _inst_2))) (Int.cast.{u1} R (Ring.toIntCast.{u1} R _inst_1) z)
+Case conversion may be inaccurate. Consider using '#align is_self_adjoint_int_cast isSelfAdjoint_intCastₓ'. -/
 @[simp]
-theorem isSelfAdjoint_int_cast (z : ℤ) : IsSelfAdjoint (z : R) :=
+theorem isSelfAdjoint_intCast (z : ℤ) : IsSelfAdjoint (z : R) :=
   star_intCast _
-#align is_self_adjoint_int_cast isSelfAdjoint_int_cast
+#align is_self_adjoint_int_cast isSelfAdjoint_intCast
 
 end Ring
 
@@ -333,21 +351,17 @@ variable [DivisionSemiring R] [StarRing R]
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : DivisionSemiring.{u1} R] [_inst_2 : StarRing.{u1} R (Semiring.toNonUnitalSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R _inst_1))] {x : R}, (IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonUnitalSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (Semiring.toNonUnitalSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R _inst_1)) _inst_2))) x) -> (IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonUnitalSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (Semiring.toNonUnitalSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R _inst_1)) _inst_2))) (Inv.inv.{u1} R (DivInvMonoid.toHasInv.{u1} R (GroupWithZero.toDivInvMonoid.{u1} R (DivisionSemiring.toGroupWithZero.{u1} R _inst_1))) x))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1))))] {x : R}, (IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2))) x) -> (IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2))) (Inv.inv.{u1} R (Field.toInv.{u1} R _inst_1) x))
+  forall {R : Type.{u1}} [_inst_1 : DivisionSemiring.{u1} R] [_inst_2 : StarRing.{u1} R (Semiring.toNonUnitalSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R _inst_1))] {x : R}, (IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (Semiring.toNonUnitalSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R _inst_1)) _inst_2))) x) -> (IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (Semiring.toNonUnitalSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R _inst_1)) _inst_2))) (Inv.inv.{u1} R (DivisionSemiring.toInv.{u1} R _inst_1) x))
 Case conversion may be inaccurate. Consider using '#align is_self_adjoint.inv IsSelfAdjoint.invₓ'. -/
 theorem inv {x : R} (hx : IsSelfAdjoint x) : IsSelfAdjoint x⁻¹ := by
   simp only [isSelfAdjoint_iff, star_inv', hx.star_eq]
 #align is_self_adjoint.inv IsSelfAdjoint.inv
 
-/- warning: is_self_adjoint.zpow -> IsSelfAdjoint.zpow is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : DivisionSemiring.{u1} R] [_inst_2 : StarRing.{u1} R (Semiring.toNonUnitalSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R _inst_1))] {x : R}, (IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonUnitalSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (Semiring.toNonUnitalSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R _inst_1)) _inst_2))) x) -> (forall (n : Int), IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonUnitalSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (Semiring.toNonUnitalSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R _inst_1)) _inst_2))) (HPow.hPow.{u1, 0, u1} R Int R (instHPow.{u1, 0} R Int (DivInvMonoid.Pow.{u1} R (GroupWithZero.toDivInvMonoid.{u1} R (DivisionSemiring.toGroupWithZero.{u1} R _inst_1)))) x n))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1))))] {x : R}, (IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2))) x) -> (forall (n : Int), IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2))) (HPow.hPow.{u1, 0, u1} R Int R (instHPow.{u1, 0} R Int (DivInvMonoid.Pow.{u1} R (DivisionRing.toDivInvMonoid.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) x n))
-Case conversion may be inaccurate. Consider using '#align is_self_adjoint.zpow IsSelfAdjoint.zpowₓ'. -/
+#print IsSelfAdjoint.zpow /-
 theorem zpow {x : R} (hx : IsSelfAdjoint x) (n : ℤ) : IsSelfAdjoint (x ^ n) := by
   simp only [isSelfAdjoint_iff, star_zpow₀, hx.star_eq]
 #align is_self_adjoint.zpow IsSelfAdjoint.zpow
+-/
 
 end DivisionSemiring
 
@@ -355,9 +369,15 @@ section DivisionRing
 
 variable [DivisionRing R] [StarRing R]
 
-theorem isSelfAdjoint_rat_cast (x : ℚ) : IsSelfAdjoint (x : R) :=
+/- warning: is_self_adjoint_rat_cast -> isSelfAdjoint_ratCast is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : DivisionRing.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))] (x : Rat), IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) _inst_2))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Rat R (HasLiftT.mk.{1, succ u1} Rat R (CoeTCₓ.coe.{1, succ u1} Rat R (Rat.castCoe.{u1} R (DivisionRing.toHasRatCast.{u1} R _inst_1)))) x)
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : DivisionRing.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))] (x : Rat), IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) _inst_2))) (Rat.cast.{u1} R (DivisionRing.toRatCast.{u1} R _inst_1) x)
+Case conversion may be inaccurate. Consider using '#align is_self_adjoint_rat_cast isSelfAdjoint_ratCastₓ'. -/
+theorem isSelfAdjoint_ratCast (x : ℚ) : IsSelfAdjoint (x : R) :=
   star_ratCast _
-#align is_self_adjoint_rat_cast isSelfAdjoint_rat_cast
+#align is_self_adjoint_rat_cast isSelfAdjoint_ratCast
 
 end DivisionRing
 
@@ -369,7 +389,7 @@ variable [Field R] [StarRing R]
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1))))] {x : R} {y : R}, (IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1))))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2))) x) -> (IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1))))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2))) y) -> (IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1))))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2))) (HDiv.hDiv.{u1, u1, u1} R R R (instHDiv.{u1} R (DivInvMonoid.toHasDiv.{u1} R (DivisionRing.toDivInvMonoid.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) x y))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1))))] {x : R} {y : R}, (IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2))) x) -> (IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2))) y) -> (IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2))) (HDiv.hDiv.{u1, u1, u1} R R R (instHDiv.{u1} R (Field.toDiv.{u1} R _inst_1)) x y))
+  forall {R : Type.{u1}} [_inst_1 : Semifield.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R (Semifield.toCommSemiring.{u1} R _inst_1)))] {x : R} {y : R}, (IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R _inst_1)))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R (Semifield.toCommSemiring.{u1} R _inst_1))) _inst_2))) x) -> (IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R _inst_1)))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R (Semifield.toCommSemiring.{u1} R _inst_1))) _inst_2))) y) -> (IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R _inst_1)))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R (Semifield.toCommSemiring.{u1} R _inst_1))) _inst_2))) (HDiv.hDiv.{u1, u1, u1} R R R (instHDiv.{u1} R (Semifield.toDiv.{u1} R _inst_1)) x y))
 Case conversion may be inaccurate. Consider using '#align is_self_adjoint.div IsSelfAdjoint.divₓ'. -/
 theorem div {x y : R} (hx : IsSelfAdjoint x) (hy : IsSelfAdjoint y) : IsSelfAdjoint (x / y) := by
   simp only [isSelfAdjoint_iff, star_div', hx.star_eq, hy.star_eq]
@@ -385,7 +405,7 @@ variable [Star R] [AddMonoid A] [StarAddMonoid A] [SMul R A] [StarModule R A]
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : Star.{u1} R] [_inst_2 : AddMonoid.{u2} A] [_inst_3 : StarAddMonoid.{u2} A _inst_2] [_inst_4 : SMul.{u1, u2} R A] [_inst_5 : StarModule.{u1, u2} R A _inst_1 (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A _inst_2 _inst_3)) _inst_4] {r : R}, (IsSelfAdjoint.{u1} R _inst_1 r) -> (forall {x : A}, (IsSelfAdjoint.{u2} A (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A _inst_2 _inst_3)) x) -> (IsSelfAdjoint.{u2} A (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A _inst_2 _inst_3)) (SMul.smul.{u1, u2} R A _inst_4 r x)))
 but is expected to have type
-  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : Star.{u2} R] [_inst_2 : TrivialStar.{u2} R _inst_1] [_inst_3 : AddGroup.{u1} A] [_inst_4 : StarAddMonoid.{u1} A (SubNegMonoid.toAddMonoid.{u1} A (AddGroup.toSubNegMonoid.{u1} A _inst_3))] [_inst_5 : SMul.{u2, u1} R A] [r : StarModule.{u2, u1} R A _inst_1 (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (SubNegMonoid.toAddMonoid.{u1} A (AddGroup.toSubNegMonoid.{u1} A _inst_3)) _inst_4)) _inst_5] (hr : R) {x : A}, (IsSelfAdjoint.{u1} A (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (SubNegMonoid.toAddMonoid.{u1} A (AddGroup.toSubNegMonoid.{u1} A _inst_3)) _inst_4)) x) -> (IsSelfAdjoint.{u1} A (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (SubNegMonoid.toAddMonoid.{u1} A (AddGroup.toSubNegMonoid.{u1} A _inst_3)) _inst_4)) (HSMul.hSMul.{u2, u1, u1} R A A (instHSMul.{u2, u1} R A _inst_5) hr x))
+  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : Star.{u2} R] [_inst_2 : AddMonoid.{u1} A] [_inst_3 : StarAddMonoid.{u1} A _inst_2] [_inst_4 : SMul.{u2, u1} R A] [_inst_5 : StarModule.{u2, u1} R A _inst_1 (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A _inst_2 _inst_3)) _inst_4] {r : R}, (IsSelfAdjoint.{u2} R _inst_1 r) -> (forall {x : A}, (IsSelfAdjoint.{u1} A (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A _inst_2 _inst_3)) x) -> (IsSelfAdjoint.{u1} A (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A _inst_2 _inst_3)) (HSMul.hSMul.{u2, u1, u1} R A A (instHSMul.{u2, u1} R A _inst_4) r x)))
 Case conversion may be inaccurate. Consider using '#align is_self_adjoint.smul IsSelfAdjoint.smulₓ'. -/
 theorem smul {r : R} (hr : IsSelfAdjoint r) {x : A} (hx : IsSelfAdjoint x) :
     IsSelfAdjoint (r • x) := by simp only [isSelfAdjoint_iff, star_smul, hr.star_eq, hx.star_eq]
@@ -474,10 +494,10 @@ instance [Nontrivial R] : Nontrivial (selfAdjoint R) :=
   ⟨⟨0, 1, Subtype.ne_of_val_ne zero_ne_one⟩⟩
 
 instance : NatCast (selfAdjoint R) :=
-  ⟨fun n => ⟨n, isSelfAdjoint_nat_cast _⟩⟩
+  ⟨fun n => ⟨n, isSelfAdjoint_natCast _⟩⟩
 
 instance : IntCast (selfAdjoint R) :=
-  ⟨fun n => ⟨n, isSelfAdjoint_int_cast _⟩⟩
+  ⟨fun n => ⟨n, isSelfAdjoint_intCast _⟩⟩
 
 instance : Pow (selfAdjoint R) ℕ :=
   ⟨fun x n => ⟨(x : R) ^ n, x.Prop.pow n⟩⟩
@@ -571,7 +591,7 @@ theorem val_zpow (x : selfAdjoint R) (z : ℤ) : ↑(x ^ z) = (x : R) ^ z :=
 #align self_adjoint.coe_zpow selfAdjoint.val_zpow
 
 instance : HasRatCast (selfAdjoint R) :=
-  ⟨fun n => ⟨n, isSelfAdjoint_rat_cast n⟩⟩
+  ⟨fun n => ⟨n, isSelfAdjoint_ratCast n⟩⟩
 
 /- warning: self_adjoint.coe_rat_cast -> selfAdjoint.val_ratCast is a dubious translation:
 lean 3 declaration is
@@ -592,7 +612,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align self_adjoint.has_qsmul selfAdjoint.instQSMulₓ'. -/
 instance instQSMul : SMul ℚ (selfAdjoint R) :=
   ⟨fun a x =>
-    ⟨a • x, by rw [Rat.smul_def] <;> exact IsSelfAdjoint.mul (isSelfAdjoint_rat_cast a) x.prop⟩⟩
+    ⟨a • x, by rw [Rat.smul_def] <;> exact IsSelfAdjoint.mul (isSelfAdjoint_ratCast a) x.prop⟩⟩
 #align self_adjoint.has_qsmul selfAdjoint.instQSMul
 
 /- warning: self_adjoint.coe_rat_smul -> selfAdjoint.val_rat_smul is a dubious translation:
@@ -776,6 +796,12 @@ end SMul
 
 end skewAdjoint
 
+/- warning: is_self_adjoint.smul_mem_skew_adjoint -> IsSelfAdjoint.smul_mem_skewAdjoint is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} A] [_inst_3 : Module.{u1, u2} R A (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} A _inst_2)] [_inst_4 : StarAddMonoid.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1))))] [_inst_5 : StarAddMonoid.{u2} A (SubNegMonoid.toAddMonoid.{u2} A (AddGroup.toSubNegMonoid.{u2} A (AddCommGroup.toAddGroup.{u2} A _inst_2)))] [_inst_6 : StarModule.{u1, u2} R A (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1)))) _inst_4)) (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (SubNegMonoid.toAddMonoid.{u2} A (AddGroup.toSubNegMonoid.{u2} A (AddCommGroup.toAddGroup.{u2} A _inst_2))) _inst_5)) (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (AddCommGroup.toAddCommMonoid.{u2} A _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (AddCommGroup.toAddCommMonoid.{u2} A _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (AddCommGroup.toAddCommMonoid.{u2} A _inst_2)))) (Module.toMulActionWithZero.{u1, u2} R A (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} A _inst_2) _inst_3))))] {r : R}, (Membership.Mem.{u1, u1} R (AddSubgroup.{u1} R (AddCommGroup.toAddGroup.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))) (SetLike.hasMem.{u1, u1} (AddSubgroup.{u1} R (AddCommGroup.toAddGroup.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))) R (AddSubgroup.setLike.{u1} R (AddCommGroup.toAddGroup.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))))) r (skewAdjoint.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) _inst_4)) -> (forall {a : A}, (IsSelfAdjoint.{u2} A (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (SubNegMonoid.toAddMonoid.{u2} A (AddGroup.toSubNegMonoid.{u2} A (AddCommGroup.toAddGroup.{u2} A _inst_2))) _inst_5)) a) -> (Membership.Mem.{u2, u2} A (AddSubgroup.{u2} A (AddCommGroup.toAddGroup.{u2} A _inst_2)) (SetLike.hasMem.{u2, u2} (AddSubgroup.{u2} A (AddCommGroup.toAddGroup.{u2} A _inst_2)) A (AddSubgroup.setLike.{u2} A (AddCommGroup.toAddGroup.{u2} A _inst_2))) (SMul.smul.{u1, u2} R A (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (AddCommGroup.toAddCommMonoid.{u2} A _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (AddCommGroup.toAddCommMonoid.{u2} A _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (AddCommGroup.toAddCommMonoid.{u2} A _inst_2)))) (Module.toMulActionWithZero.{u1, u2} R A (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} A _inst_2) _inst_3)))) r a) (skewAdjoint.{u2} A _inst_2 _inst_5)))
+but is expected to have type
+  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} A] [_inst_3 : Module.{u2, u1} R A (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} A _inst_2)] [_inst_4 : StarAddMonoid.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (Ring.toAddGroupWithOne.{u2} R _inst_1)))] [_inst_5 : StarAddMonoid.{u1} A (SubNegMonoid.toAddMonoid.{u1} A (AddGroup.toSubNegMonoid.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_2)))] [_inst_6 : StarModule.{u2, u1} R A (InvolutiveStar.toStar.{u2} R (StarAddMonoid.toInvolutiveStar.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (Ring.toAddGroupWithOne.{u2} R _inst_1))) _inst_4)) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (SubNegMonoid.toAddMonoid.{u1} A (AddGroup.toSubNegMonoid.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_2))) _inst_5)) (SMulZeroClass.toSMul.{u2, u1} R A (NegZeroClass.toZero.{u1} A (SubNegZeroMonoid.toNegZeroClass.{u1} A (SubtractionMonoid.toSubNegZeroMonoid.{u1} A (SubtractionCommMonoid.toSubtractionMonoid.{u1} A (AddCommGroup.toDivisionAddCommMonoid.{u1} A _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} R A (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (NegZeroClass.toZero.{u1} A (SubNegZeroMonoid.toNegZeroClass.{u1} A (SubtractionMonoid.toSubNegZeroMonoid.{u1} A (SubtractionCommMonoid.toSubtractionMonoid.{u1} A (AddCommGroup.toDivisionAddCommMonoid.{u1} A _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} R A (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (NegZeroClass.toZero.{u1} A (SubNegZeroMonoid.toNegZeroClass.{u1} A (SubtractionMonoid.toSubNegZeroMonoid.{u1} A (SubtractionCommMonoid.toSubtractionMonoid.{u1} A (AddCommGroup.toDivisionAddCommMonoid.{u1} A _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R A (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} A _inst_2) _inst_3))))] {r : R}, (Membership.mem.{u2, u2} R (AddSubgroup.{u2} R (AddCommGroup.toAddGroup.{u2} R (Ring.toAddCommGroup.{u2} R _inst_1))) (SetLike.instMembership.{u2, u2} (AddSubgroup.{u2} R (AddCommGroup.toAddGroup.{u2} R (Ring.toAddCommGroup.{u2} R _inst_1))) R (AddSubgroup.instSetLikeAddSubgroup.{u2} R (AddCommGroup.toAddGroup.{u2} R (Ring.toAddCommGroup.{u2} R _inst_1)))) r (skewAdjoint.{u2} R (Ring.toAddCommGroup.{u2} R _inst_1) _inst_4)) -> (forall {a : A}, (IsSelfAdjoint.{u1} A (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (SubNegMonoid.toAddMonoid.{u1} A (AddGroup.toSubNegMonoid.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_2))) _inst_5)) a) -> (Membership.mem.{u1, u1} A (AddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_2)) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_2)) A (AddSubgroup.instSetLikeAddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_2))) (HSMul.hSMul.{u2, u1, u1} R A A (instHSMul.{u2, u1} R A (SMulZeroClass.toSMul.{u2, u1} R A (NegZeroClass.toZero.{u1} A (SubNegZeroMonoid.toNegZeroClass.{u1} A (SubtractionMonoid.toSubNegZeroMonoid.{u1} A (SubtractionCommMonoid.toSubtractionMonoid.{u1} A (AddCommGroup.toDivisionAddCommMonoid.{u1} A _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} R A (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (NegZeroClass.toZero.{u1} A (SubNegZeroMonoid.toNegZeroClass.{u1} A (SubtractionMonoid.toSubNegZeroMonoid.{u1} A (SubtractionCommMonoid.toSubtractionMonoid.{u1} A (AddCommGroup.toDivisionAddCommMonoid.{u1} A _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} R A (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (NegZeroClass.toZero.{u1} A (SubNegZeroMonoid.toNegZeroClass.{u1} A (SubtractionMonoid.toSubNegZeroMonoid.{u1} A (SubtractionCommMonoid.toSubtractionMonoid.{u1} A (AddCommGroup.toDivisionAddCommMonoid.{u1} A _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R A (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} A _inst_2) _inst_3))))) r a) (skewAdjoint.{u1} A _inst_2 _inst_5)))
+Case conversion may be inaccurate. Consider using '#align is_self_adjoint.smul_mem_skew_adjoint IsSelfAdjoint.smul_mem_skewAdjointₓ'. -/
 /-- Scalar multiplication of a self-adjoint element by a skew-adjoint element produces a
 skew-adjoint element. -/
 theorem IsSelfAdjoint.smul_mem_skewAdjoint [Ring R] [AddCommGroup A] [Module R A] [StarAddMonoid R]
@@ -784,6 +810,12 @@ theorem IsSelfAdjoint.smul_mem_skewAdjoint [Ring R] [AddCommGroup A] [Module R A
   (star_smul _ _).trans <| (congr_arg₂ _ hr ha).trans <| neg_smul _ _
 #align is_self_adjoint.smul_mem_skew_adjoint IsSelfAdjoint.smul_mem_skewAdjoint
 
+/- warning: is_self_adjoint_smul_of_mem_skew_adjoint -> isSelfAdjoint_smul_of_mem_skewAdjoint is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} A] [_inst_3 : Module.{u1, u2} R A (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} A _inst_2)] [_inst_4 : StarAddMonoid.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1))))] [_inst_5 : StarAddMonoid.{u2} A (SubNegMonoid.toAddMonoid.{u2} A (AddGroup.toSubNegMonoid.{u2} A (AddCommGroup.toAddGroup.{u2} A _inst_2)))] [_inst_6 : StarModule.{u1, u2} R A (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1)))) _inst_4)) (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (SubNegMonoid.toAddMonoid.{u2} A (AddGroup.toSubNegMonoid.{u2} A (AddCommGroup.toAddGroup.{u2} A _inst_2))) _inst_5)) (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (AddCommGroup.toAddCommMonoid.{u2} A _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (AddCommGroup.toAddCommMonoid.{u2} A _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (AddCommGroup.toAddCommMonoid.{u2} A _inst_2)))) (Module.toMulActionWithZero.{u1, u2} R A (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} A _inst_2) _inst_3))))] {r : R}, (Membership.Mem.{u1, u1} R (AddSubgroup.{u1} R (AddCommGroup.toAddGroup.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))) (SetLike.hasMem.{u1, u1} (AddSubgroup.{u1} R (AddCommGroup.toAddGroup.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))) R (AddSubgroup.setLike.{u1} R (AddCommGroup.toAddGroup.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))))) r (skewAdjoint.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) _inst_4)) -> (forall {a : A}, (Membership.Mem.{u2, u2} A (AddSubgroup.{u2} A (AddCommGroup.toAddGroup.{u2} A _inst_2)) (SetLike.hasMem.{u2, u2} (AddSubgroup.{u2} A (AddCommGroup.toAddGroup.{u2} A _inst_2)) A (AddSubgroup.setLike.{u2} A (AddCommGroup.toAddGroup.{u2} A _inst_2))) a (skewAdjoint.{u2} A _inst_2 _inst_5)) -> (IsSelfAdjoint.{u2} A (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (SubNegMonoid.toAddMonoid.{u2} A (AddGroup.toSubNegMonoid.{u2} A (AddCommGroup.toAddGroup.{u2} A _inst_2))) _inst_5)) (SMul.smul.{u1, u2} R A (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (AddCommGroup.toAddCommMonoid.{u2} A _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (AddCommGroup.toAddCommMonoid.{u2} A _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (AddCommGroup.toAddCommMonoid.{u2} A _inst_2)))) (Module.toMulActionWithZero.{u1, u2} R A (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} A _inst_2) _inst_3)))) r a)))
+but is expected to have type
+  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} A] [_inst_3 : Module.{u2, u1} R A (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} A _inst_2)] [_inst_4 : StarAddMonoid.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (Ring.toAddGroupWithOne.{u2} R _inst_1)))] [_inst_5 : StarAddMonoid.{u1} A (SubNegMonoid.toAddMonoid.{u1} A (AddGroup.toSubNegMonoid.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_2)))] [_inst_6 : StarModule.{u2, u1} R A (InvolutiveStar.toStar.{u2} R (StarAddMonoid.toInvolutiveStar.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (Ring.toAddGroupWithOne.{u2} R _inst_1))) _inst_4)) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (SubNegMonoid.toAddMonoid.{u1} A (AddGroup.toSubNegMonoid.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_2))) _inst_5)) (SMulZeroClass.toSMul.{u2, u1} R A (NegZeroClass.toZero.{u1} A (SubNegZeroMonoid.toNegZeroClass.{u1} A (SubtractionMonoid.toSubNegZeroMonoid.{u1} A (SubtractionCommMonoid.toSubtractionMonoid.{u1} A (AddCommGroup.toDivisionAddCommMonoid.{u1} A _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} R A (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (NegZeroClass.toZero.{u1} A (SubNegZeroMonoid.toNegZeroClass.{u1} A (SubtractionMonoid.toSubNegZeroMonoid.{u1} A (SubtractionCommMonoid.toSubtractionMonoid.{u1} A (AddCommGroup.toDivisionAddCommMonoid.{u1} A _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} R A (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (NegZeroClass.toZero.{u1} A (SubNegZeroMonoid.toNegZeroClass.{u1} A (SubtractionMonoid.toSubNegZeroMonoid.{u1} A (SubtractionCommMonoid.toSubtractionMonoid.{u1} A (AddCommGroup.toDivisionAddCommMonoid.{u1} A _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R A (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} A _inst_2) _inst_3))))] {r : R}, (Membership.mem.{u2, u2} R (AddSubgroup.{u2} R (AddCommGroup.toAddGroup.{u2} R (Ring.toAddCommGroup.{u2} R _inst_1))) (SetLike.instMembership.{u2, u2} (AddSubgroup.{u2} R (AddCommGroup.toAddGroup.{u2} R (Ring.toAddCommGroup.{u2} R _inst_1))) R (AddSubgroup.instSetLikeAddSubgroup.{u2} R (AddCommGroup.toAddGroup.{u2} R (Ring.toAddCommGroup.{u2} R _inst_1)))) r (skewAdjoint.{u2} R (Ring.toAddCommGroup.{u2} R _inst_1) _inst_4)) -> (forall {a : A}, (Membership.mem.{u1, u1} A (AddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_2)) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_2)) A (AddSubgroup.instSetLikeAddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_2))) a (skewAdjoint.{u1} A _inst_2 _inst_5)) -> (IsSelfAdjoint.{u1} A (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (SubNegMonoid.toAddMonoid.{u1} A (AddGroup.toSubNegMonoid.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_2))) _inst_5)) (HSMul.hSMul.{u2, u1, u1} R A A (instHSMul.{u2, u1} R A (SMulZeroClass.toSMul.{u2, u1} R A (NegZeroClass.toZero.{u1} A (SubNegZeroMonoid.toNegZeroClass.{u1} A (SubtractionMonoid.toSubNegZeroMonoid.{u1} A (SubtractionCommMonoid.toSubtractionMonoid.{u1} A (AddCommGroup.toDivisionAddCommMonoid.{u1} A _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} R A (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (NegZeroClass.toZero.{u1} A (SubNegZeroMonoid.toNegZeroClass.{u1} A (SubtractionMonoid.toSubNegZeroMonoid.{u1} A (SubtractionCommMonoid.toSubtractionMonoid.{u1} A (AddCommGroup.toDivisionAddCommMonoid.{u1} A _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} R A (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (NegZeroClass.toZero.{u1} A (SubNegZeroMonoid.toNegZeroClass.{u1} A (SubtractionMonoid.toSubNegZeroMonoid.{u1} A (SubtractionCommMonoid.toSubtractionMonoid.{u1} A (AddCommGroup.toDivisionAddCommMonoid.{u1} A _inst_2))))) (Module.toMulActionWithZero.{u2, u1} R A (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} A _inst_2) _inst_3))))) r a)))
+Case conversion may be inaccurate. Consider using '#align is_self_adjoint_smul_of_mem_skew_adjoint isSelfAdjoint_smul_of_mem_skewAdjointₓ'. -/
 /-- Scalar multiplication of a skew-adjoint element by a skew-adjoint element produces a
 self-adjoint element. -/
 theorem isSelfAdjoint_smul_of_mem_skewAdjoint [Ring R] [AddCommGroup A] [Module R A]

9abfa6f0

bump to nightly-2023-03-28-22

mathlib commit https://github.com/leanprover-community/mathlib/commit/728baa2f54e6062c5879a3e397ac6bac323e506f

c7ebe29d

Diff

@@ -123,7 +123,7 @@ theorem mul_star_self [Semigroup R] [StarSemigroup R] (x : R) : IsSelfAdjoint (x
 lean 3 declaration is
   forall {F : Type.{u1}} {R : Type.{u2}} {S : Type.{u3}} [_inst_1 : Star.{u2} R] [_inst_2 : Star.{u3} S] [_inst_3 : StarHomClass.{u1, u2, u3} F R S _inst_1 _inst_2] {x : R}, (IsSelfAdjoint.{u2} R _inst_1 x) -> (forall (f : F), IsSelfAdjoint.{u3} S _inst_2 (coeFn.{succ u1, max (succ u2) (succ u3)} F (fun (_x : F) => R -> S) (FunLike.hasCoeToFun.{succ u1, succ u2, succ u3} F R (fun (_x : R) => S) (StarHomClass.toFunLike.{u1, u2, u3} F R S _inst_1 _inst_2 _inst_3)) f x))
 but is expected to have type
-  forall {F : Type.{u3}} {R : Type.{u2}} {S : Type.{u1}} [_inst_1 : Star.{u2} R] [_inst_2 : Star.{u1} S] [_inst_3 : StarHomClass.{u3, u2, u1} F R S _inst_1 _inst_2] {x : R}, (IsSelfAdjoint.{u2} R _inst_1 x) -> (forall (f : F), IsSelfAdjoint.{u1} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3024 : R) => S) x) _inst_2 (FunLike.coe.{succ u3, succ u2, succ u1} F R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3024 : R) => S) _x) (StarHomClass.toFunLike.{u3, u2, u1} F R S _inst_1 _inst_2 _inst_3) f x))
+  forall {F : Type.{u3}} {R : Type.{u2}} {S : Type.{u1}} [_inst_1 : Star.{u2} R] [_inst_2 : Star.{u1} S] [_inst_3 : StarHomClass.{u3, u2, u1} F R S _inst_1 _inst_2] {x : R}, (IsSelfAdjoint.{u2} R _inst_1 x) -> (forall (f : F), IsSelfAdjoint.{u1} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3050 : R) => S) x) _inst_2 (FunLike.coe.{succ u3, succ u2, succ u1} F R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3050 : R) => S) _x) (StarHomClass.toFunLike.{u3, u2, u1} F R S _inst_1 _inst_2 _inst_3) f x))
 Case conversion may be inaccurate. Consider using '#align is_self_adjoint.star_hom_apply IsSelfAdjoint.starHom_applyₓ'. -/
 /-- Functions in a `star_hom_class` preserve self-adjoint elements. -/
 theorem starHom_apply {F R S : Type _} [Star R] [Star S] [StarHomClass F R S] {x : R}

9abfa6f0

bump to nightly-2023-03-27-02

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

0e4ebd8c

Diff

@@ -484,7 +484,7 @@ instance : Pow (selfAdjoint R) ℕ :=
 
 /- warning: self_adjoint.coe_pow -> selfAdjoint.val_pow is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1))] (x : coeSort.{succ u1, succ (succ u1)} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R (AddSubgroup.setLike.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))) (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1)) _inst_2))) (n : Nat), Eq.{succ u1} R ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, 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(SetLike.hasCoeToSort.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R (AddSubgroup.setLike.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))) (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1)) _inst_2))) R (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R (AddSubgroup.setLike.{u1} R 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 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1))] (x : Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1)))) x (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1)) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1)) _inst_2)))) (n : Nat), Eq.{succ u1} R (Subtype.val.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x (SetLike.coe.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1))) (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1)) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1)) _inst_2)))) (HPow.hPow.{u1, 0, u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1)))) x (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1)) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1)) _inst_2)))) Nat (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1)))) x (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1)) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1)) _inst_2)))) (instHPow.{u1, 0} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1)))) x (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1)) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1)) _inst_2)))) Nat (selfAdjoint.instPowSubtypeMemAddSubgroupToAddGroupToAddGroupWithOneInstMembershipInstSetLikeAddSubgroupSelfAdjointToStarAddMonoidToNonUnitalSemiringToNonUnitalRingNat.{u1} R _inst_1 _inst_2)) x n)) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (Subtype.val.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x (SetLike.coe.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1))) (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1)) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1)) _inst_2)))) x) n)
 Case conversion may be inaccurate. Consider using '#align self_adjoint.coe_pow selfAdjoint.val_powₓ'. -/
@@ -535,7 +535,7 @@ instance : Inv (selfAdjoint R) where inv x := ⟨x.val⁻¹, x.Prop.inv⟩
 
 /- warning: self_adjoint.coe_inv -> selfAdjoint.val_inv is a dubious translation:
 lean 3 declaration is
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R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2))) R (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) R (AddSubgroup.setLike.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))))) (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} 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(selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2))))))) x))
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1))))] (x : Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) x (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2)))), Eq.{succ u1} R (Subtype.val.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x (SetLike.coe.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2)))) (Inv.inv.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) x (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2)))) (selfAdjoint.instInvSubtypeMemAddSubgroupToAddGroupToAddGroupWithOneToRingToDivisionRingInstMembershipInstSetLikeAddSubgroupSelfAdjointToStarAddMonoidToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingToCommRing.{u1} R _inst_1 _inst_2) x)) (Inv.inv.{u1} R (Field.toInv.{u1} R _inst_1) (Subtype.val.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x (SetLike.coe.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2)))) x))
 Case conversion may be inaccurate. Consider using '#align self_adjoint.coe_inv selfAdjoint.val_invₓ'. -/
@@ -548,7 +548,7 @@ instance : Div (selfAdjoint R) where div x y := ⟨x / y, x.Prop.div y.Prop⟩
 
 /- warning: self_adjoint.coe_div -> selfAdjoint.val_div is a dubious translation:
 lean 3 declaration is
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 but is expected to have type
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_inst_2)))) y))
 Case conversion may be inaccurate. Consider using '#align self_adjoint.coe_div selfAdjoint.val_divₓ'. -/
@@ -561,7 +561,7 @@ instance : Pow (selfAdjoint R) ℤ where pow x z := ⟨x ^ z, x.Prop.zpow z⟩
 
 /- warning: self_adjoint.coe_zpow -> selfAdjoint.val_zpow is a dubious translation:
 lean 3 declaration is
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(Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2))) R (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) R (AddSubgroup.setLike.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))))) (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2))) R (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) R (AddSubgroup.setLike.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))))) (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2))) R (coeSubtype.{succ u1} R (fun (x : R) => Membership.Mem.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (SetLike.hasMem.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) R (AddSubgroup.setLike.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))))) x (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2))))))) x) z)
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1))))] (x : Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) x (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2)))) (z : Int), Eq.{succ u1} R (Subtype.val.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x (SetLike.coe.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2)))) (HPow.hPow.{u1, 0, u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) x (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2)))) Int (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) x (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2)))) (instHPow.{u1, 0} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) x (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2)))) Int (selfAdjoint.instPowSubtypeMemAddSubgroupToAddGroupToAddGroupWithOneToRingToDivisionRingInstMembershipInstSetLikeAddSubgroupSelfAdjointToStarAddMonoidToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingToCommRingInt.{u1} R _inst_1 _inst_2)) x z)) (HPow.hPow.{u1, 0, u1} R Int R (instHPow.{u1, 0} R Int (DivInvMonoid.Pow.{u1} R (DivisionRing.toDivInvMonoid.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (Subtype.val.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x (SetLike.coe.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2)))) x) z)
 Case conversion may be inaccurate. Consider using '#align self_adjoint.coe_zpow selfAdjoint.val_zpowₓ'. -/
@@ -575,7 +575,7 @@ instance : HasRatCast (selfAdjoint R) :=
 
 /- warning: self_adjoint.coe_rat_cast -> selfAdjoint.val_ratCast is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1))))] (x : Rat), Eq.{succ u1} R ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) R (AddSubgroup.setLike.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))))) (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2))) R (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) R (AddSubgroup.setLike.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))))) (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2))) R (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R 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(NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) R (AddSubgroup.setLike.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))))) (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2))) R (coeSubtype.{succ u1} R (fun (x : R) => Membership.Mem.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (SetLike.hasMem.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) R (AddSubgroup.setLike.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))))) x (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2))))))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Rat (coeSort.{succ u1, succ (succ u1)} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R 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+  forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1))))] (x : Rat), Eq.{succ u1} R ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) R (AddSubgroup.setLike.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R 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(AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) R (AddSubgroup.setLike.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))))) (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2))) R (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R 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(NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2))))))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Rat (coeSort.{succ u1, succ (succ u1)} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) R (AddSubgroup.setLike.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))))) (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2))) (HasLiftT.mk.{1, succ u1} Rat (coeSort.{succ u1, succ (succ u1)} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) R (AddSubgroup.setLike.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R 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(AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) R (AddSubgroup.setLike.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))))) (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2))) (selfAdjoint.hasRatCast.{u1} R _inst_1 _inst_2)))) x)) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Rat R (HasLiftT.mk.{1, succ u1} Rat R (CoeTCₓ.coe.{1, succ u1} Rat R (Rat.castCoe.{u1} R (DivisionRing.toHasRatCast.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) x)
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1))))] (x : Rat), Eq.{succ u1} R (Subtype.val.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x (SetLike.coe.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2)))) (Rat.cast.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) x (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2)))) (selfAdjoint.instRatCastSubtypeMemAddSubgroupToAddGroupToAddGroupWithOneToRingToDivisionRingInstMembershipInstSetLikeAddSubgroupSelfAdjointToStarAddMonoidToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingToCommRing.{u1} R _inst_1 _inst_2) x)) (Rat.cast.{u1} R (Field.toRatCast.{u1} R _inst_1) x)
 Case conversion may be inaccurate. Consider using '#align self_adjoint.coe_rat_cast selfAdjoint.val_ratCastₓ'. -/
@@ -586,7 +586,7 @@ theorem val_ratCast (x : ℚ) : ↑(x : selfAdjoint R) = (x : R) :=
 
 /- warning: self_adjoint.has_qsmul -> selfAdjoint.instQSMul is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1))))], SMul.{0, u1} Rat (coeSort.{succ u1, succ (succ u1)} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) R (AddSubgroup.setLike.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))))) (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2)))
+  forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1))))], SMul.{0, u1} Rat (coeSort.{succ u1, succ (succ u1)} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) R (AddSubgroup.setLike.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))))) (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2)))
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1))))], SMul.{0, u1} Rat (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) x (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2))))
 Case conversion may be inaccurate. Consider using '#align self_adjoint.has_qsmul selfAdjoint.instQSMulₓ'. -/
@@ -597,7 +597,7 @@ instance instQSMul : SMul ℚ (selfAdjoint R) :=
 
 /- warning: self_adjoint.coe_rat_smul -> selfAdjoint.val_rat_smul is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1))))] (x : coeSort.{succ u1, succ (succ u1)} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) R (AddSubgroup.setLike.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))))) (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2))) (a : Rat), Eq.{succ u1} R ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) R (AddSubgroup.setLike.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))))) (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2))) R (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) R (AddSubgroup.setLike.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))))) (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2))) R (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) R (AddSubgroup.setLike.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))))) (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2))) R (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) R (AddSubgroup.setLike.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))))) (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2))) R (coeSubtype.{succ u1} R (fun (x : R) => Membership.Mem.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (SetLike.hasMem.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) R (AddSubgroup.setLike.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))))) x (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2))))))) (SMul.smul.{0, u1} Rat (coeSort.{succ u1, succ (succ u1)} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) R (AddSubgroup.setLike.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))))) (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2))) (selfAdjoint.instQSMul.{u1} R _inst_1 _inst_2) a x)) (SMul.smul.{0, u1} Rat R (SMulZeroClass.toHasSmul.{0, u1} Rat R (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))))) (DistribSMul.toSmulZeroClass.{0, u1} Rat R (AddMonoid.toAddZeroClass.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))))) (Rat.distribSMul.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) a ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R 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 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align self_adjoint.coe_rat_smul selfAdjoint.val_rat_smulₓ'. -/

9abfa6f0

bump to nightly-2023-03-24-22

mathlib commit https://github.com/leanprover-community/mathlib/commit/b19481deb571022990f1baa9cbf9172e6757a479

6eace303

Diff

@@ -463,16 +463,12 @@ variable [Ring R] [StarRing R]
 instance : One (selfAdjoint R) :=
   ⟨⟨1, isSelfAdjoint_one R⟩⟩
 
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(NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) R (AddSubgroup.setLike.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))) (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1)) _inst_2))) (selfAdjoint.hasOne.{u1} R _inst_1 _inst_2))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))))))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1))], Eq.{succ u1} R (Subtype.val.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x (SetLike.coe.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1))) (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1)) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1)) _inst_2)))) (OfNat.ofNat.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1)))) x (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1)) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1)) _inst_2)))) 1 (One.toOfNat1.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1)))) x (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1)) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1)) _inst_2)))) (selfAdjoint.instOneSubtypeMemAddSubgroupToAddGroupToAddGroupWithOneInstMembershipInstSetLikeAddSubgroupSelfAdjointToStarAddMonoidToNonUnitalSemiringToNonUnitalRing.{u1} R _inst_1 _inst_2)))) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (NonAssocRing.toOne.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))
-Case conversion may be inaccurate. Consider using '#align self_adjoint.coe_one selfAdjoint.val_oneₓ'. -/
+#print selfAdjoint.val_one /-
 @[simp, norm_cast]
 theorem val_one : ↑(1 : selfAdjoint R) = (1 : R) :=
   rfl
 #align self_adjoint.coe_one selfAdjoint.val_one
+-/
 
 instance [Nontrivial R] : Nontrivial (selfAdjoint R) :=
   ⟨⟨0, 1, Subtype.ne_of_val_ne zero_ne_one⟩⟩

9abfa6f0

bump to nightly-2023-03-21-02

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

c67df486

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Frédéric Dupuis
 
 ! This file was ported from Lean 3 source module algebra.star.self_adjoint
-! leanprover-community/mathlib commit 30413fc89f202a090a54d78e540963ed3de0056e
+! leanprover-community/mathlib commit 9abfa6f0727d5adc99067e325e15d1a9de17fd8e
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -197,6 +197,20 @@ theorem sub {x y : R} (hx : IsSelfAdjoint x) (hy : IsSelfAdjoint y) : IsSelfAdjo
 
 end AddGroup
 
+section AddCommMonoid
+
+variable [AddCommMonoid R] [StarAddMonoid R]
+
+theorem isSelfAdjoint_add_star_self (x : R) : IsSelfAdjoint (x + star x) := by
+  simp only [isSelfAdjoint_iff, add_comm, star_add, star_star]
+#align is_self_adjoint_add_star_self isSelfAdjoint_add_star_self
+
+theorem isSelfAdjoint_star_add_self (x : R) : IsSelfAdjoint (star x + x) := by
+  simp only [isSelfAdjoint_iff, add_comm, star_add, star_star]
+#align is_self_adjoint_star_add_self isSelfAdjoint_star_add_self
+
+end AddCommMonoid
+
 section Semigroup
 
 variable [Semigroup R] [StarSemigroup R]

30413fc8

bump to nightly-2023-03-18-02

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

24261a71

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Frédéric Dupuis
 
 ! This file was ported from Lean 3 source module algebra.star.self_adjoint
-! leanprover-community/mathlib commit 1e3201306d4d9eb1fd54c60d7c4510ad5126f6f9
+! leanprover-community/mathlib commit 30413fc89f202a090a54d78e540963ed3de0056e
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -311,13 +311,13 @@ theorem isSelfAdjoint_int_cast (z : ℤ) : IsSelfAdjoint (z : R) :=
 
 end Ring
 
-section DivisionRing
+section DivisionSemiring
 
-variable [DivisionRing R] [StarRing R]
+variable [DivisionSemiring R] [StarRing R]
 
 /- warning: is_self_adjoint.inv -> IsSelfAdjoint.inv is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : DivisionRing.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))] {x : R}, (IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) _inst_2))) x) -> (IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) _inst_2))) (Inv.inv.{u1} R (DivInvMonoid.toHasInv.{u1} R (DivisionRing.toDivInvMonoid.{u1} R _inst_1)) x))
+  forall {R : Type.{u1}} [_inst_1 : DivisionSemiring.{u1} R] [_inst_2 : StarRing.{u1} R (Semiring.toNonUnitalSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R _inst_1))] {x : R}, (IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonUnitalSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (Semiring.toNonUnitalSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R _inst_1)) _inst_2))) x) -> (IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonUnitalSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (Semiring.toNonUnitalSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R _inst_1)) _inst_2))) (Inv.inv.{u1} R (DivInvMonoid.toHasInv.{u1} R (GroupWithZero.toDivInvMonoid.{u1} R (DivisionSemiring.toGroupWithZero.{u1} R _inst_1))) x))
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1))))] {x : R}, (IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2))) x) -> (IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2))) (Inv.inv.{u1} R (Field.toInv.{u1} R _inst_1) x))
 Case conversion may be inaccurate. Consider using '#align is_self_adjoint.inv IsSelfAdjoint.invₓ'. -/
@@ -327,7 +327,7 @@ theorem inv {x : R} (hx : IsSelfAdjoint x) : IsSelfAdjoint x⁻¹ := by
 
 /- warning: is_self_adjoint.zpow -> IsSelfAdjoint.zpow is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : DivisionRing.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))] {x : R}, (IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) _inst_2))) x) -> (forall (n : Int), IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) _inst_2))) (HPow.hPow.{u1, 0, u1} R Int R (instHPow.{u1, 0} R Int (DivInvMonoid.Pow.{u1} R (DivisionRing.toDivInvMonoid.{u1} R _inst_1))) x n))
+  forall {R : Type.{u1}} [_inst_1 : DivisionSemiring.{u1} R] [_inst_2 : StarRing.{u1} R (Semiring.toNonUnitalSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R _inst_1))] {x : R}, (IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonUnitalSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (Semiring.toNonUnitalSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R _inst_1)) _inst_2))) x) -> (forall (n : Int), IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonUnitalSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (Semiring.toNonUnitalSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R _inst_1)) _inst_2))) (HPow.hPow.{u1, 0, u1} R Int R (instHPow.{u1, 0} R Int (DivInvMonoid.Pow.{u1} R (GroupWithZero.toDivInvMonoid.{u1} R (DivisionSemiring.toGroupWithZero.{u1} R _inst_1)))) x n))
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1))))] {x : R}, (IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2))) x) -> (forall (n : Int), IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2))) (HPow.hPow.{u1, 0, u1} R Int R (instHPow.{u1, 0} R Int (DivInvMonoid.Pow.{u1} R (DivisionRing.toDivInvMonoid.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) x n))
 Case conversion may be inaccurate. Consider using '#align is_self_adjoint.zpow IsSelfAdjoint.zpowₓ'. -/
@@ -335,6 +335,12 @@ theorem zpow {x : R} (hx : IsSelfAdjoint x) (n : ℤ) : IsSelfAdjoint (x ^ n) :=
   simp only [isSelfAdjoint_iff, star_zpow₀, hx.star_eq]
 #align is_self_adjoint.zpow IsSelfAdjoint.zpow
 
+end DivisionSemiring
+
+section DivisionRing
+
+variable [DivisionRing R] [StarRing R]
+
 theorem isSelfAdjoint_rat_cast (x : ℚ) : IsSelfAdjoint (x : R) :=
   star_ratCast _
 #align is_self_adjoint_rat_cast isSelfAdjoint_rat_cast

1e320130

bump to nightly-2023-03-17-00

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce7e9d53d4bbc38065db3b595cd5bd73c323bc1d

c85864d4

Diff

@@ -123,7 +123,7 @@ theorem mul_star_self [Semigroup R] [StarSemigroup R] (x : R) : IsSelfAdjoint (x
 lean 3 declaration is
   forall {F : Type.{u1}} {R : Type.{u2}} {S : Type.{u3}} [_inst_1 : Star.{u2} R] [_inst_2 : Star.{u3} S] [_inst_3 : StarHomClass.{u1, u2, u3} F R S _inst_1 _inst_2] {x : R}, (IsSelfAdjoint.{u2} R _inst_1 x) -> (forall (f : F), IsSelfAdjoint.{u3} S _inst_2 (coeFn.{succ u1, max (succ u2) (succ u3)} F (fun (_x : F) => R -> S) (FunLike.hasCoeToFun.{succ u1, succ u2, succ u3} F R (fun (_x : R) => S) (StarHomClass.toFunLike.{u1, u2, u3} F R S _inst_1 _inst_2 _inst_3)) f x))
 but is expected to have type
-  forall {F : Type.{u3}} {R : Type.{u2}} {S : Type.{u1}} [_inst_1 : Star.{u2} R] [_inst_2 : Star.{u1} S] [_inst_3 : StarHomClass.{u3, u2, u1} F R S _inst_1 _inst_2] {x : R}, (IsSelfAdjoint.{u2} R _inst_1 x) -> (forall (f : F), IsSelfAdjoint.{u1} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3016 : R) => S) x) _inst_2 (FunLike.coe.{succ u3, succ u2, succ u1} F R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3016 : R) => S) _x) (StarHomClass.toFunLike.{u3, u2, u1} F R S _inst_1 _inst_2 _inst_3) f x))
+  forall {F : Type.{u3}} {R : Type.{u2}} {S : Type.{u1}} [_inst_1 : Star.{u2} R] [_inst_2 : Star.{u1} S] [_inst_3 : StarHomClass.{u3, u2, u1} F R S _inst_1 _inst_2] {x : R}, (IsSelfAdjoint.{u2} R _inst_1 x) -> (forall (f : F), IsSelfAdjoint.{u1} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3024 : R) => S) x) _inst_2 (FunLike.coe.{succ u3, succ u2, succ u1} F R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3024 : R) => S) _x) (StarHomClass.toFunLike.{u3, u2, u1} F R S _inst_1 _inst_2 _inst_3) f x))
 Case conversion may be inaccurate. Consider using '#align is_self_adjoint.star_hom_apply IsSelfAdjoint.starHom_applyₓ'. -/
 /-- Functions in a `star_hom_class` preserve self-adjoint elements. -/
 theorem starHom_apply {F R S : Type _} [Star R] [Star S] [StarHomClass F R S] {x : R}

1e320130

bump to nightly-2023-03-14-02

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

d4b38a42

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Frédéric Dupuis
 
 ! This file was ported from Lean 3 source module algebra.star.self_adjoint
-! leanprover-community/mathlib commit 671d5d9a0cca76de2933cff8ee3c29b7533f9caf
+! leanprover-community/mathlib commit 1e3201306d4d9eb1fd54c60d7c4510ad5126f6f9
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -38,6 +38,7 @@ We also define `is_star_normal R`, a `Prop` that states that an element `x` sati
 
 ## TODO
 
+* Define `is_skew_adjoint` to match `is_self_adjoint`.
 * Define `λ z x, z * x * star z` (i.e. conjugation by `z`) as a monoid action of `R` on `R`
   (similar to the existing `conj_act` for groups), and then state the fact that `self_adjoint R` is
   invariant under it.
@@ -759,6 +760,22 @@ end SMul
 
 end skewAdjoint
 
+/-- Scalar multiplication of a self-adjoint element by a skew-adjoint element produces a
+skew-adjoint element. -/
+theorem IsSelfAdjoint.smul_mem_skewAdjoint [Ring R] [AddCommGroup A] [Module R A] [StarAddMonoid R]
+    [StarAddMonoid A] [StarModule R A] {r : R} (hr : r ∈ skewAdjoint R) {a : A}
+    (ha : IsSelfAdjoint a) : r • a ∈ skewAdjoint A :=
+  (star_smul _ _).trans <| (congr_arg₂ _ hr ha).trans <| neg_smul _ _
+#align is_self_adjoint.smul_mem_skew_adjoint IsSelfAdjoint.smul_mem_skewAdjoint
+
+/-- Scalar multiplication of a skew-adjoint element by a skew-adjoint element produces a
+self-adjoint element. -/
+theorem isSelfAdjoint_smul_of_mem_skewAdjoint [Ring R] [AddCommGroup A] [Module R A]
+    [StarAddMonoid R] [StarAddMonoid A] [StarModule R A] {r : R} (hr : r ∈ skewAdjoint R) {a : A}
+    (ha : a ∈ skewAdjoint A) : IsSelfAdjoint (r • a) :=
+  (star_smul _ _).trans <| (congr_arg₂ _ hr ha).trans <| neg_smul_neg _ _
+#align is_self_adjoint_smul_of_mem_skew_adjoint isSelfAdjoint_smul_of_mem_skewAdjoint
+
 /- warning: is_star_normal_zero -> isStarNormal_zero is a dubious translation:
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_2 : StarRing.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_1)], IsStarNormal.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_1) _inst_2))) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))

671d5d9a

bump to nightly-2023-03-11-22

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

a8ee822f

Diff

@@ -122,7 +122,7 @@ theorem mul_star_self [Semigroup R] [StarSemigroup R] (x : R) : IsSelfAdjoint (x
 lean 3 declaration is
   forall {F : Type.{u1}} {R : Type.{u2}} {S : Type.{u3}} [_inst_1 : Star.{u2} R] [_inst_2 : Star.{u3} S] [_inst_3 : StarHomClass.{u1, u2, u3} F R S _inst_1 _inst_2] {x : R}, (IsSelfAdjoint.{u2} R _inst_1 x) -> (forall (f : F), IsSelfAdjoint.{u3} S _inst_2 (coeFn.{succ u1, max (succ u2) (succ u3)} F (fun (_x : F) => R -> S) (FunLike.hasCoeToFun.{succ u1, succ u2, succ u3} F R (fun (_x : R) => S) (StarHomClass.toFunLike.{u1, u2, u3} F R S _inst_1 _inst_2 _inst_3)) f x))
 but is expected to have type
-  forall {F : Type.{u3}} {R : Type.{u2}} {S : Type.{u1}} [_inst_1 : Star.{u2} R] [_inst_2 : Star.{u1} S] [_inst_3 : StarHomClass.{u3, u2, u1} F R S _inst_1 _inst_2] {x : R}, (IsSelfAdjoint.{u2} R _inst_1 x) -> (forall (f : F), IsSelfAdjoint.{u1} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3011 : R) => S) x) _inst_2 (FunLike.coe.{succ u3, succ u2, succ u1} F R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3011 : R) => S) _x) (StarHomClass.toFunLike.{u3, u2, u1} F R S _inst_1 _inst_2 _inst_3) f x))
+  forall {F : Type.{u3}} {R : Type.{u2}} {S : Type.{u1}} [_inst_1 : Star.{u2} R] [_inst_2 : Star.{u1} S] [_inst_3 : StarHomClass.{u3, u2, u1} F R S _inst_1 _inst_2] {x : R}, (IsSelfAdjoint.{u2} R _inst_1 x) -> (forall (f : F), IsSelfAdjoint.{u1} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3016 : R) => S) x) _inst_2 (FunLike.coe.{succ u3, succ u2, succ u1} F R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3016 : R) => S) _x) (StarHomClass.toFunLike.{u3, u2, u1} F R S _inst_1 _inst_2 _inst_3) f x))
 Case conversion may be inaccurate. Consider using '#align is_self_adjoint.star_hom_apply IsSelfAdjoint.starHom_applyₓ'. -/
 /-- Functions in a `star_hom_class` preserve self-adjoint elements. -/
 theorem starHom_apply {F R S : Type _} [Star R] [Star S] [StarHomClass F R S] {x : R}
@@ -553,14 +553,14 @@ theorem val_zpow (x : selfAdjoint R) (z : ℤ) : ↑(x ^ z) = (x : R) ^ z :=
   rfl
 #align self_adjoint.coe_zpow selfAdjoint.val_zpow
 
-instance : RatCast (selfAdjoint R) :=
+instance : HasRatCast (selfAdjoint R) :=
   ⟨fun n => ⟨n, isSelfAdjoint_rat_cast n⟩⟩
 
 /- warning: self_adjoint.coe_rat_cast -> selfAdjoint.val_ratCast is a dubious translation:
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1))))] (x : Rat), Eq.{succ u1} R ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) R (AddSubgroup.setLike.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))))) (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2))) R (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) R (AddSubgroup.setLike.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))))) (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2))) R (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) R (AddSubgroup.setLike.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))))) (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2))) R (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) R (AddSubgroup.setLike.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))))) (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2))) R (coeSubtype.{succ u1} R (fun (x : R) => Membership.Mem.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (SetLike.hasMem.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) R (AddSubgroup.setLike.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))))) x (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2))))))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Rat (coeSort.{succ u1, succ (succ u1)} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) R (AddSubgroup.setLike.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))))) (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2))) (HasLiftT.mk.{1, succ u1} Rat (coeSort.{succ u1, succ (succ u1)} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) R (AddSubgroup.setLike.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))))) (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2))) (CoeTCₓ.coe.{1, succ u1} Rat (coeSort.{succ u1, succ (succ u1)} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) R (AddSubgroup.setLike.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))))) (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2))) (Rat.castCoe.{u1} (coeSort.{succ u1, succ (succ u1)} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) R (AddSubgroup.setLike.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))))) (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2))) (selfAdjoint.hasRatCast.{u1} R _inst_1 _inst_2)))) x)) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Rat R (HasLiftT.mk.{1, succ u1} Rat R (CoeTCₓ.coe.{1, succ u1} Rat R (Rat.castCoe.{u1} R (DivisionRing.toHasRatCast.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) x)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1))))] (x : Rat), Eq.{succ u1} R (Subtype.val.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x (SetLike.coe.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2)))) (RatCast.ratCast.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) x (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2)))) (selfAdjoint.instRatCastSubtypeMemAddSubgroupToAddGroupToAddGroupWithOneToRingToDivisionRingInstMembershipInstSetLikeAddSubgroupSelfAdjointToStarAddMonoidToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingToCommRing.{u1} R _inst_1 _inst_2) x)) (RatCast.ratCast.{u1} R (Field.toRatCast.{u1} R _inst_1) x)
+  forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1))))] (x : Rat), Eq.{succ u1} R (Subtype.val.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x (SetLike.coe.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2)))) (Rat.cast.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) x (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2)))) (selfAdjoint.instRatCastSubtypeMemAddSubgroupToAddGroupToAddGroupWithOneToRingToDivisionRingInstMembershipInstSetLikeAddSubgroupSelfAdjointToStarAddMonoidToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingToCommRing.{u1} R _inst_1 _inst_2) x)) (Rat.cast.{u1} R (Field.toRatCast.{u1} R _inst_1) x)
 Case conversion may be inaccurate. Consider using '#align self_adjoint.coe_rat_cast selfAdjoint.val_ratCastₓ'. -/
 @[simp, norm_cast]
 theorem val_ratCast (x : ℚ) : ↑(x : selfAdjoint R) = (x : R) :=

671d5d9a

bump to nightly-2023-03-09-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/21e3562c5e12d846c7def5eff8cdbc520d7d4936

061741a1

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Frédéric Dupuis
 
 ! This file was ported from Lean 3 source module algebra.star.self_adjoint
-! leanprover-community/mathlib commit 50832daea47b195a48b5b33b1c8b2162c48c3afc
+! leanprover-community/mathlib commit 671d5d9a0cca76de2933cff8ee3c29b7533f9caf
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -71,6 +71,12 @@ theorem star_comm_self' [Mul R] [Star R] (x : R) [IsStarNormal x] : star x * x =
 
 namespace IsSelfAdjoint
 
+-- named to match `commute.all`
+/-- All elements are self-adjoint when `star` is trivial. -/
+theorem all [Star R] [TrivialStar R] (r : R) : IsSelfAdjoint r :=
+  star_trivial _
+#align is_self_adjoint.all IsSelfAdjoint.all
+
 #print IsSelfAdjoint.star_eq /-
 theorem star_eq [Star R] {x : R} (hx : IsSelfAdjoint x) : star x = x :=
   hx
@@ -124,15 +130,15 @@ theorem starHom_apply {F R S : Type _} [Star R] [Star S] [StarHomClass F R S] {x
   show star (f x) = f x from map_star f x ▸ congr_arg f hx
 #align is_self_adjoint.star_hom_apply IsSelfAdjoint.starHom_apply
 
-section AddGroup
+section AddMonoid
 
-variable [AddGroup R] [StarAddMonoid R]
+variable [AddMonoid R] [StarAddMonoid R]
 
 variable (R)
 
 /- warning: is_self_adjoint_zero -> isSelfAdjoint_zero is a dubious translation:
 lean 3 declaration is
-  forall (R : Type.{u1}) [_inst_1 : AddGroup.{u1} R] [_inst_2 : StarAddMonoid.{u1} R (SubNegMonoid.toAddMonoid.{u1} R (AddGroup.toSubNegMonoid.{u1} R _inst_1))], IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (SubNegMonoid.toAddMonoid.{u1} R (AddGroup.toSubNegMonoid.{u1} R _inst_1)) _inst_2)) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (SubNegMonoid.toAddMonoid.{u1} R (AddGroup.toSubNegMonoid.{u1} R _inst_1)))))))
+  forall (R : Type.{u1}) [_inst_1 : AddMonoid.{u1} R] [_inst_2 : StarAddMonoid.{u1} R _inst_1], IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R _inst_1 _inst_2)) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R _inst_1)))))
 but is expected to have type
   forall (R : Type.{u1}) [_inst_1 : AddGroup.{u1} R] [_inst_2 : StarAddMonoid.{u1} R (SubNegMonoid.toAddMonoid.{u1} R (AddGroup.toSubNegMonoid.{u1} R _inst_1))], IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (SubNegMonoid.toAddMonoid.{u1} R (AddGroup.toSubNegMonoid.{u1} R _inst_1)) _inst_2)) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (NegZeroClass.toZero.{u1} R (SubNegZeroMonoid.toNegZeroClass.{u1} R (SubtractionMonoid.toSubNegZeroMonoid.{u1} R (AddGroup.toSubtractionMonoid.{u1} R _inst_1))))))
 Case conversion may be inaccurate. Consider using '#align is_self_adjoint_zero isSelfAdjoint_zeroₓ'. -/
@@ -144,7 +150,7 @@ variable {R}
 
 /- warning: is_self_adjoint.add -> IsSelfAdjoint.add is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : AddGroup.{u1} R] [_inst_2 : StarAddMonoid.{u1} R (SubNegMonoid.toAddMonoid.{u1} R (AddGroup.toSubNegMonoid.{u1} R _inst_1))] {x : R} {y : R}, (IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (SubNegMonoid.toAddMonoid.{u1} R (AddGroup.toSubNegMonoid.{u1} R _inst_1)) _inst_2)) x) -> (IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (SubNegMonoid.toAddMonoid.{u1} R (AddGroup.toSubNegMonoid.{u1} R _inst_1)) _inst_2)) y) -> (IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (SubNegMonoid.toAddMonoid.{u1} R (AddGroup.toSubNegMonoid.{u1} R _inst_1)) _inst_2)) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (AddZeroClass.toHasAdd.{u1} R (AddMonoid.toAddZeroClass.{u1} R (SubNegMonoid.toAddMonoid.{u1} R (AddGroup.toSubNegMonoid.{u1} R _inst_1))))) x y))
+  forall {R : Type.{u1}} [_inst_1 : AddMonoid.{u1} R] [_inst_2 : StarAddMonoid.{u1} R _inst_1] {x : R} {y : R}, (IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R _inst_1 _inst_2)) x) -> (IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R _inst_1 _inst_2)) y) -> (IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R _inst_1 _inst_2)) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (AddZeroClass.toHasAdd.{u1} R (AddMonoid.toAddZeroClass.{u1} R _inst_1))) x y))
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : AddGroup.{u1} R] [_inst_2 : StarAddMonoid.{u1} R (SubNegMonoid.toAddMonoid.{u1} R (AddGroup.toSubNegMonoid.{u1} R _inst_1))] {x : R} {y : R}, (IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (SubNegMonoid.toAddMonoid.{u1} R (AddGroup.toSubNegMonoid.{u1} R _inst_1)) _inst_2)) x) -> (IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (SubNegMonoid.toAddMonoid.{u1} R (AddGroup.toSubNegMonoid.{u1} R _inst_1)) _inst_2)) y) -> (IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (SubNegMonoid.toAddMonoid.{u1} R (AddGroup.toSubNegMonoid.{u1} R _inst_1)) _inst_2)) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (AddZeroClass.toAdd.{u1} R (AddMonoid.toAddZeroClass.{u1} R (SubNegMonoid.toAddMonoid.{u1} R (AddGroup.toSubNegMonoid.{u1} R _inst_1))))) x y))
 Case conversion may be inaccurate. Consider using '#align is_self_adjoint.add IsSelfAdjoint.addₓ'. -/
@@ -152,6 +158,22 @@ theorem add {x y : R} (hx : IsSelfAdjoint x) (hy : IsSelfAdjoint y) : IsSelfAdjo
   simp only [isSelfAdjoint_iff, star_add, hx.star_eq, hy.star_eq]
 #align is_self_adjoint.add IsSelfAdjoint.add
 
+/- warning: is_self_adjoint.bit0 -> IsSelfAdjoint.bit0 is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : AddMonoid.{u1} R] [_inst_2 : StarAddMonoid.{u1} R _inst_1] {x : R}, (IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R _inst_1 _inst_2)) x) -> (IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R _inst_1 _inst_2)) (bit0.{u1} R (AddZeroClass.toHasAdd.{u1} R (AddMonoid.toAddZeroClass.{u1} R _inst_1)) x))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : AddGroup.{u1} R] [_inst_2 : StarAddMonoid.{u1} R (SubNegMonoid.toAddMonoid.{u1} R (AddGroup.toSubNegMonoid.{u1} R _inst_1))] {x : R}, (IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (SubNegMonoid.toAddMonoid.{u1} R (AddGroup.toSubNegMonoid.{u1} R _inst_1)) _inst_2)) x) -> (IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (SubNegMonoid.toAddMonoid.{u1} R (AddGroup.toSubNegMonoid.{u1} R _inst_1)) _inst_2)) (bit0.{u1} R (AddZeroClass.toAdd.{u1} R (AddMonoid.toAddZeroClass.{u1} R (SubNegMonoid.toAddMonoid.{u1} R (AddGroup.toSubNegMonoid.{u1} R _inst_1)))) x))
+Case conversion may be inaccurate. Consider using '#align is_self_adjoint.bit0 IsSelfAdjoint.bit0ₓ'. -/
+theorem bit0 {x : R} (hx : IsSelfAdjoint x) : IsSelfAdjoint (bit0 x) := by
+  simp only [isSelfAdjoint_iff, star_bit0, hx.star_eq]
+#align is_self_adjoint.bit0 IsSelfAdjoint.bit0
+
+end AddMonoid
+
+section AddGroup
+
+variable [AddGroup R] [StarAddMonoid R]
+
 /- warning: is_self_adjoint.neg -> IsSelfAdjoint.neg is a dubious translation:
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : AddGroup.{u1} R] [_inst_2 : StarAddMonoid.{u1} R (SubNegMonoid.toAddMonoid.{u1} R (AddGroup.toSubNegMonoid.{u1} R _inst_1))] {x : R}, (IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (SubNegMonoid.toAddMonoid.{u1} R (AddGroup.toSubNegMonoid.{u1} R _inst_1)) _inst_2)) x) -> (IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (SubNegMonoid.toAddMonoid.{u1} R (AddGroup.toSubNegMonoid.{u1} R _inst_1)) _inst_2)) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R _inst_1)) x))
@@ -172,25 +194,15 @@ theorem sub {x y : R} (hx : IsSelfAdjoint x) (hy : IsSelfAdjoint y) : IsSelfAdjo
   simp only [isSelfAdjoint_iff, star_sub, hx.star_eq, hy.star_eq]
 #align is_self_adjoint.sub IsSelfAdjoint.sub
 
-/- warning: is_self_adjoint.bit0 -> IsSelfAdjoint.bit0 is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : AddGroup.{u1} R] [_inst_2 : StarAddMonoid.{u1} R (SubNegMonoid.toAddMonoid.{u1} R (AddGroup.toSubNegMonoid.{u1} R _inst_1))] {x : R}, (IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (SubNegMonoid.toAddMonoid.{u1} R (AddGroup.toSubNegMonoid.{u1} R _inst_1)) _inst_2)) x) -> (IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (SubNegMonoid.toAddMonoid.{u1} R (AddGroup.toSubNegMonoid.{u1} R _inst_1)) _inst_2)) (bit0.{u1} R (AddZeroClass.toHasAdd.{u1} R (AddMonoid.toAddZeroClass.{u1} R (SubNegMonoid.toAddMonoid.{u1} R (AddGroup.toSubNegMonoid.{u1} R _inst_1)))) x))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : AddGroup.{u1} R] [_inst_2 : StarAddMonoid.{u1} R (SubNegMonoid.toAddMonoid.{u1} R (AddGroup.toSubNegMonoid.{u1} R _inst_1))] {x : R}, (IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (SubNegMonoid.toAddMonoid.{u1} R (AddGroup.toSubNegMonoid.{u1} R _inst_1)) _inst_2)) x) -> (IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (SubNegMonoid.toAddMonoid.{u1} R (AddGroup.toSubNegMonoid.{u1} R _inst_1)) _inst_2)) (bit0.{u1} R (AddZeroClass.toAdd.{u1} R (AddMonoid.toAddZeroClass.{u1} R (SubNegMonoid.toAddMonoid.{u1} R (AddGroup.toSubNegMonoid.{u1} R _inst_1)))) x))
-Case conversion may be inaccurate. Consider using '#align is_self_adjoint.bit0 IsSelfAdjoint.bit0ₓ'. -/
-theorem bit0 {x : R} (hx : IsSelfAdjoint x) : IsSelfAdjoint (bit0 x) := by
-  simp only [isSelfAdjoint_iff, star_bit0, hx.star_eq]
-#align is_self_adjoint.bit0 IsSelfAdjoint.bit0
-
 end AddGroup
 
-section NonUnitalSemiring
+section Semigroup
 
-variable [NonUnitalSemiring R] [StarRing R]
+variable [Semigroup R] [StarSemigroup R]
 
 /- warning: is_self_adjoint.conjugate -> IsSelfAdjoint.conjugate is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : NonUnitalSemiring.{u1} R] [_inst_2 : StarRing.{u1} R _inst_1] {x : R}, (IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_1))) (StarRing.toStarAddMonoid.{u1} R _inst_1 _inst_2))) x) -> (forall (z : R), IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_1))) (StarRing.toStarAddMonoid.{u1} R _inst_1 _inst_2))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_1)))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_1)))) z x) (Star.star.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_1))) (StarRing.toStarAddMonoid.{u1} R _inst_1 _inst_2))) z)))
+  forall {R : Type.{u1}} [_inst_1 : Semigroup.{u1} R] [_inst_2 : StarSemigroup.{u1} R _inst_1] {x : R}, (IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarSemigroup.toHasInvolutiveStar.{u1} R _inst_1 _inst_2)) x) -> (forall (z : R), IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarSemigroup.toHasInvolutiveStar.{u1} R _inst_1 _inst_2)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Semigroup.toHasMul.{u1} R _inst_1)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Semigroup.toHasMul.{u1} R _inst_1)) z x) (Star.star.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarSemigroup.toHasInvolutiveStar.{u1} R _inst_1 _inst_2)) z)))
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : NonUnitalSemiring.{u1} R] [_inst_2 : StarRing.{u1} R _inst_1] {x : R}, (IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_1))) (StarRing.toStarAddMonoid.{u1} R _inst_1 _inst_2))) x) -> (forall (z : R), IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_1))) (StarRing.toStarAddMonoid.{u1} R _inst_1 _inst_2))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_1))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_1))) z x) (Star.star.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_1))) (StarRing.toStarAddMonoid.{u1} R _inst_1 _inst_2))) z)))
 Case conversion may be inaccurate. Consider using '#align is_self_adjoint.conjugate IsSelfAdjoint.conjugateₓ'. -/
@@ -200,7 +212,7 @@ theorem conjugate {x : R} (hx : IsSelfAdjoint x) (z : R) : IsSelfAdjoint (z * x
 
 /- warning: is_self_adjoint.conjugate' -> IsSelfAdjoint.conjugate' is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : NonUnitalSemiring.{u1} R] [_inst_2 : StarRing.{u1} R _inst_1] {x : R}, (IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_1))) (StarRing.toStarAddMonoid.{u1} R _inst_1 _inst_2))) x) -> (forall (z : R), IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_1))) (StarRing.toStarAddMonoid.{u1} R _inst_1 _inst_2))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_1)))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_1)))) (Star.star.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_1))) (StarRing.toStarAddMonoid.{u1} R _inst_1 _inst_2))) z) x) z))
+  forall {R : Type.{u1}} [_inst_1 : Semigroup.{u1} R] [_inst_2 : StarSemigroup.{u1} R _inst_1] {x : R}, (IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarSemigroup.toHasInvolutiveStar.{u1} R _inst_1 _inst_2)) x) -> (forall (z : R), IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarSemigroup.toHasInvolutiveStar.{u1} R _inst_1 _inst_2)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Semigroup.toHasMul.{u1} R _inst_1)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Semigroup.toHasMul.{u1} R _inst_1)) (Star.star.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarSemigroup.toHasInvolutiveStar.{u1} R _inst_1 _inst_2)) z) x) z))
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : NonUnitalSemiring.{u1} R] [_inst_2 : StarRing.{u1} R _inst_1] {x : R}, (IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_1))) (StarRing.toStarAddMonoid.{u1} R _inst_1 _inst_2))) x) -> (forall (z : R), IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_1))) (StarRing.toStarAddMonoid.{u1} R _inst_1 _inst_2))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_1))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_1))) (Star.star.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_1))) (StarRing.toStarAddMonoid.{u1} R _inst_1 _inst_2))) z) x) z))
 Case conversion may be inaccurate. Consider using '#align is_self_adjoint.conjugate' IsSelfAdjoint.conjugate'ₓ'. -/
@@ -210,7 +222,7 @@ theorem conjugate' {x : R} (hx : IsSelfAdjoint x) (z : R) : IsSelfAdjoint (star
 
 /- warning: is_self_adjoint.is_star_normal -> IsSelfAdjoint.isStarNormal is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : NonUnitalSemiring.{u1} R] [_inst_2 : StarRing.{u1} R _inst_1] {x : R}, (IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_1))) (StarRing.toStarAddMonoid.{u1} R _inst_1 _inst_2))) x) -> (IsStarNormal.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_1))) (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_1))) (StarRing.toStarAddMonoid.{u1} R _inst_1 _inst_2))) x)
+  forall {R : Type.{u1}} [_inst_1 : Semigroup.{u1} R] [_inst_2 : StarSemigroup.{u1} R _inst_1] {x : R}, (IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarSemigroup.toHasInvolutiveStar.{u1} R _inst_1 _inst_2)) x) -> (IsStarNormal.{u1} R (Semigroup.toHasMul.{u1} R _inst_1) (InvolutiveStar.toHasStar.{u1} R (StarSemigroup.toHasInvolutiveStar.{u1} R _inst_1 _inst_2)) x)
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : NonUnitalSemiring.{u1} R] [_inst_2 : StarRing.{u1} R _inst_1] {x : R}, (IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_1))) (StarRing.toStarAddMonoid.{u1} R _inst_1 _inst_2))) x) -> (IsStarNormal.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_1)) (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_1))) (StarRing.toStarAddMonoid.{u1} R _inst_1 _inst_2))) x)
 Case conversion may be inaccurate. Consider using '#align is_self_adjoint.is_star_normal IsSelfAdjoint.isStarNormalₓ'. -/
@@ -218,25 +230,45 @@ theorem isStarNormal {x : R} (hx : IsSelfAdjoint x) : IsStarNormal x :=
   ⟨by simp only [hx.star_eq]⟩
 #align is_self_adjoint.is_star_normal IsSelfAdjoint.isStarNormal
 
-end NonUnitalSemiring
+end Semigroup
 
-section Ring
+section Monoid
 
-variable [Ring R] [StarRing R]
+variable [Monoid R] [StarSemigroup R]
 
 variable (R)
 
-#print isSelfAdjoint_one /-
+/- warning: is_self_adjoint_one -> isSelfAdjoint_one is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) [_inst_1 : Monoid.{u1} R] [_inst_2 : StarSemigroup.{u1} R (Monoid.toSemigroup.{u1} R _inst_1)], IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarSemigroup.toHasInvolutiveStar.{u1} R (Monoid.toSemigroup.{u1} R _inst_1) _inst_2)) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (MulOneClass.toHasOne.{u1} R (Monoid.toMulOneClass.{u1} R _inst_1)))))
+but is expected to have type
+  forall (R : Type.{u1}) [_inst_1 : Ring.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1))], IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1)) _inst_2))) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (NonAssocRing.toOne.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))
+Case conversion may be inaccurate. Consider using '#align is_self_adjoint_one isSelfAdjoint_oneₓ'. -/
 theorem isSelfAdjoint_one : IsSelfAdjoint (1 : R) :=
   star_one R
 #align is_self_adjoint_one isSelfAdjoint_one
--/
 
 variable {R}
 
+/- warning: is_self_adjoint.pow -> IsSelfAdjoint.pow is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Monoid.{u1} R] [_inst_2 : StarSemigroup.{u1} R (Monoid.toSemigroup.{u1} R _inst_1)] {x : R}, (IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarSemigroup.toHasInvolutiveStar.{u1} R (Monoid.toSemigroup.{u1} R _inst_1) _inst_2)) x) -> (forall (n : Nat), IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarSemigroup.toHasInvolutiveStar.{u1} R (Monoid.toSemigroup.{u1} R _inst_1) _inst_2)) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R _inst_1)) x n))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1))] {x : R}, (IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1)) _inst_2))) x) -> (forall (n : Nat), IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1)) _inst_2))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) x n))
+Case conversion may be inaccurate. Consider using '#align is_self_adjoint.pow IsSelfAdjoint.powₓ'. -/
+theorem pow {x : R} (hx : IsSelfAdjoint x) (n : ℕ) : IsSelfAdjoint (x ^ n) := by
+  simp only [isSelfAdjoint_iff, star_pow, hx.star_eq]
+#align is_self_adjoint.pow IsSelfAdjoint.pow
+
+end Monoid
+
+section Semiring
+
+variable [Semiring R] [StarRing R]
+
 /- warning: is_self_adjoint.bit1 -> IsSelfAdjoint.bit1 is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1))] {x : R}, (IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1)) _inst_2))) x) -> (IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1)) _inst_2))) (bit1.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (NonAssocRing.toAddGroupWithOne.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Distrib.toHasAdd.{u1} R (Ring.toDistrib.{u1} R _inst_1)) x))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_2 : StarRing.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_1)] {x : R}, (IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_1) _inst_2))) x) -> (IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (Semiring.toNonUnitalSemiring.{u1} R _inst_1) _inst_2))) (bit1.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Distrib.toHasAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) x))
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1))] {x : R}, (IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1)) _inst_2))) x) -> (IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1)) _inst_2))) (bit1.{u1} R (NonAssocRing.toOne.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))) x))
 Case conversion may be inaccurate. Consider using '#align is_self_adjoint.bit1 IsSelfAdjoint.bit1ₓ'. -/
@@ -244,25 +276,20 @@ theorem bit1 {x : R} (hx : IsSelfAdjoint x) : IsSelfAdjoint (bit1 x) := by
   simp only [isSelfAdjoint_iff, star_bit1, hx.star_eq]
 #align is_self_adjoint.bit1 IsSelfAdjoint.bit1
 
-/- warning: is_self_adjoint.pow -> IsSelfAdjoint.pow is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1))] {x : R}, (IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1)) _inst_2))) x) -> (forall (n : Nat), IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1)) _inst_2))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R _inst_1))) x n))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1))] {x : R}, (IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1)) _inst_2))) x) -> (forall (n : Nat), IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R _inst_1))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R _inst_1)) _inst_2))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) x n))
-Case conversion may be inaccurate. Consider using '#align is_self_adjoint.pow IsSelfAdjoint.powₓ'. -/
-theorem pow {x : R} (hx : IsSelfAdjoint x) (n : ℕ) : IsSelfAdjoint (x ^ n) := by
-  simp only [isSelfAdjoint_iff, star_pow, hx.star_eq]
-#align is_self_adjoint.pow IsSelfAdjoint.pow
+@[simp]
+theorem isSelfAdjoint_nat_cast (n : ℕ) : IsSelfAdjoint (n : R) :=
+  star_natCast _
+#align is_self_adjoint_nat_cast isSelfAdjoint_nat_cast
 
-end Ring
+end Semiring
 
-section NonUnitalCommRing
+section CommSemigroup
 
-variable [NonUnitalCommRing R] [StarRing R]
+variable [CommSemigroup R] [StarSemigroup R]
 
 /- warning: is_self_adjoint.mul -> IsSelfAdjoint.mul is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : NonUnitalCommRing.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R _inst_1))] {x : R} {y : R}, (IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R _inst_1)) _inst_2))) x) -> (IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R _inst_1)) _inst_2))) y) -> (IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R _inst_1)) _inst_2))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R _inst_1)))))) x y))
+  forall {R : Type.{u1}} [_inst_1 : CommSemigroup.{u1} R] [_inst_2 : StarSemigroup.{u1} R (CommSemigroup.toSemigroup.{u1} R _inst_1)] {x : R} {y : R}, (IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarSemigroup.toHasInvolutiveStar.{u1} R (CommSemigroup.toSemigroup.{u1} R _inst_1) _inst_2)) x) -> (IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarSemigroup.toHasInvolutiveStar.{u1} R (CommSemigroup.toSemigroup.{u1} R _inst_1) _inst_2)) y) -> (IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarSemigroup.toHasInvolutiveStar.{u1} R (CommSemigroup.toSemigroup.{u1} R _inst_1) _inst_2)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Semigroup.toHasMul.{u1} R (CommSemigroup.toSemigroup.{u1} R _inst_1))) x y))
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : NonUnitalCommRing.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R _inst_1))] {x : R} {y : R}, (IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (SubNegMonoid.toAddMonoid.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddCommGroup.toAddGroup.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R _inst_1)))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R _inst_1)) _inst_2))) x) -> (IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (SubNegMonoid.toAddMonoid.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddCommGroup.toAddGroup.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R _inst_1)))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R _inst_1)) _inst_2))) y) -> (IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (SubNegMonoid.toAddMonoid.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddCommGroup.toAddGroup.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R _inst_1)))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R _inst_1)) _inst_2))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonUnitalRing.toNonUnitalNonAssocRing.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R _inst_1)))) x y))
 Case conversion may be inaccurate. Consider using '#align is_self_adjoint.mul IsSelfAdjoint.mulₓ'. -/
@@ -270,15 +297,26 @@ theorem mul {x y : R} (hx : IsSelfAdjoint x) (hy : IsSelfAdjoint y) : IsSelfAdjo
   simp only [isSelfAdjoint_iff, star_mul', hx.star_eq, hy.star_eq]
 #align is_self_adjoint.mul IsSelfAdjoint.mul
 
-end NonUnitalCommRing
+end CommSemigroup
 
-section Field
+section Ring
 
-variable [Field R] [StarRing R]
+variable [Ring R] [StarRing R]
+
+@[simp]
+theorem isSelfAdjoint_int_cast (z : ℤ) : IsSelfAdjoint (z : R) :=
+  star_intCast _
+#align is_self_adjoint_int_cast isSelfAdjoint_int_cast
+
+end Ring
+
+section DivisionRing
+
+variable [DivisionRing R] [StarRing R]
 
 /- warning: is_self_adjoint.inv -> IsSelfAdjoint.inv is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1))))] {x : R}, (IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1))))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2))) x) -> (IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1))))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2))) (Inv.inv.{u1} R (DivInvMonoid.toHasInv.{u1} R (DivisionRing.toDivInvMonoid.{u1} R (Field.toDivisionRing.{u1} R _inst_1))) x))
+  forall {R : Type.{u1}} [_inst_1 : DivisionRing.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))] {x : R}, (IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) _inst_2))) x) -> (IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) _inst_2))) (Inv.inv.{u1} R (DivInvMonoid.toHasInv.{u1} R (DivisionRing.toDivInvMonoid.{u1} R _inst_1)) x))
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1))))] {x : R}, (IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2))) x) -> (IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2))) (Inv.inv.{u1} R (Field.toInv.{u1} R _inst_1) x))
 Case conversion may be inaccurate. Consider using '#align is_self_adjoint.inv IsSelfAdjoint.invₓ'. -/
@@ -286,6 +324,26 @@ theorem inv {x : R} (hx : IsSelfAdjoint x) : IsSelfAdjoint x⁻¹ := by
   simp only [isSelfAdjoint_iff, star_inv', hx.star_eq]
 #align is_self_adjoint.inv IsSelfAdjoint.inv
 
+/- warning: is_self_adjoint.zpow -> IsSelfAdjoint.zpow is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : DivisionRing.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))] {x : R}, (IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) _inst_2))) x) -> (forall (n : Int), IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1)))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (Ring.toNonUnitalRing.{u1} R (DivisionRing.toRing.{u1} R _inst_1))) _inst_2))) (HPow.hPow.{u1, 0, u1} R Int R (instHPow.{u1, 0} R Int (DivInvMonoid.Pow.{u1} R (DivisionRing.toDivInvMonoid.{u1} R _inst_1))) x n))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1))))] {x : R}, (IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2))) x) -> (forall (n : Int), IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2))) (HPow.hPow.{u1, 0, u1} R Int R (instHPow.{u1, 0} R Int (DivInvMonoid.Pow.{u1} R (DivisionRing.toDivInvMonoid.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) x n))
+Case conversion may be inaccurate. Consider using '#align is_self_adjoint.zpow IsSelfAdjoint.zpowₓ'. -/
+theorem zpow {x : R} (hx : IsSelfAdjoint x) (n : ℤ) : IsSelfAdjoint (x ^ n) := by
+  simp only [isSelfAdjoint_iff, star_zpow₀, hx.star_eq]
+#align is_self_adjoint.zpow IsSelfAdjoint.zpow
+
+theorem isSelfAdjoint_rat_cast (x : ℚ) : IsSelfAdjoint (x : R) :=
+  star_ratCast _
+#align is_self_adjoint_rat_cast isSelfAdjoint_rat_cast
+
+end DivisionRing
+
+section Field
+
+variable [Field R] [StarRing R]
+
 /- warning: is_self_adjoint.div -> IsSelfAdjoint.div is a dubious translation:
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1))))] {x : R} {y : R}, (IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1))))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2))) x) -> (IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1))))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2))) y) -> (IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1))))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2))) (HDiv.hDiv.{u1, u1, u1} R R R (instHDiv.{u1} R (DivInvMonoid.toHasDiv.{u1} R (DivisionRing.toDivInvMonoid.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) x y))
@@ -296,26 +354,20 @@ theorem div {x y : R} (hx : IsSelfAdjoint x) (hy : IsSelfAdjoint y) : IsSelfAdjo
   simp only [isSelfAdjoint_iff, star_div', hx.star_eq, hy.star_eq]
 #align is_self_adjoint.div IsSelfAdjoint.div
 
-#print IsSelfAdjoint.zpow /-
-theorem zpow {x : R} (hx : IsSelfAdjoint x) (n : ℤ) : IsSelfAdjoint (x ^ n) := by
-  simp only [isSelfAdjoint_iff, star_zpow₀, hx.star_eq]
-#align is_self_adjoint.zpow IsSelfAdjoint.zpow
--/
-
 end Field
 
 section SMul
 
-variable [Star R] [TrivialStar R] [AddGroup A] [StarAddMonoid A]
+variable [Star R] [AddMonoid A] [StarAddMonoid A] [SMul R A] [StarModule R A]
 
 /- warning: is_self_adjoint.smul -> IsSelfAdjoint.smul is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : Star.{u1} R] [_inst_2 : TrivialStar.{u1} R _inst_1] [_inst_3 : AddGroup.{u2} A] [_inst_4 : StarAddMonoid.{u2} A (SubNegMonoid.toAddMonoid.{u2} A (AddGroup.toSubNegMonoid.{u2} A _inst_3))] [_inst_5 : SMul.{u1, u2} R A] [_inst_6 : StarModule.{u1, u2} R A _inst_1 (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (SubNegMonoid.toAddMonoid.{u2} A (AddGroup.toSubNegMonoid.{u2} A _inst_3)) _inst_4)) _inst_5] (r : R) {x : A}, (IsSelfAdjoint.{u2} A (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (SubNegMonoid.toAddMonoid.{u2} A (AddGroup.toSubNegMonoid.{u2} A _inst_3)) _inst_4)) x) -> (IsSelfAdjoint.{u2} A (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (SubNegMonoid.toAddMonoid.{u2} A (AddGroup.toSubNegMonoid.{u2} A _inst_3)) _inst_4)) (SMul.smul.{u1, u2} R A _inst_5 r x))
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : Star.{u1} R] [_inst_2 : AddMonoid.{u2} A] [_inst_3 : StarAddMonoid.{u2} A _inst_2] [_inst_4 : SMul.{u1, u2} R A] [_inst_5 : StarModule.{u1, u2} R A _inst_1 (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A _inst_2 _inst_3)) _inst_4] {r : R}, (IsSelfAdjoint.{u1} R _inst_1 r) -> (forall {x : A}, (IsSelfAdjoint.{u2} A (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A _inst_2 _inst_3)) x) -> (IsSelfAdjoint.{u2} A (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A _inst_2 _inst_3)) (SMul.smul.{u1, u2} R A _inst_4 r x)))
 but is expected to have type
-  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : Star.{u2} R] [_inst_2 : TrivialStar.{u2} R _inst_1] [_inst_3 : AddGroup.{u1} A] [_inst_4 : StarAddMonoid.{u1} A (SubNegMonoid.toAddMonoid.{u1} A (AddGroup.toSubNegMonoid.{u1} A _inst_3))] [_inst_5 : SMul.{u2, u1} R A] [_inst_6 : StarModule.{u2, u1} R A _inst_1 (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (SubNegMonoid.toAddMonoid.{u1} A (AddGroup.toSubNegMonoid.{u1} A _inst_3)) _inst_4)) _inst_5] (r : R) {x : A}, (IsSelfAdjoint.{u1} A (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (SubNegMonoid.toAddMonoid.{u1} A (AddGroup.toSubNegMonoid.{u1} A _inst_3)) _inst_4)) x) -> (IsSelfAdjoint.{u1} A (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (SubNegMonoid.toAddMonoid.{u1} A (AddGroup.toSubNegMonoid.{u1} A _inst_3)) _inst_4)) (HSMul.hSMul.{u2, u1, u1} R A A (instHSMul.{u2, u1} R A _inst_5) r x))
+  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : Star.{u2} R] [_inst_2 : TrivialStar.{u2} R _inst_1] [_inst_3 : AddGroup.{u1} A] [_inst_4 : StarAddMonoid.{u1} A (SubNegMonoid.toAddMonoid.{u1} A (AddGroup.toSubNegMonoid.{u1} A _inst_3))] [_inst_5 : SMul.{u2, u1} R A] [r : StarModule.{u2, u1} R A _inst_1 (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (SubNegMonoid.toAddMonoid.{u1} A (AddGroup.toSubNegMonoid.{u1} A _inst_3)) _inst_4)) _inst_5] (hr : R) {x : A}, (IsSelfAdjoint.{u1} A (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (SubNegMonoid.toAddMonoid.{u1} A (AddGroup.toSubNegMonoid.{u1} A _inst_3)) _inst_4)) x) -> (IsSelfAdjoint.{u1} A (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (SubNegMonoid.toAddMonoid.{u1} A (AddGroup.toSubNegMonoid.{u1} A _inst_3)) _inst_4)) (HSMul.hSMul.{u2, u1, u1} R A A (instHSMul.{u2, u1} R A _inst_5) hr x))
 Case conversion may be inaccurate. Consider using '#align is_self_adjoint.smul IsSelfAdjoint.smulₓ'. -/
-theorem smul [SMul R A] [StarModule R A] (r : R) {x : A} (hx : IsSelfAdjoint x) :
-    IsSelfAdjoint (r • x) := by simp only [isSelfAdjoint_iff, star_smul, star_trivial, hx.star_eq]
+theorem smul {r : R} (hr : IsSelfAdjoint r) {x : A} (hx : IsSelfAdjoint x) :
+    IsSelfAdjoint (r • x) := by simp only [isSelfAdjoint_iff, star_smul, hr.star_eq, hx.star_eq]
 #align is_self_adjoint.smul IsSelfAdjoint.smul
 
 end SMul
@@ -405,16 +457,10 @@ instance [Nontrivial R] : Nontrivial (selfAdjoint R) :=
   ⟨⟨0, 1, Subtype.ne_of_val_ne zero_ne_one⟩⟩
 
 instance : NatCast (selfAdjoint R) :=
-  ⟨fun n =>
-    ⟨n,
-      Nat.recOn n (by simp [zero_mem]) fun k hk =>
-        (@Nat.cast_succ R _ k).symm ▸ add_mem hk (isSelfAdjoint_one R)⟩⟩
+  ⟨fun n => ⟨n, isSelfAdjoint_nat_cast _⟩⟩
 
 instance : IntCast (selfAdjoint R) :=
-  ⟨fun n =>
-    ⟨n, by
-      cases n <;> simp [show ↑n ∈ selfAdjoint R from (n : selfAdjoint R).2]
-      refine' add_mem (isSelfAdjoint_one R).neg (n : selfAdjoint R).2.neg⟩⟩
+  ⟨fun n => ⟨n, isSelfAdjoint_int_cast _⟩⟩
 
 instance : Pow (selfAdjoint R) ℕ :=
   ⟨fun x n => ⟨(x : R) ^ n, x.Prop.pow n⟩⟩
@@ -507,19 +553,8 @@ theorem val_zpow (x : selfAdjoint R) (z : ℤ) : ↑(x ^ z) = (x : R) ^ z :=
   rfl
 #align self_adjoint.coe_zpow selfAdjoint.val_zpow
 
-/- warning: self_adjoint.rat_cast_mem -> selfAdjoint.ratCast_mem is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1))))] (x : Rat), IsSelfAdjoint.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1))))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Rat R (HasLiftT.mk.{1, succ u1} Rat R (CoeTCₓ.coe.{1, succ u1} Rat R (Rat.castCoe.{u1} R (DivisionRing.toHasRatCast.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) x)
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1))))] (x : Rat), IsSelfAdjoint.{u1} R (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2))) (RatCast.ratCast.{u1} R (Field.toRatCast.{u1} R _inst_1) x)
-Case conversion may be inaccurate. Consider using '#align self_adjoint.rat_cast_mem selfAdjoint.ratCast_memₓ'. -/
-theorem ratCast_mem : ∀ x : ℚ, IsSelfAdjoint (x : R)
-  | ⟨a, b, h1, h2⟩ => by
-    rw [IsSelfAdjoint, Rat.cast_mk', star_mul', star_inv', star_natCast, star_intCast]
-#align self_adjoint.rat_cast_mem selfAdjoint.ratCast_mem
-
 instance : RatCast (selfAdjoint R) :=
-  ⟨fun n => ⟨n, ratCast_mem n⟩⟩
+  ⟨fun n => ⟨n, isSelfAdjoint_rat_cast n⟩⟩
 
 /- warning: self_adjoint.coe_rat_cast -> selfAdjoint.val_ratCast is a dubious translation:
 lean 3 declaration is
@@ -539,7 +574,8 @@ but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : Field.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1))))], SMul.{0, u1} Rat (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))) R (AddSubgroup.instSetLikeAddSubgroup.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) x (selfAdjoint.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (Ring.toAddGroupWithOne.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R (Field.toCommRing.{u1} R _inst_1)))) _inst_2))))
 Case conversion may be inaccurate. Consider using '#align self_adjoint.has_qsmul selfAdjoint.instQSMulₓ'. -/
 instance instQSMul : SMul ℚ (selfAdjoint R) :=
-  ⟨fun a x => ⟨a • x, by rw [Rat.smul_def] <;> exact (rat_cast_mem a).mul x.prop⟩⟩
+  ⟨fun a x =>
+    ⟨a • x, by rw [Rat.smul_def] <;> exact IsSelfAdjoint.mul (isSelfAdjoint_rat_cast a) x.prop⟩⟩
 #align self_adjoint.has_qsmul selfAdjoint.instQSMul
 
 /- warning: self_adjoint.coe_rat_smul -> selfAdjoint.val_rat_smul is a dubious translation:
@@ -566,7 +602,7 @@ section SMul
 variable [Star R] [TrivialStar R] [AddGroup A] [StarAddMonoid A]
 
 instance [SMul R A] [StarModule R A] : SMul R (selfAdjoint A) :=
-  ⟨fun r x => ⟨r • x, x.Prop.smul r⟩⟩
+  ⟨fun r x => ⟨r • x, (IsSelfAdjoint.all _).smul x.Prop⟩⟩
 
 /- warning: self_adjoint.coe_smul -> selfAdjoint.val_smul is a dubious translation:
 lean 3 declaration is

50832dae

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

a6ece354

chore: split Algebra.Module.Basic (#12501)

Similar to #12486, which did this for Algebra.Algebra.Basic.

Splits Algebra.Module.Defs off Algebra.Module.Basic. Most imports only need the Defs file, which has significantly smaller imports. The remaining Algebra.Module.Basic is now a grab-bag of unrelated results, and should probably be split further or rehomed.

This is mostly motivated by the wasted effort during minimization upon encountering Algebra.Module.Basic.

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

7d5102df

Diff

@@ -3,7 +3,7 @@ Copyright (c) 2021 Frédéric Dupuis. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Frédéric Dupuis
 -/
-import Mathlib.Algebra.Module.Basic
+import Mathlib.Algebra.Module.Defs
 import Mathlib.Algebra.Star.Pi
 import Mathlib.GroupTheory.Subgroup.Basic

a6ece354

feat: NNRat.cast (#11203)

Define the canonical coercion from the nonnegative rationals to any division semiring.

From LeanAPAP

1a5d1288

Diff

@@ -265,6 +265,8 @@ theorem zpow {x : R} (hx : IsSelfAdjoint x) (n : ℤ) : IsSelfAdjoint (x ^ n) :=
   simp only [isSelfAdjoint_iff, star_zpow₀, hx.star_eq]
 #align is_self_adjoint.zpow IsSelfAdjoint.zpow
 
+lemma _root_.isSelfAdjoint_nnratCast (q : ℚ≥0) : IsSelfAdjoint (q : R) := star_nnratCast _
+
 end DivisionSemiring
 
 section DivisionRing
@@ -430,24 +432,32 @@ theorem val_zpow (x : selfAdjoint R) (z : ℤ) : ↑(x ^ z) = (x : R) ^ z :=
   rfl
 #align self_adjoint.coe_zpow selfAdjoint.val_zpow
 
+instance instNNRatCast : NNRatCast (selfAdjoint R) where
+  nnratCast q := ⟨q, isSelfAdjoint_nnratCast q⟩
+
 instance instRatCast : RatCast (selfAdjoint R) where
   ratCast q := ⟨q, isSelfAdjoint_ratCast q⟩
 
+@[simp, norm_cast] lemma val_nnratCast (q : ℚ≥0) : (q : selfAdjoint R) = (q : R) := rfl
 @[simp, norm_cast] lemma val_ratCast (q : ℚ) : (q : selfAdjoint R) = (q : R) := rfl
 #align self_adjoint.coe_rat_cast selfAdjoint.val_ratCast
 
+instance instSMulNNRat : SMul ℚ≥0 (selfAdjoint R) where
+  smul a x := ⟨a • (x : R), by rw [NNRat.smul_def]; exact (isSelfAdjoint_nnratCast a).mul x.prop⟩
+
 instance instSMulRat : SMul ℚ (selfAdjoint R) where
   smul a x := ⟨a • (x : R), by rw [Rat.smul_def]; exact (isSelfAdjoint_ratCast a).mul x.prop⟩
 #align self_adjoint.has_qsmul selfAdjoint.instSMulRat
 
+@[simp, norm_cast] lemma val_nnqsmul (q : ℚ≥0) (x : selfAdjoint R) : ↑(q • x) = q • (x : R) := rfl
 @[simp, norm_cast] lemma val_qsmul (q : ℚ) (x : selfAdjoint R) : ↑(q • x) = q • (x : R) := rfl
 #align self_adjoint.coe_rat_smul selfAdjoint.val_qsmul
 
 instance instField : Field (selfAdjoint R) :=
   Subtype.coe_injective.field _  (selfAdjoint R).coe_zero val_one
     (selfAdjoint R).coe_add val_mul (selfAdjoint R).coe_neg (selfAdjoint R).coe_sub
-    val_inv val_div (swap (selfAdjoint R).coe_nsmul) (by intros; rfl)
-    val_qsmul val_pow val_zpow (fun _ => rfl) (fun _ => rfl) val_ratCast
+    val_inv val_div (swap (selfAdjoint R).coe_nsmul) (by intros; rfl) val_nnqsmul
+    val_qsmul val_pow val_zpow (fun _ => rfl) (fun _ => rfl) val_nnratCast val_ratCast
 
 end Field

a6ece354

chore(Field/InjSurj): Tidy (#11480)

Among other things, change the nsmul, zsmul, qsmul fields to have n/q come before x, because this matches the lemmas we want to write about them. It would be preferrable to perform the same changes to the AddMonoid/AddGroup-like typeclasses, but this is impossible with the current to_additive framework, so instead I have inserted some Function.swap at the interface between AddMonoid/AddGroup and Ring/Field.

Reduce the diff of #11203

64e5ddf0

Diff

@@ -397,7 +397,7 @@ variable [CommRing R] [StarRing R]
 instance : CommRing (selfAdjoint R) :=
   Function.Injective.commRing _ Subtype.coe_injective (selfAdjoint R).coe_zero val_one
     (selfAdjoint R).coe_add val_mul (selfAdjoint R).coe_neg (selfAdjoint R).coe_sub
-    (selfAdjoint R).coe_nsmul (selfAdjoint R).coe_zsmul val_pow
+    (by intros; rfl) (by intros; rfl) val_pow
     (fun _ => rfl) fun _ => rfl
 
 end CommRing
@@ -430,29 +430,24 @@ theorem val_zpow (x : selfAdjoint R) (z : ℤ) : ↑(x ^ z) = (x : R) ^ z :=
   rfl
 #align self_adjoint.coe_zpow selfAdjoint.val_zpow
 
-instance : RatCast (selfAdjoint R) where
-  ratCast n := ⟨n, isSelfAdjoint_ratCast n⟩
+instance instRatCast : RatCast (selfAdjoint R) where
+  ratCast q := ⟨q, isSelfAdjoint_ratCast q⟩
 
-@[simp, norm_cast]
-theorem val_ratCast (x : ℚ) : ↑(x : selfAdjoint R) = (x : R) :=
-  rfl
+@[simp, norm_cast] lemma val_ratCast (q : ℚ) : (q : selfAdjoint R) = (q : R) := rfl
 #align self_adjoint.coe_rat_cast selfAdjoint.val_ratCast
 
-instance instQSMul : SMul ℚ (selfAdjoint R) where
-  smul a x :=
-    ⟨a • (x : R), by rw [Rat.smul_def]; exact IsSelfAdjoint.mul (isSelfAdjoint_ratCast a) x.prop⟩
-#align self_adjoint.has_qsmul selfAdjoint.instQSMul
+instance instSMulRat : SMul ℚ (selfAdjoint R) where
+  smul a x := ⟨a • (x : R), by rw [Rat.smul_def]; exact (isSelfAdjoint_ratCast a).mul x.prop⟩
+#align self_adjoint.has_qsmul selfAdjoint.instSMulRat
 
-@[simp, norm_cast]
-theorem val_rat_smul (x : selfAdjoint R) (a : ℚ) : ↑(a • x) = a • (x : R) :=
-  rfl
-#align self_adjoint.coe_rat_smul selfAdjoint.val_rat_smul
+@[simp, norm_cast] lemma val_qsmul (q : ℚ) (x : selfAdjoint R) : ↑(q • x) = q • (x : R) := rfl
+#align self_adjoint.coe_rat_smul selfAdjoint.val_qsmul
 
-instance : Field (selfAdjoint R) :=
-  Function.Injective.field _ Subtype.coe_injective (selfAdjoint R).coe_zero val_one
+instance instField : Field (selfAdjoint R) :=
+  Subtype.coe_injective.field _  (selfAdjoint R).coe_zero val_one
     (selfAdjoint R).coe_add val_mul (selfAdjoint R).coe_neg (selfAdjoint R).coe_sub
-    val_inv val_div (selfAdjoint R).coe_nsmul (selfAdjoint R).coe_zsmul
-    val_rat_smul val_pow val_zpow (fun _ => rfl) (fun _ => rfl) val_ratCast
+    val_inv val_div (swap (selfAdjoint R).coe_nsmul) (by intros; rfl)
+    val_qsmul val_pow val_zpow (fun _ => rfl) (fun _ => rfl) val_ratCast
 
 end Field

a6ece354

chore: Delete Init.Data.Subtype.Basic (#11887)

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

cfc96fe7

Diff

@@ -3,7 +3,6 @@ Copyright (c) 2021 Frédéric Dupuis. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Frédéric Dupuis
 -/
-import Mathlib.Init.Data.Subtype.Basic
 import Mathlib.Algebra.Module.Basic
 import Mathlib.Algebra.Star.Pi
 import Mathlib.GroupTheory.Subgroup.Basic
@@ -359,7 +358,7 @@ theorem val_one : ↑(1 : selfAdjoint R) = (1 : R) :=
 #align self_adjoint.coe_one selfAdjoint.val_one
 
 instance [Nontrivial R] : Nontrivial (selfAdjoint R) :=
-  ⟨⟨0, 1, Subtype.ne_of_val_ne zero_ne_one⟩⟩
+  ⟨⟨0, 1, ne_of_apply_ne Subtype.val zero_ne_one⟩⟩
 
 instance : NatCast (selfAdjoint R) where
   natCast n := ⟨n, isSelfAdjoint_natCast _⟩

a6ece354

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

Empty lines were removed by executing the following Python script twice

import os
import re


# Loop through each file in the repository
for dir_path, dirs, files in os.walk('.'):
  for filename in files:
    if filename.endswith('.lean'):
      file_path = os.path.join(dir_path, filename)

      # Open the file and read its contents
      with open(file_path, 'r') as file:
        content = file.read()

      # Use a regular expression to replace sequences of "variable" lines separated by empty lines
      # with sequences without empty lines
      modified_content = re.sub(r'(variable.*\n)\n(variable(?! .* in))', r'\1\2', content)

      # Write the modified content back to the file
      with open(file_path, 'w') as file:
        file.write(modified_content)

75c86f04

Diff

@@ -115,7 +115,6 @@ theorem _root_.isSelfAdjoint_starHom_apply {F R S : Type*} [Star R] [Star S] [Fu
 section AddMonoid
 
 variable [AddMonoid R] [StarAddMonoid R]
-
 variable (R)
 
 @[simp] theorem _root_.isSelfAdjoint_zero : IsSelfAdjoint (0 : R) := star_zero R
@@ -184,7 +183,6 @@ end Semigroup
 section MulOneClass
 
 variable [MulOneClass R] [StarMul R]
-
 variable (R)
 
 @[simp] theorem _root_.isSelfAdjoint_one : IsSelfAdjoint (1 : R) :=

a6ece354

chore: add lemmas for nat literals corresponding to lemmas for nat casts (#8006)

I loogled for every occurrence of "cast", Nat and "natCast" and where the casted nat was n, and made sure there were corresponding @[simp] lemmas for 0, 1, and OfNat.ofNat n. This is necessary in general for simp confluence. Example:

import Mathlib

variable {α : Type*} [LinearOrderedRing α] (m n : ℕ) [m.AtLeastTwo] [n.AtLeastTwo]

example : ((OfNat.ofNat m : ℕ) : α) ≤ ((OfNat.ofNat n : ℕ) : α) ↔ (OfNat.ofNat m : ℕ) ≤ (OfNat.ofNat n : ℕ) := by
  simp only [Nat.cast_le] -- this `@[simp]` lemma can apply

example : ((OfNat.ofNat m : ℕ) : α) ≤ ((OfNat.ofNat n : ℕ) : α) ↔ (OfNat.ofNat m : α) ≤ (OfNat.ofNat n : α) := by
  simp only [Nat.cast_ofNat] -- and so can this one

example : (OfNat.ofNat m : α) ≤ (OfNat.ofNat n : α) ↔ (OfNat.ofNat m : ℕ) ≤ (OfNat.ofNat n : ℕ) := by
  simp -- fails! `simp` doesn't have a lemma to bridge their results. confluence issue.

As far as I know, the only file this PR leaves with ofNat gaps is PartENat.lean. #8002 is addressing that file in parallel.

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

bbe9baad

Diff

@@ -218,6 +218,12 @@ theorem _root_.isSelfAdjoint_natCast (n : ℕ) : IsSelfAdjoint (n : R) :=
   star_natCast _
 #align is_self_adjoint_nat_cast isSelfAdjoint_natCast
 
+-- See note [no_index around OfNat.ofNat]
+@[simp]
+theorem _root_.isSelfAdjoint_ofNat (n : ℕ) [n.AtLeastTwo] :
+    IsSelfAdjoint (no_index (OfNat.ofNat n : R)) :=
+  _root_.isSelfAdjoint_natCast n
+
 end Semiring
 
 section CommSemigroup

a6ece354

chore: bump aesop; update syntax (#10955)

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

46974e92

Diff

@@ -538,7 +538,7 @@ section SMul
 
 variable [Star R] [TrivialStar R] [AddCommGroup A] [StarAddMonoid A]
 
-@[aesop safe apply (rule_sets [SetLike])]
+@[aesop safe apply (rule_sets := [SetLike])]
 theorem smul_mem [Monoid R] [DistribMulAction R A] [StarModule R A] (r : R) {x : A}
     (h : x ∈ skewAdjoint A) : r • x ∈ skewAdjoint A := by
   rw [mem_iff, star_smul, star_trivial, mem_iff.mp h, smul_neg r]

a6ece354

feat: unitary elements are normal (#10778)

c63ddc25

Diff

@@ -596,6 +596,11 @@ protected instance IsStarNormal.neg [Ring R] [StarAddMonoid R] {x : R} [IsStarNo
     IsStarNormal (-x) :=
   ⟨show star (-x) * -x = -x * star (-x) by simp_rw [star_neg, neg_mul_neg, star_comm_self']⟩
 
+protected instance IsStarNormal.map {F R S : Type*} [Mul R] [Star R] [Mul S] [Star S]
+    [FunLike F R S] [MulHomClass F R S] [StarHomClass F R S] (f : F) (r : R) [hr : IsStarNormal r] :
+    IsStarNormal (f r) where
+  star_comm_self := by simpa [map_star] using congr(f $(hr.star_comm_self))
+
 -- see Note [lower instance priority]
 instance (priority := 100) TrivialStar.isStarNormal [Mul R] [StarMul R] [TrivialStar R]
     {x : R} : IsStarNormal x :=

a6ece354

refactor(Data/FunLike): use unbundled inheritance from FunLike (#8386)

The FunLike hierarchy is very big and gets scanned through each time we need a coercion (via the CoeFun instance). It looks like unbundled inheritance suits Lean 4 better here. The only class that still extends FunLike is EquivLike, since that has a custom coe_injective' field that is easier to implement. All other classes should take FunLike or EquivLike as a parameter.

Zulip thread

Important changes

Previously, morphism classes would be Type-valued and extend FunLike:

/-- `MyHomClass F A B` states that `F` is a type of `MyClass.op`-preserving morphisms.
You should extend this class when you extend `MyHom`. -/
class MyHomClass (F : Type*) (A B : outParam <| Type*) [MyClass A] [MyClass B]
  extends FunLike F A B :=
(map_op : ∀ (f : F) (x y : A), f (MyClass.op x y) = MyClass.op (f x) (f y))

After this PR, they should be Prop-valued and take FunLike as a parameter:

/-- `MyHomClass F A B` states that `F` is a type of `MyClass.op`-preserving morphisms.
You should extend this class when you extend `MyHom`. -/
class MyHomClass (F : Type*) (A B : outParam <| Type*) [MyClass A] [MyClass B]
  [FunLike F A B] : Prop :=
(map_op : ∀ (f : F) (x y : A), f (MyClass.op x y) = MyClass.op (f x) (f y))

(Note that A B stay marked as outParam even though they are not purely required to be so due to the FunLike parameter already filling them in. This is required to see through type synonyms, which is important in the category theory library. Also, I think keeping them as outParam is slightly faster.)

Similarly, MyEquivClass should take EquivLike as a parameter.

As a result, every mention of [MyHomClass F A B] should become [FunLike F A B] [MyHomClass F A B].

Remaining issues

Slower (failing) search

While overall this gives some great speedups, there are some cases that are noticeably slower. In particular, a failing application of a lemma such as map_mul is more expensive. This is due to suboptimal processing of arguments. For example:

variable [FunLike F M N] [Mul M] [Mul N] (f : F) (x : M) (y : M)

theorem map_mul [MulHomClass F M N] : f (x * y) = f x * f y

example [AddHomClass F A B] : f (x * y) = f x * f y := map_mul f _ _

Before this PR, applying map_mul f gives the goals [Mul ?M] [Mul ?N] [MulHomClass F ?M ?N]. Since M and N are out_params, [MulHomClass F ?M ?N] is synthesized first, supplies values for ?M and ?N and then the Mul M and Mul N instances can be found.

After this PR, the goals become [FunLike F ?M ?N] [Mul ?M] [Mul ?N] [MulHomClass F ?M ?N]. Now [FunLike F ?M ?N] is synthesized first, supplies values for ?M and ?N and then the Mul M and Mul N instances can be found, before trying MulHomClass F M N which fails. Since the Mul hierarchy is very big, this can be slow to fail, especially when there is no such Mul instance.

A long-term but harder to achieve solution would be to specify the order in which instance goals get solved. For example, we'd like to change the arguments to map_mul to look like [FunLike F M N] [Mul M] [Mul N] [highPriority <| MulHomClass F M N] because MulHomClass fails or succeeds much faster than the others.

As a consequence, the simpNF linter is much slower since by design it tries and fails to apply many map_ lemmas. The same issue occurs a few times in existing calls to simp [map_mul], where map_mul is tried "too soon" and fails. Thanks to the speedup of leanprover/lean4#2478 the impact is very limited, only in files that already were close to the timeout.

`simp` not firing sometimes

This affects map_smulₛₗ and related definitions. For simp lemmas Lean apparently uses a slightly different mechanism to find instances, so that rw can find every argument to map_smulₛₗ successfully but simp can't: leanprover/lean4#3701.

Missing instances due to unification failing

Especially in the category theory library, we might sometimes have a type A which is also accessible as a synonym (Bundled A hA).1. Instance synthesis doesn't always work if we have f : A →* B but x * y : (Bundled A hA).1 or vice versa. This seems to be mostly fixed by keeping A B as outParams in MulHomClass F A B. (Presumably because Lean will do a definitional check A =?= (Bundled A hA).1 instead of using the syntax in the discrimination tree.)

Workaround for issues

The timeouts can be worked around for now by specifying which map_mul we mean, either as map_mul f for some explicit f, or as e.g. MonoidHomClass.map_mul.

map_smulₛₗ not firing as simp lemma can be worked around by going back to the pre-FunLike situation and making LinearMap.map_smulₛₗ a simp lemma instead of the generic map_smulₛₗ. Writing simp [map_smulₛₗ _] also works.

Co-authored-by: Matthew Ballard <matt@mrb.email> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Scott Morrison <scott@tqft.net> Co-authored-by: Anne Baanen <Vierkantor@users.noreply.github.com>

c6a73d4f

Diff

@@ -101,15 +101,15 @@ lemma commute_iff {R : Type*} [Mul R] [StarMul R] {x y : R}
   · simpa only [star_mul, hx.star_eq, hy.star_eq] using h.symm
 
 /-- Functions in a `StarHomClass` preserve self-adjoint elements. -/
-theorem starHom_apply {F R S : Type*} [Star R] [Star S] [StarHomClass F R S] {x : R}
-    (hx : IsSelfAdjoint x) (f : F) : IsSelfAdjoint (f x) :=
+theorem starHom_apply {F R S : Type*} [Star R] [Star S] [FunLike F R S] [StarHomClass F R S]
+    {x : R} (hx : IsSelfAdjoint x) (f : F) : IsSelfAdjoint (f x) :=
   show star (f x) = f x from map_star f x ▸ congr_arg f hx
 #align is_self_adjoint.star_hom_apply IsSelfAdjoint.starHom_apply
 
 /- note: this lemma is *not* marked as `simp` so that Lean doesn't look for a `[TrivialStar R]`
 instance every time it sees `⊢ IsSelfAdjoint (f x)`, which will likely occur relatively often. -/
-theorem _root_.isSelfAdjoint_starHom_apply {F R S : Type*} [Star R] [Star S] [StarHomClass F R S]
-    [TrivialStar R] (f : F) (x : R) : IsSelfAdjoint (f x) :=
+theorem _root_.isSelfAdjoint_starHom_apply {F R S : Type*} [Star R] [Star S] [FunLike F R S]
+    [StarHomClass F R S] [TrivialStar R] (f : F) (x : R) : IsSelfAdjoint (f x) :=
   (IsSelfAdjoint.all x).starHom_apply f
 
 section AddMonoid

a6ece354

chore: reduce imports (#9830)

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

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

f4c4ca61

Diff

@@ -3,9 +3,10 @@ Copyright (c) 2021 Frédéric Dupuis. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Frédéric Dupuis
 -/
+import Mathlib.Init.Data.Subtype.Basic
+import Mathlib.Algebra.Module.Basic
 import Mathlib.Algebra.Star.Pi
 import Mathlib.GroupTheory.Subgroup.Basic
-import Mathlib.Init.Data.Subtype.Basic
 
 #align_import algebra.star.self_adjoint from "leanprover-community/mathlib"@"a6ece35404f60597c651689c1b46ead86de5ac1b"

a6ece354

feat: add isStarNormal_neg (#9748)

Also rename isStarNormal_star_self to isStarNormal_star.

e38a8499

Diff

@@ -586,10 +586,14 @@ instance isStarNormal_one [MulOneClass R] [StarMul R] : IsStarNormal (1 : R) :=
   ⟨by simp only [Commute.refl, star_comm_self, star_one]⟩
 #align is_star_normal_one isStarNormal_one
 
-instance isStarNormal_star_self [Mul R] [StarMul R] {x : R} [IsStarNormal x] :
+protected instance IsStarNormal.star [Mul R] [StarMul R] {x : R} [IsStarNormal x] :
     IsStarNormal (star x) :=
   ⟨show star (star x) * star x = star x * star (star x) by rw [star_star, star_comm_self']⟩
-#align is_star_normal_star_self isStarNormal_star_self
+#align is_star_normal_star_self IsStarNormal.star
+
+protected instance IsStarNormal.neg [Ring R] [StarAddMonoid R] {x : R} [IsStarNormal x] :
+    IsStarNormal (-x) :=
+  ⟨show star (-x) * -x = -x * star (-x) by simp_rw [star_neg, neg_mul_neg, star_comm_self']⟩
 
 -- see Note [lower instance priority]
 instance (priority := 100) TrivialStar.isStarNormal [Mul R] [StarMul R] [TrivialStar R]

a6ece354

feat: Every star ring is a Nat-star module (#9470)

and other basic star lemmas

From LeanAPAP

83b4d8db

Diff

@@ -3,7 +3,7 @@ Copyright (c) 2021 Frédéric Dupuis. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Frédéric Dupuis
 -/
-import Mathlib.Algebra.Star.Basic
+import Mathlib.Algebra.Star.Pi
 import Mathlib.GroupTheory.Subgroup.Basic
 import Mathlib.Init.Data.Subtype.Basic
 
@@ -40,6 +40,7 @@ We also define `IsStarNormal R`, a `Prop` that states that an element `x` satisf
 
 -/
 
+open Function
 
 variable {R A : Type*}
 
@@ -116,8 +117,7 @@ variable [AddMonoid R] [StarAddMonoid R]
 
 variable (R)
 
-theorem _root_.isSelfAdjoint_zero : IsSelfAdjoint (0 : R) :=
-  star_zero R
+@[simp] theorem _root_.isSelfAdjoint_zero : IsSelfAdjoint (0 : R) := star_zero R
 #align is_self_adjoint_zero isSelfAdjoint_zero
 
 variable {R}
@@ -186,7 +186,7 @@ variable [MulOneClass R] [StarMul R]
 
 variable (R)
 
-theorem _root_.isSelfAdjoint_one : IsSelfAdjoint (1 : R) :=
+@[simp] theorem _root_.isSelfAdjoint_one : IsSelfAdjoint (1 : R) :=
   star_one R
 #align is_self_adjoint_one isSelfAdjoint_one
 
@@ -229,6 +229,15 @@ theorem mul {x y : R} (hx : IsSelfAdjoint x) (hy : IsSelfAdjoint y) : IsSelfAdjo
 
 end CommSemigroup
 
+section CommSemiring
+variable {α : Type*} [CommSemiring α] [StarRing α] {a : α}
+
+open scoped ComplexConjugate
+
+lemma conj_eq (ha : IsSelfAdjoint a) : conj a = a := ha.star_eq
+
+end CommSemiring
+
 section Ring
 
 variable [Ring R] [StarRing R]
@@ -593,3 +602,13 @@ instance (priority := 100) CommMonoid.isStarNormal [CommMonoid R] [StarMul R] {x
     IsStarNormal x :=
   ⟨mul_comm _ _⟩
 #align comm_monoid.is_star_normal CommMonoid.isStarNormal
+
+
+namespace Pi
+variable {ι : Type*} {α : ι → Type*} [∀ i, Star (α i)] {f : ∀ i, α i}
+
+protected lemma isSelfAdjoint : IsSelfAdjoint f ↔ ∀ i, IsSelfAdjoint (f i) := funext_iff
+
+alias ⟨_root_.IsSelfAdjoint.apply, _⟩ := Pi.isSelfAdjoint
+
+end Pi

a6ece354

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

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

Lemmas like pow_mem should be included in the rule set:

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

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

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

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

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

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

214e72fd

Diff

@@ -528,6 +528,7 @@ section SMul
 
 variable [Star R] [TrivialStar R] [AddCommGroup A] [StarAddMonoid A]
 
+@[aesop safe apply (rule_sets [SetLike])]
 theorem smul_mem [Monoid R] [DistribMulAction R A] [StarModule R A] (r : R) {x : A}
     (h : x ∈ skewAdjoint A) : r • x ∈ skewAdjoint A := by
   rw [mem_iff, star_smul, star_trivial, mem_iff.mp h, smul_neg r]

a6ece354

feat: self-adjoint elements commute iff their product is self-adjoint (#7318)

d1b87450

Diff

@@ -91,6 +91,13 @@ theorem mul_star_self [Mul R] [StarMul R] (x : R) : IsSelfAdjoint (x * star x) :
   simpa only [star_star] using star_mul_self (star x)
 #align is_self_adjoint.mul_star_self IsSelfAdjoint.mul_star_self
 
+/-- Self-adjoint elements commute if and only if their product is self-adjoint. -/
+lemma commute_iff {R : Type*} [Mul R] [StarMul R] {x y : R}
+    (hx : IsSelfAdjoint x) (hy : IsSelfAdjoint y) : Commute x y ↔ IsSelfAdjoint (x * y) := by
+  refine ⟨fun h ↦ ?_, fun h ↦ ?_⟩
+  · rw [isSelfAdjoint_iff, star_mul, hx.star_eq, hy.star_eq, h.eq]
+  · simpa only [star_mul, hx.star_eq, hy.star_eq] using h.symm
+
 /-- Functions in a `StarHomClass` preserve self-adjoint elements. -/
 theorem starHom_apply {F R S : Type*} [Star R] [Star S] [StarHomClass F R S] {x : R}
     (hx : IsSelfAdjoint x) (f : F) : IsSelfAdjoint (f x) :=

a6ece354

refactor(Algebra/Star/*): Allow for star operation on non-associative algebras (#6562)

Typically a * operation on a mathematical structure R equipped with a multiplication is an involutive anti-automorphism i.e.

∀ r s : R, star (r * s) = star s * star r

Currently mathlib defines a class StarSemigroup to be a semigroup satisfying this property. However, the requirement for the multiplication to be associative is unnecessarily restrictive. There are important classes of star-algebra which are not associative (e.g. JB*-algebras).

This PR removes the requirement for a StarSemigroup to be a semigroup, merely requiring it to have a multiplication.

I've changed the name from StarSemigroup to StarMul since it's no longer a semigroup.

Zulip discussion

Previously opened as a mathlib PR https://github.com/leanprover-community/mathlib/pull/17949

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

85c04e73

Diff

@@ -82,12 +82,12 @@ theorem star_iff [InvolutiveStar R] {x : R} : IsSelfAdjoint (star x) ↔ IsSelfA
 #align is_self_adjoint.star_iff IsSelfAdjoint.star_iff
 
 @[simp]
-theorem star_mul_self [Semigroup R] [StarSemigroup R] (x : R) : IsSelfAdjoint (star x * x) := by
+theorem star_mul_self [Mul R] [StarMul R] (x : R) : IsSelfAdjoint (star x * x) := by
   simp only [IsSelfAdjoint, star_mul, star_star]
 #align is_self_adjoint.star_mul_self IsSelfAdjoint.star_mul_self
 
 @[simp]
-theorem mul_star_self [Semigroup R] [StarSemigroup R] (x : R) : IsSelfAdjoint (x * star x) := by
+theorem mul_star_self [Mul R] [StarMul R] (x : R) : IsSelfAdjoint (x * star x) := by
   simpa only [star_star] using star_mul_self (star x)
 #align is_self_adjoint.mul_star_self IsSelfAdjoint.mul_star_self
 
@@ -157,7 +157,7 @@ end AddCommMonoid
 
 section Semigroup
 
-variable [Semigroup R] [StarSemigroup R]
+variable [Semigroup R] [StarMul R]
 
 theorem conjugate {x : R} (hx : IsSelfAdjoint x) (z : R) : IsSelfAdjoint (z * x * star z) := by
   simp only [isSelfAdjoint_iff, star_mul, star_star, mul_assoc, hx.star_eq]
@@ -173,9 +173,9 @@ theorem isStarNormal {x : R} (hx : IsSelfAdjoint x) : IsStarNormal x :=
 
 end Semigroup
 
-section Monoid
+section MulOneClass
 
-variable [Monoid R] [StarSemigroup R]
+variable [MulOneClass R] [StarMul R]
 
 variable (R)
 
@@ -183,7 +183,11 @@ theorem _root_.isSelfAdjoint_one : IsSelfAdjoint (1 : R) :=
   star_one R
 #align is_self_adjoint_one isSelfAdjoint_one
 
-variable {R}
+end MulOneClass
+
+section Monoid
+
+variable [Monoid R] [StarMul R]
 
 theorem pow {x : R} (hx : IsSelfAdjoint x) (n : ℕ) : IsSelfAdjoint (x ^ n) := by
   simp only [isSelfAdjoint_iff, star_pow, hx.star_eq]
@@ -210,7 +214,7 @@ end Semiring
 
 section CommSemigroup
 
-variable [CommSemigroup R] [StarSemigroup R]
+variable [CommSemigroup R] [StarMul R]
 
 theorem mul {x y : R} (hx : IsSelfAdjoint x) (hy : IsSelfAdjoint y) : IsSelfAdjoint (x * y) := by
   simp only [isSelfAdjoint_iff, star_mul', hx.star_eq, hy.star_eq]
@@ -561,23 +565,23 @@ instance isStarNormal_zero [Semiring R] [StarRing R] : IsStarNormal (0 : R) :=
   ⟨by simp only [Commute.refl, star_comm_self, star_zero]⟩
 #align is_star_normal_zero isStarNormal_zero
 
-instance isStarNormal_one [Monoid R] [StarSemigroup R] : IsStarNormal (1 : R) :=
+instance isStarNormal_one [MulOneClass R] [StarMul R] : IsStarNormal (1 : R) :=
   ⟨by simp only [Commute.refl, star_comm_self, star_one]⟩
 #align is_star_normal_one isStarNormal_one
 
-instance isStarNormal_star_self [Monoid R] [StarSemigroup R] {x : R} [IsStarNormal x] :
+instance isStarNormal_star_self [Mul R] [StarMul R] {x : R} [IsStarNormal x] :
     IsStarNormal (star x) :=
   ⟨show star (star x) * star x = star x * star (star x) by rw [star_star, star_comm_self']⟩
 #align is_star_normal_star_self isStarNormal_star_self
 
 -- see Note [lower instance priority]
-instance (priority := 100) TrivialStar.isStarNormal [Monoid R] [StarSemigroup R] [TrivialStar R]
+instance (priority := 100) TrivialStar.isStarNormal [Mul R] [StarMul R] [TrivialStar R]
     {x : R} : IsStarNormal x :=
   ⟨by rw [star_trivial]⟩
 #align has_trivial_star.is_star_normal TrivialStar.isStarNormal
 
 -- see Note [lower instance priority]
-instance (priority := 100) CommMonoid.isStarNormal [CommMonoid R] [StarSemigroup R] {x : R} :
+instance (priority := 100) CommMonoid.isStarNormal [CommMonoid R] [StarMul R] {x : R} :
     IsStarNormal x :=
   ⟨mul_comm _ _⟩
 #align comm_monoid.is_star_normal CommMonoid.isStarNormal

a6ece354

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

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

This has nice performance benefits.

32de3f67

Diff

@@ -41,7 +41,7 @@ We also define `IsStarNormal R`, a `Prop` that states that an element `x` satisf
 -/
 
 
-variable {R A : Type _}
+variable {R A : Type*}
 
 /-- An element is self-adjoint if it is equal to its star. -/
 def IsSelfAdjoint [Star R] (x : R) : Prop :=
@@ -92,14 +92,14 @@ theorem mul_star_self [Semigroup R] [StarSemigroup R] (x : R) : IsSelfAdjoint (x
 #align is_self_adjoint.mul_star_self IsSelfAdjoint.mul_star_self
 
 /-- Functions in a `StarHomClass` preserve self-adjoint elements. -/
-theorem starHom_apply {F R S : Type _} [Star R] [Star S] [StarHomClass F R S] {x : R}
+theorem starHom_apply {F R S : Type*} [Star R] [Star S] [StarHomClass F R S] {x : R}
     (hx : IsSelfAdjoint x) (f : F) : IsSelfAdjoint (f x) :=
   show star (f x) = f x from map_star f x ▸ congr_arg f hx
 #align is_self_adjoint.star_hom_apply IsSelfAdjoint.starHom_apply
 
 /- note: this lemma is *not* marked as `simp` so that Lean doesn't look for a `[TrivialStar R]`
 instance every time it sees `⊢ IsSelfAdjoint (f x)`, which will likely occur relatively often. -/
-theorem _root_.isSelfAdjoint_starHom_apply {F R S : Type _} [Star R] [Star S] [StarHomClass F R S]
+theorem _root_.isSelfAdjoint_starHom_apply {F R S : Type*} [Star R] [Star S] [StarHomClass F R S]
     [TrivialStar R] (f : F) (x : R) : IsSelfAdjoint (f x) :=
   (IsSelfAdjoint.all x).starHom_apply f

a6ece354

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

depends on: #5966

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

89aa3a3b

Diff

@@ -2,16 +2,13 @@
 Copyright (c) 2021 Frédéric Dupuis. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Frédéric Dupuis
-
-! This file was ported from Lean 3 source module algebra.star.self_adjoint
-! leanprover-community/mathlib commit a6ece35404f60597c651689c1b46ead86de5ac1b
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Algebra.Star.Basic
 import Mathlib.GroupTheory.Subgroup.Basic
 import Mathlib.Init.Data.Subtype.Basic
 
+#align_import algebra.star.self_adjoint from "leanprover-community/mathlib"@"a6ece35404f60597c651689c1b46ead86de5ac1b"
+
 /-!
 # Self-adjoint, skew-adjoint and normal elements of a star additive group

a6ece354

feat: add two basic lemmas about selfAdjoint elements (#5169)

selfAdjoint elements are automatically normal
the image of an element under a star-preserving map in a space with a TrivialStar is self-adjoint

7c90ee69

Diff

@@ -100,6 +100,12 @@ theorem starHom_apply {F R S : Type _} [Star R] [Star S] [StarHomClass F R S] {x
   show star (f x) = f x from map_star f x ▸ congr_arg f hx
 #align is_self_adjoint.star_hom_apply IsSelfAdjoint.starHom_apply
 
+/- note: this lemma is *not* marked as `simp` so that Lean doesn't look for a `[TrivialStar R]`
+instance every time it sees `⊢ IsSelfAdjoint (f x)`, which will likely occur relatively often. -/
+theorem _root_.isSelfAdjoint_starHom_apply {F R S : Type _} [Star R] [Star S] [StarHomClass F R S]
+    [TrivialStar R] (f : F) (x : R) : IsSelfAdjoint (f x) :=
+  (IsSelfAdjoint.all x).starHom_apply f
+
 section AddMonoid
 
 variable [AddMonoid R] [StarAddMonoid R]
@@ -314,6 +320,10 @@ instance : Inhabited (selfAdjoint R) :=
 
 end AddGroup
 
+instance isStarNormal [NonUnitalRing R] [StarRing R] (x : selfAdjoint R) :
+    IsStarNormal (x : R) :=
+  x.prop.isStarNormal
+
 section Ring
 
 variable [Ring R] [StarRing R]

a6ece354

chore: whitespace changes remaining after merging lean#2074 workarounds (#4032)

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Mauricio Collares <mauricio@collares.org>

674cdb10

Diff

@@ -329,8 +329,8 @@ theorem val_one : ↑(1 : selfAdjoint R) = (1 : R) :=
 instance [Nontrivial R] : Nontrivial (selfAdjoint R) :=
   ⟨⟨0, 1, Subtype.ne_of_val_ne zero_ne_one⟩⟩
 
-instance : NatCast (selfAdjoint R) :=
-  ⟨fun n => ⟨n, isSelfAdjoint_natCast _⟩⟩
+instance : NatCast (selfAdjoint R) where
+  natCast n := ⟨n, isSelfAdjoint_natCast _⟩
 
 instance : IntCast (selfAdjoint R) where
   intCast n := ⟨n, isSelfAdjoint_intCast _⟩
@@ -375,21 +375,24 @@ section Field
 
 variable [Field R] [StarRing R]
 
-instance : Inv (selfAdjoint R) where inv x := ⟨x.val⁻¹, x.prop.inv⟩
+instance : Inv (selfAdjoint R) where
+  inv x := ⟨x.val⁻¹, x.prop.inv⟩
 
 @[simp, norm_cast]
 theorem val_inv (x : selfAdjoint R) : ↑x⁻¹ = (x : R)⁻¹ :=
   rfl
 #align self_adjoint.coe_inv selfAdjoint.val_inv
 
-instance : Div (selfAdjoint R) where div x y := ⟨x / y, x.prop.div y.prop⟩
+instance : Div (selfAdjoint R) where
+  div x y := ⟨x / y, x.prop.div y.prop⟩
 
 @[simp, norm_cast]
 theorem val_div (x y : selfAdjoint R) : ↑(x / y) = (x / y : R) :=
   rfl
 #align self_adjoint.coe_div selfAdjoint.val_div
 
-instance : Pow (selfAdjoint R) ℤ where pow x z := ⟨(x : R) ^ z, x.prop.zpow z⟩
+instance : Pow (selfAdjoint R) ℤ where
+  pow x z := ⟨(x : R) ^ z, x.prop.zpow z⟩
 
 @[simp, norm_cast]
 theorem val_zpow (x : selfAdjoint R) (z : ℤ) : ↑(x ^ z) = (x : R) ^ z :=

a6ece354

chore: delete 2074 references (#4030)

1877b122

Diff

@@ -329,9 +329,8 @@ theorem val_one : ↑(1 : selfAdjoint R) = (1 : R) :=
 instance [Nontrivial R] : Nontrivial (selfAdjoint R) :=
   ⟨⟨0, 1, Subtype.ne_of_val_ne zero_ne_one⟩⟩
 
-instance : NatCast (selfAdjoint R) where
-  -- porting note: `(_)` works around lean4#2074
-  natCast n := ⟨n, @isSelfAdjoint_natCast _ _ (_) n⟩
+instance : NatCast (selfAdjoint R) :=
+  ⟨fun n => ⟨n, isSelfAdjoint_natCast _⟩⟩
 
 instance : IntCast (selfAdjoint R) where
   intCast n := ⟨n, isSelfAdjoint_intCast _⟩
@@ -376,27 +375,21 @@ section Field
 
 variable [Field R] [StarRing R]
 
-instance : Inv (selfAdjoint R) where
-  -- porting note: `(_)` works around lean4#2074
-  inv x := ⟨x.val⁻¹, @IsSelfAdjoint.inv _ _ (_) _ x.prop⟩
+instance : Inv (selfAdjoint R) where inv x := ⟨x.val⁻¹, x.prop.inv⟩
 
 @[simp, norm_cast]
 theorem val_inv (x : selfAdjoint R) : ↑x⁻¹ = (x : R)⁻¹ :=
   rfl
 #align self_adjoint.coe_inv selfAdjoint.val_inv
 
-instance : Div (selfAdjoint R) where
-  -- porting note: `(_)` works around lean4#2074
-  div x y := ⟨x / y, @IsSelfAdjoint.div _ _ (_) _ _ x.prop y.prop⟩
+instance : Div (selfAdjoint R) where div x y := ⟨x / y, x.prop.div y.prop⟩
 
 @[simp, norm_cast]
 theorem val_div (x y : selfAdjoint R) : ↑(x / y) = (x / y : R) :=
   rfl
 #align self_adjoint.coe_div selfAdjoint.val_div
 
-instance : Pow (selfAdjoint R) ℤ where
-  -- porting note: `(_)` works around lean4#2074
-  pow x z := ⟨(x : R) ^ z, @IsSelfAdjoint.zpow _ _ (_) _ x.prop z⟩
+instance : Pow (selfAdjoint R) ℤ where pow x z := ⟨(x : R) ^ z, x.prop.zpow z⟩
 
 @[simp, norm_cast]
 theorem val_zpow (x : selfAdjoint R) (z : ℤ) : ↑(x ^ z) = (x : R) ^ z :=

a6ece354

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

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

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

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

a6e1045f

Diff

@@ -364,7 +364,6 @@ section CommRing
 
 variable [CommRing R] [StarRing R]
 
-set_option synthInstance.etaExperiment true in
 instance : CommRing (selfAdjoint R) :=
   Function.Injective.commRing _ Subtype.coe_injective (selfAdjoint R).coe_zero val_one
     (selfAdjoint R).coe_add val_mul (selfAdjoint R).coe_neg (selfAdjoint R).coe_sub
@@ -404,7 +403,6 @@ theorem val_zpow (x : selfAdjoint R) (z : ℤ) : ↑(x ^ z) = (x : R) ^ z :=
   rfl
 #align self_adjoint.coe_zpow selfAdjoint.val_zpow
 
-set_option synthInstance.etaExperiment true in
 instance : RatCast (selfAdjoint R) where
   ratCast n := ⟨n, isSelfAdjoint_ratCast n⟩
 
@@ -413,7 +411,6 @@ theorem val_ratCast (x : ℚ) : ↑(x : selfAdjoint R) = (x : R) :=
   rfl
 #align self_adjoint.coe_rat_cast selfAdjoint.val_ratCast
 
-set_option synthInstance.etaExperiment true in
 instance instQSMul : SMul ℚ (selfAdjoint R) where
   smul a x :=
     ⟨a • (x : R), by rw [Rat.smul_def]; exact IsSelfAdjoint.mul (isSelfAdjoint_ratCast a) x.prop⟩
@@ -424,7 +421,6 @@ theorem val_rat_smul (x : selfAdjoint R) (a : ℚ) : ↑(a • x) = a • (x : R
   rfl
 #align self_adjoint.coe_rat_smul selfAdjoint.val_rat_smul
 
-set_option synthInstance.etaExperiment true in
 instance : Field (selfAdjoint R) :=
   Function.Injective.field _ Subtype.coe_injective (selfAdjoint R).coe_zero val_one
     (selfAdjoint R).coe_add val_mul (selfAdjoint R).coe_neg (selfAdjoint R).coe_sub

a6ece354

chore(*): tweak priorities for linear algebra (#3840)

We make sure that the canonical path from NonAssocSemiring to Ring passes through Semiring, as this is a path which is followed all the time in linear algebra where the defining semilinear map σ : R →+* S depends on the NonAssocSemiring structure of R and S while the module definition depends on the Semiring structure.

Tt is not currently possible to adjust priorities by hand (see lean4#2115). Instead, the last declared instance is used, so we make sure that Semiring is declared after NonAssocRing, so that Semiring -> NonAssocSemiring is tried before NonAssocRing -> NonAssocSemiring.

0d22228a

Diff

@@ -364,6 +364,7 @@ section CommRing
 
 variable [CommRing R] [StarRing R]
 
+set_option synthInstance.etaExperiment true in
 instance : CommRing (selfAdjoint R) :=
   Function.Injective.commRing _ Subtype.coe_injective (selfAdjoint R).coe_zero val_one
     (selfAdjoint R).coe_add val_mul (selfAdjoint R).coe_neg (selfAdjoint R).coe_sub
@@ -403,6 +404,7 @@ theorem val_zpow (x : selfAdjoint R) (z : ℤ) : ↑(x ^ z) = (x : R) ^ z :=
   rfl
 #align self_adjoint.coe_zpow selfAdjoint.val_zpow
 
+set_option synthInstance.etaExperiment true in
 instance : RatCast (selfAdjoint R) where
   ratCast n := ⟨n, isSelfAdjoint_ratCast n⟩
 
@@ -411,6 +413,7 @@ theorem val_ratCast (x : ℚ) : ↑(x : selfAdjoint R) = (x : R) :=
   rfl
 #align self_adjoint.coe_rat_cast selfAdjoint.val_ratCast
 
+set_option synthInstance.etaExperiment true in
 instance instQSMul : SMul ℚ (selfAdjoint R) where
   smul a x :=
     ⟨a • (x : R), by rw [Rat.smul_def]; exact IsSelfAdjoint.mul (isSelfAdjoint_ratCast a) x.prop⟩
@@ -421,6 +424,7 @@ theorem val_rat_smul (x : selfAdjoint R) (a : ℚ) : ↑(a • x) = a • (x : R
   rfl
 #align self_adjoint.coe_rat_smul selfAdjoint.val_rat_smul
 
+set_option synthInstance.etaExperiment true in
 instance : Field (selfAdjoint R) :=
   Function.Injective.field _ Subtype.coe_injective (selfAdjoint R).coe_zero val_one
     (selfAdjoint R).coe_add val_mul (selfAdjoint R).coe_neg (selfAdjoint R).coe_sub

a6ece354

chore: forward-port leanprover-community/mathlib#18687 (#3202)

This change was already applied in a previous forward-port in order to fix compilation. The porting note can now be removed, since mathlib3 now contains the same generalization.

algebra.star.self_adjoint@9abfa6f0727d5adc99067e325e15d1a9de17fd8e..a6ece35404f60597c651689c1b46ead86de5ac1b

fcca249d

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Frédéric Dupuis
 
 ! This file was ported from Lean 3 source module algebra.star.self_adjoint
-! leanprover-community/mathlib commit 9abfa6f0727d5adc99067e325e15d1a9de17fd8e
+! leanprover-community/mathlib commit a6ece35404f60597c651689c1b46ead86de5ac1b
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -252,7 +252,6 @@ end DivisionRing
 
 section Semifield
 
--- porting note: generalize to `Semifield` to fix lean4#2074-related errors
 variable [Semifield R] [StarRing R]
 
 theorem div {x y : R} (hx : IsSelfAdjoint x) (hy : IsSelfAdjoint y) : IsSelfAdjoint (x / y) := by

9abfa6f0

chore: re-port Mathlib.Algebra.Star.SelfAdjoint (#3159)

This file was sufficiently far out of sync that it seemed sensible to just report it.

A fresh output from mathport is included as a first commit; making it possible to diff both against the version in mathlib, and the version from mathlib.

The change to Mathlib.Algebra.Star.Module was forgotten in #2926.

10563d10

Diff

@@ -4,12 +4,13 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Frédéric Dupuis
 
 ! This file was ported from Lean 3 source module algebra.star.self_adjoint
-! leanprover-community/mathlib commit f93c11933efbc3c2f0299e47b8ff83e9b539cbf6
+! leanprover-community/mathlib commit 9abfa6f0727d5adc99067e325e15d1a9de17fd8e
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
 import Mathlib.Algebra.Star.Basic
 import Mathlib.GroupTheory.Subgroup.Basic
+import Mathlib.Init.Data.Subtype.Basic
 
 /-!
 # Self-adjoint, skew-adjoint and normal elements of a star additive group
@@ -29,13 +30,14 @@ We also define `IsStarNormal R`, a `Prop` that states that an element `x` satisf
   and not `Module (selfAdjoint ℂ) (selfAdjoint R)`. We solve this issue by adding the typeclass
   `[TrivialStar R₃]`, of which `ℝ` is an instance (registered in `Data/Real/Basic`), and then
   add a `[Module R₃ (selfAdjoint R)]` instance whenever we have
-  `[module R₃ R] [TrivialStar R₃]`. (Another approach would have been to define
-  `[starInvariantScalars R₃ R]` to express the fact that `star (x • v) = x • star v`, but
+  `[Module R₃ R] [TrivialStar R₃]`. (Another approach would have been to define
+  `[StarInvariantScalars R₃ R]` to express the fact that `star (x • v) = x • star v`, but
   this typeclass would have the disadvantage of taking two type arguments.)
 
 ## TODO
 
-* Define `fun z x ↦ z * x * star z` (i.e. conjugation by `z`) as a monoid action of `R` on `R`
+* Define `IsSkewAdjoint` to match `IsSelfAdjoint`.
+* Define `fun z x => z * x * star z` (i.e. conjugation by `z`) as a monoid action of `R` on `R`
   (similar to the existing `ConjAct` for groups), and then state the fact that `selfAdjoint R` is
   invariant under it.
 
@@ -63,6 +65,12 @@ theorem star_comm_self' [Mul R] [Star R] (x : R) [IsStarNormal x] : star x * x =
 
 namespace IsSelfAdjoint
 
+-- named to match `Commute.allₓ`
+/-- All elements are self-adjoint when `star` is trivial. -/
+theorem all [Star R] [TrivialStar R] (r : R) : IsSelfAdjoint r :=
+  star_trivial _
+#align is_self_adjoint.all IsSelfAdjoint.all
+
 theorem star_eq [Star R] {x : R} (hx : IsSelfAdjoint x) : star x = x :=
   hx
 #align is_self_adjoint.star_eq IsSelfAdjoint.star_eq
@@ -92,9 +100,9 @@ theorem starHom_apply {F R S : Type _} [Star R] [Star S] [StarHomClass F R S] {x
   show star (f x) = f x from map_star f x ▸ congr_arg f hx
 #align is_self_adjoint.star_hom_apply IsSelfAdjoint.starHom_apply
 
-section AddGroup
+section AddMonoid
 
-variable [AddGroup R] [StarAddMonoid R]
+variable [AddMonoid R] [StarAddMonoid R]
 
 variable (R)
 
@@ -108,6 +116,18 @@ theorem add {x y : R} (hx : IsSelfAdjoint x) (hy : IsSelfAdjoint y) : IsSelfAdjo
   simp only [isSelfAdjoint_iff, star_add, hx.star_eq, hy.star_eq]
 #align is_self_adjoint.add IsSelfAdjoint.add
 
+set_option linter.deprecated false in
+@[deprecated]
+theorem bit0 {x : R} (hx : IsSelfAdjoint x) : IsSelfAdjoint (bit0 x) := by
+  simp only [isSelfAdjoint_iff, star_bit0, hx.star_eq]
+#align is_self_adjoint.bit0 IsSelfAdjoint.bit0
+
+end AddMonoid
+
+section AddGroup
+
+variable [AddGroup R] [StarAddMonoid R]
+
 theorem neg {x : R} (hx : IsSelfAdjoint x) : IsSelfAdjoint (-x) := by
   simp only [isSelfAdjoint_iff, star_neg, hx.star_eq]
 #align is_self_adjoint.neg IsSelfAdjoint.neg
@@ -116,17 +136,25 @@ theorem sub {x y : R} (hx : IsSelfAdjoint x) (hy : IsSelfAdjoint y) : IsSelfAdjo
   simp only [isSelfAdjoint_iff, star_sub, hx.star_eq, hy.star_eq]
 #align is_self_adjoint.sub IsSelfAdjoint.sub
 
-set_option linter.deprecated false in
-@[deprecated]
-theorem bit0 {x : R} (hx : IsSelfAdjoint x) : IsSelfAdjoint (bit0 x) := by
-  simp only [isSelfAdjoint_iff, star_bit0, hx.star_eq]
-#align is_self_adjoint.bit0 IsSelfAdjoint.bit0
-
 end AddGroup
 
-section NonUnitalSemiring
+section AddCommMonoid
+
+variable [AddCommMonoid R] [StarAddMonoid R]
+
+theorem _root_.isSelfAdjoint_add_star_self (x : R) : IsSelfAdjoint (x + star x) := by
+  simp only [isSelfAdjoint_iff, add_comm, star_add, star_star]
+#align is_self_adjoint_add_star_self isSelfAdjoint_add_star_self
 
-variable [NonUnitalSemiring R] [StarRing R]
+theorem _root_.isSelfAdjoint_star_add_self (x : R) : IsSelfAdjoint (star x + x) := by
+  simp only [isSelfAdjoint_iff, add_comm, star_add, star_star]
+#align is_self_adjoint_star_add_self isSelfAdjoint_star_add_self
+
+end AddCommMonoid
+
+section Semigroup
+
+variable [Semigroup R] [StarSemigroup R]
 
 theorem conjugate {x : R} (hx : IsSelfAdjoint x) (z : R) : IsSelfAdjoint (z * x * star z) := by
   simp only [isSelfAdjoint_iff, star_mul, star_star, mul_assoc, hx.star_eq]
@@ -136,15 +164,15 @@ theorem conjugate' {x : R} (hx : IsSelfAdjoint x) (z : R) : IsSelfAdjoint (star
   simp only [isSelfAdjoint_iff, star_mul, star_star, mul_assoc, hx.star_eq]
 #align is_self_adjoint.conjugate' IsSelfAdjoint.conjugate'
 
-theorem isStarNormal {x : R} (hx : IsSelfAdjoint x) : IsStarNormal x where
-  star_comm_self := show star x * x = x * star x by simp only [hx.star_eq]
+theorem isStarNormal {x : R} (hx : IsSelfAdjoint x) : IsStarNormal x :=
+  ⟨by simp only [Commute, SemiconjBy, hx.star_eq]⟩
 #align is_self_adjoint.is_star_normal IsSelfAdjoint.isStarNormal
 
-end NonUnitalSemiring
+end Semigroup
 
-section Ring
+section Monoid
 
-variable [Ring R] [StarRing R]
+variable [Monoid R] [StarSemigroup R]
 
 variable (R)
 
@@ -154,60 +182,91 @@ theorem _root_.isSelfAdjoint_one : IsSelfAdjoint (1 : R) :=
 
 variable {R}
 
+theorem pow {x : R} (hx : IsSelfAdjoint x) (n : ℕ) : IsSelfAdjoint (x ^ n) := by
+  simp only [isSelfAdjoint_iff, star_pow, hx.star_eq]
+#align is_self_adjoint.pow IsSelfAdjoint.pow
+
+end Monoid
+
+section Semiring
+
+variable [Semiring R] [StarRing R]
+
 set_option linter.deprecated false in
 @[deprecated]
 theorem bit1 {x : R} (hx : IsSelfAdjoint x) : IsSelfAdjoint (bit1 x) := by
-  -- Porting note: added
-  let inst : StarRing R := ‹_›
-  rw [isSelfAdjoint_iff, @star_bit1 _ _ inst, hx.star_eq]
+  simp only [isSelfAdjoint_iff, star_bit1, hx.star_eq]
 #align is_self_adjoint.bit1 IsSelfAdjoint.bit1
 
-theorem pow {x : R} (hx : IsSelfAdjoint x) (n : ℕ) : IsSelfAdjoint (x ^ n) := by
-  simp only [isSelfAdjoint_iff, star_pow, hx.star_eq]
-#align is_self_adjoint.pow IsSelfAdjoint.pow
+@[simp]
+theorem _root_.isSelfAdjoint_natCast (n : ℕ) : IsSelfAdjoint (n : R) :=
+  star_natCast _
+#align is_self_adjoint_nat_cast isSelfAdjoint_natCast
 
-end Ring
+end Semiring
 
-section NonUnitalCommRing
+section CommSemigroup
 
-variable [NonUnitalCommRing R] [StarRing R]
+variable [CommSemigroup R] [StarSemigroup R]
 
 theorem mul {x y : R} (hx : IsSelfAdjoint x) (hy : IsSelfAdjoint y) : IsSelfAdjoint (x * y) := by
   simp only [isSelfAdjoint_iff, star_mul', hx.star_eq, hy.star_eq]
 #align is_self_adjoint.mul IsSelfAdjoint.mul
 
-end NonUnitalCommRing
+end CommSemigroup
 
-section Field
+section Ring
 
-variable [Field R] [StarRing R]
+variable [Ring R] [StarRing R]
 
-theorem inv {x : R} (hx : IsSelfAdjoint x) : IsSelfAdjoint x⁻¹ :=
-  -- porting note: hack for lean4#2074, remove after forward-porting other changes to this file
-  set_option synthInstance.etaExperiment true in by
-    simp only [isSelfAdjoint_iff, star_inv', hx.star_eq]
-#align is_self_adjoint.inv IsSelfAdjoint.inv
+@[simp]
+theorem _root_.isSelfAdjoint_intCast (z : ℤ) : IsSelfAdjoint (z : R) :=
+  star_intCast _
+#align is_self_adjoint_int_cast isSelfAdjoint_intCast
 
-theorem div {x y : R} (hx : IsSelfAdjoint x) (hy : IsSelfAdjoint y) : IsSelfAdjoint (x / y) :=
-  -- porting note: hack for lean4#2074, remove after forward-porting other changes to this file
-  set_option synthInstance.etaExperiment true in by
-    simp only [isSelfAdjoint_iff, star_div', hx.star_eq, hy.star_eq]
-#align is_self_adjoint.div IsSelfAdjoint.div
+end Ring
+
+section DivisionSemiring
 
-theorem zpow {x : R} (hx : IsSelfAdjoint x) (n : ℤ) : IsSelfAdjoint (x ^ n) :=
-  -- porting note: hack for lean4#2074, remove after forward-porting other changes to this file
-  set_option synthInstance.etaExperiment true in by
-    simp only [isSelfAdjoint_iff, star_zpow₀, hx.star_eq]
+variable [DivisionSemiring R] [StarRing R]
+
+theorem inv {x : R} (hx : IsSelfAdjoint x) : IsSelfAdjoint x⁻¹ := by
+  simp only [isSelfAdjoint_iff, star_inv', hx.star_eq]
+#align is_self_adjoint.inv IsSelfAdjoint.inv
+
+theorem zpow {x : R} (hx : IsSelfAdjoint x) (n : ℤ) : IsSelfAdjoint (x ^ n) := by
+  simp only [isSelfAdjoint_iff, star_zpow₀, hx.star_eq]
 #align is_self_adjoint.zpow IsSelfAdjoint.zpow
 
-end Field
+end DivisionSemiring
+
+section DivisionRing
+
+variable [DivisionRing R] [StarRing R]
+
+theorem _root_.isSelfAdjoint_ratCast (x : ℚ) : IsSelfAdjoint (x : R) :=
+  star_ratCast _
+#align is_self_adjoint_rat_cast isSelfAdjoint_ratCast
+
+end DivisionRing
+
+section Semifield
+
+-- porting note: generalize to `Semifield` to fix lean4#2074-related errors
+variable [Semifield R] [StarRing R]
+
+theorem div {x y : R} (hx : IsSelfAdjoint x) (hy : IsSelfAdjoint y) : IsSelfAdjoint (x / y) := by
+  simp only [isSelfAdjoint_iff, star_div', hx.star_eq, hy.star_eq]
+#align is_self_adjoint.div IsSelfAdjoint.div
+
+end Semifield
 
 section SMul
 
-variable [Star R] [TrivialStar R] [AddGroup A] [StarAddMonoid A]
+variable [Star R] [AddMonoid A] [StarAddMonoid A] [SMul R A] [StarModule R A]
 
-theorem smul [SMul R A] [StarModule R A] (r : R) {x : A} (hx : IsSelfAdjoint x) :
-    IsSelfAdjoint (r • x) := by simp only [isSelfAdjoint_iff, star_smul, star_trivial, hx.star_eq]
+theorem smul {r : R} (hr : IsSelfAdjoint r) {x : A} (hx : IsSelfAdjoint x) :
+    IsSelfAdjoint (r • x) := by simp only [isSelfAdjoint_iff, star_smul, hr.star_eq, hx.star_eq]
 #align is_self_adjoint.smul IsSelfAdjoint.smul
 
 end SMul
@@ -217,8 +276,7 @@ end IsSelfAdjoint
 variable (R)
 
 /-- The self-adjoint elements of a star additive group, as an additive subgroup. -/
-def selfAdjoint [AddGroup R] [StarAddMonoid R] : AddSubgroup R
-    where
+def selfAdjoint [AddGroup R] [StarAddMonoid R] : AddSubgroup R where
   carrier := { x | IsSelfAdjoint x }
   zero_mem' := star_zero R
   add_mem' hx := hx.add
@@ -226,14 +284,12 @@ def selfAdjoint [AddGroup R] [StarAddMonoid R] : AddSubgroup R
 #align self_adjoint selfAdjoint
 
 /-- The skew-adjoint elements of a star additive group, as an additive subgroup. -/
-def skewAdjoint [AddCommGroup R] [StarAddMonoid R] : AddSubgroup R
-    where
+def skewAdjoint [AddCommGroup R] [StarAddMonoid R] : AddSubgroup R where
   carrier := { x | star x = -x }
   zero_mem' := show star (0 : R) = -0 by simp only [star_zero, neg_zero]
   add_mem' := @fun x y (hx : star x = -x) (hy : star y = -y) =>
-    show star (x + y) = -(x + y) by rw [star_add, hx, hy, neg_add]
-  neg_mem' := @fun x (hx : star x = -x) =>
-    show star (-x) = - -x by simp only [hx, star_neg]
+    show star (x + y) = -(x + y) by rw [star_add x y, hx, hy, neg_add]
+  neg_mem' := @fun x (hx : star x = -x) => show star (-x) = - -x by simp only [hx, star_neg]
 #align skew_adjoint skewAdjoint
 
 variable {R}
@@ -271,22 +327,18 @@ theorem val_one : ↑(1 : selfAdjoint R) = (1 : R) :=
   rfl
 #align self_adjoint.coe_one selfAdjoint.val_one
 
-instance [Nontrivial R] : Nontrivial (selfAdjoint R) where
-  exists_pair_ne := ⟨0, 1, fun h => zero_ne_one (congrArg Subtype.val h)⟩
--- porting note: `Subtype.ne_of_val_ne` has not been ported
+instance [Nontrivial R] : Nontrivial (selfAdjoint R) :=
+  ⟨⟨0, 1, Subtype.ne_of_val_ne zero_ne_one⟩⟩
 
 instance : NatCast (selfAdjoint R) where
-  natCast := fun n =>
-    ⟨n, Nat.recOn n (by simp [zero_mem]) fun k hk =>
-      (@Nat.cast_succ R _ k).symm ▸ add_mem hk (isSelfAdjoint_one R)⟩
+  -- porting note: `(_)` works around lean4#2074
+  natCast n := ⟨n, @isSelfAdjoint_natCast _ _ (_) n⟩
 
 instance : IntCast (selfAdjoint R) where
-  intCast := fun n => ⟨n, by
-    cases' n with n n <;> simp [show ↑n ∈ selfAdjoint R from (n : selfAdjoint R).2]
-    refine' add_mem (isSelfAdjoint_one R).neg (n : selfAdjoint R).2.neg⟩
+  intCast n := ⟨n, isSelfAdjoint_intCast _⟩
 
 instance : Pow (selfAdjoint R) ℕ where
-  pow := fun x n => ⟨(x : R) ^ n, x.prop.pow n⟩
+  pow x n := ⟨(x : R) ^ n, x.prop.pow n⟩
 
 @[simp, norm_cast]
 theorem val_pow (x : selfAdjoint R) (n : ℕ) : ↑(x ^ n) = (x : R) ^ n :=
@@ -299,8 +351,8 @@ section NonUnitalCommRing
 
 variable [NonUnitalCommRing R] [StarRing R]
 
-instance : Mul (selfAdjoint R) :=
-  ⟨fun x y => ⟨(x : R) * y, x.prop.mul y.prop⟩⟩
+instance : Mul (selfAdjoint R) where
+  mul x y := ⟨(x : R) * y, x.prop.mul y.prop⟩
 
 @[simp, norm_cast]
 theorem val_mul (x y : selfAdjoint R) : ↑(x * y) = (x : R) * y :=
@@ -313,11 +365,11 @@ section CommRing
 
 variable [CommRing R] [StarRing R]
 
--- porting note: this takes waaaaay too long
 instance : CommRing (selfAdjoint R) :=
   Function.Injective.commRing _ Subtype.coe_injective (selfAdjoint R).coe_zero val_one
     (selfAdjoint R).coe_add val_mul (selfAdjoint R).coe_neg (selfAdjoint R).coe_sub
-    (selfAdjoint R).coe_nsmul (selfAdjoint R).coe_zsmul val_pow (fun _ => rfl) fun _ => rfl
+    (selfAdjoint R).coe_nsmul (selfAdjoint R).coe_zsmul val_pow
+    (fun _ => rfl) fun _ => rfl
 
 end CommRing
 
@@ -325,44 +377,44 @@ section Field
 
 variable [Field R] [StarRing R]
 
-instance : Inv (selfAdjoint R) where inv x := ⟨x.val⁻¹, x.prop.inv⟩
+instance : Inv (selfAdjoint R) where
+  -- porting note: `(_)` works around lean4#2074
+  inv x := ⟨x.val⁻¹, @IsSelfAdjoint.inv _ _ (_) _ x.prop⟩
 
 @[simp, norm_cast]
 theorem val_inv (x : selfAdjoint R) : ↑x⁻¹ = (x : R)⁻¹ :=
   rfl
 #align self_adjoint.coe_inv selfAdjoint.val_inv
 
-instance : Div (selfAdjoint R) where div x y := ⟨x / y, x.prop.div y.prop⟩
+instance : Div (selfAdjoint R) where
+  -- porting note: `(_)` works around lean4#2074
+  div x y := ⟨x / y, @IsSelfAdjoint.div _ _ (_) _ _ x.prop y.prop⟩
 
 @[simp, norm_cast]
 theorem val_div (x y : selfAdjoint R) : ↑(x / y) = (x / y : R) :=
   rfl
 #align self_adjoint.coe_div selfAdjoint.val_div
 
-instance : Pow (selfAdjoint R) ℤ where pow x z := ⟨(x : R) ^ z, x.prop.zpow z⟩
+instance : Pow (selfAdjoint R) ℤ where
+  -- porting note: `(_)` works around lean4#2074
+  pow x z := ⟨(x : R) ^ z, @IsSelfAdjoint.zpow _ _ (_) _ x.prop z⟩
 
 @[simp, norm_cast]
-theorem val_zpow (x : selfAdjoint R) (z : ℤ) : (x ^ z : R) = (x : R) ^ z :=
+theorem val_zpow (x : selfAdjoint R) (z : ℤ) : ↑(x ^ z) = (x : R) ^ z :=
   rfl
 #align self_adjoint.coe_zpow selfAdjoint.val_zpow
 
-theorem ratCast_mem : ∀ x : ℚ, IsSelfAdjoint (x : R)
-  | ⟨a, b, h1, h2⟩ =>
-    -- porting note: hack for lean4#2074, remove after forward-porting other changes to this file
-    set_option synthInstance.etaExperiment true in by
-      rw [IsSelfAdjoint, Rat.cast_mk', star_mul', star_inv', star_natCast, star_intCast]
-#align self_adjoint.rat_cast_mem selfAdjoint.ratCast_mem
-
-instance : RatCast (selfAdjoint R) :=
-  ⟨fun n => ⟨n, ratCast_mem n⟩⟩
+instance : RatCast (selfAdjoint R) where
+  ratCast n := ⟨n, isSelfAdjoint_ratCast n⟩
 
 @[simp, norm_cast]
 theorem val_ratCast (x : ℚ) : ↑(x : selfAdjoint R) = (x : R) :=
   rfl
 #align self_adjoint.coe_rat_cast selfAdjoint.val_ratCast
 
-instance instQSMul : SMul ℚ (selfAdjoint R) :=
-  ⟨fun a x => ⟨a • (x : R), by rw [Rat.smul_def]; exact (ratCast_mem a).mul x.prop⟩⟩
+instance instQSMul : SMul ℚ (selfAdjoint R) where
+  smul a x :=
+    ⟨a • (x : R), by rw [Rat.smul_def]; exact IsSelfAdjoint.mul (isSelfAdjoint_ratCast a) x.prop⟩
 #align self_adjoint.has_qsmul selfAdjoint.instQSMul
 
 @[simp, norm_cast]
@@ -370,14 +422,11 @@ theorem val_rat_smul (x : selfAdjoint R) (a : ℚ) : ↑(a • x) = a • (x : R
   rfl
 #align self_adjoint.coe_rat_smul selfAdjoint.val_rat_smul
 
--- Porting note: This takes too long. lean#2003?
-set_option maxHeartbeats 800000 in
-set_option synthInstance.maxHeartbeats 800000 in
 instance : Field (selfAdjoint R) :=
-  Function.Injective.field (↑) Subtype.coe_injective (selfAdjoint R).coe_zero val_one
-    (selfAdjoint R).coe_add val_mul (selfAdjoint R).coe_neg (selfAdjoint R).coe_sub val_inv val_div
-    (selfAdjoint R).coe_nsmul (selfAdjoint R).coe_zsmul val_rat_smul val_pow val_zpow (fun _ => rfl)
-    (fun _ => rfl) val_ratCast
+  Function.Injective.field _ Subtype.coe_injective (selfAdjoint R).coe_zero val_one
+    (selfAdjoint R).coe_add val_mul (selfAdjoint R).coe_neg (selfAdjoint R).coe_sub
+    val_inv val_div (selfAdjoint R).coe_nsmul (selfAdjoint R).coe_zsmul
+    val_rat_smul val_pow val_zpow (fun _ => rfl) (fun _ => rfl) val_ratCast
 
 end Field
 
@@ -385,8 +434,8 @@ section SMul
 
 variable [Star R] [TrivialStar R] [AddGroup A] [StarAddMonoid A]
 
-instance [SMul R A] [StarModule R A] : SMul R (selfAdjoint A) :=
-  ⟨fun r x => ⟨r • (x : A), x.prop.smul r⟩⟩
+instance [SMul R A] [StarModule R A] : SMul R (selfAdjoint A) where
+  smul r x := ⟨r • (x : A), (IsSelfAdjoint.all _).smul x.prop⟩
 
 @[simp, norm_cast]
 theorem val_smul [SMul R A] [StarModule R A] (r : R) (x : selfAdjoint A) : ↑(r • x) = r • (x : A) :=
@@ -394,7 +443,7 @@ theorem val_smul [SMul R A] [StarModule R A] (r : R) (x : selfAdjoint A) : ↑(r
 #align self_adjoint.coe_smul selfAdjoint.val_smul
 
 instance [Monoid R] [MulAction R A] [StarModule R A] : MulAction R (selfAdjoint A) :=
-  Function.Injective.mulAction Subtype.val Subtype.coe_injective val_smul
+  Function.Injective.mulAction (↑) Subtype.coe_injective val_smul
 
 instance [Monoid R] [DistribMulAction R A] [StarModule R A] : DistribMulAction R (selfAdjoint A) :=
   Function.Injective.distribMulAction (selfAdjoint A).subtype Subtype.coe_injective val_smul
@@ -451,10 +500,10 @@ theorem conjugate' {x : R} (hx : x ∈ skewAdjoint R) (z : R) : star z * x * z 
   simp only [mem_iff, star_mul, star_star, mem_iff.mp hx, neg_mul, mul_neg, mul_assoc]
 #align skew_adjoint.conjugate' skewAdjoint.conjugate'
 
-theorem isStarNormal_of_mem {x : R} (hx : x ∈ skewAdjoint R) : IsStarNormal x where
-  star_comm_self := by
-    rw [mem_iff.mpr hx]
-    exact Commute.neg_left rfl
+theorem isStarNormal_of_mem {x : R} (hx : x ∈ skewAdjoint R) : IsStarNormal x :=
+  ⟨by
+    simp only [mem_iff] at hx
+    simp only [hx, Commute.neg_left, Commute.refl]⟩
 #align skew_adjoint.is_star_normal_of_mem skewAdjoint.isStarNormal_of_mem
 
 instance (x : skewAdjoint R) : IsStarNormal (x : R) :=
@@ -471,8 +520,8 @@ theorem smul_mem [Monoid R] [DistribMulAction R A] [StarModule R A] (r : R) {x :
   rw [mem_iff, star_smul, star_trivial, mem_iff.mp h, smul_neg r]
 #align skew_adjoint.smul_mem skewAdjoint.smul_mem
 
-instance [Monoid R] [DistribMulAction R A] [StarModule R A] : SMul R (skewAdjoint A) :=
-  ⟨fun r x => ⟨r • (x : A), smul_mem r x.prop⟩⟩
+instance [Monoid R] [DistribMulAction R A] [StarModule R A] : SMul R (skewAdjoint A) where
+  smul r x := ⟨r • (x : A), smul_mem r x.prop⟩
 
 @[simp, norm_cast]
 theorem val_smul [Monoid R] [DistribMulAction R A] [StarModule R A] (r : R) (x : skewAdjoint A) :
@@ -490,12 +539,28 @@ end SMul
 
 end skewAdjoint
 
-instance isStarNormal_zero [Semiring R] [StarRing R] : IsStarNormal (0 : R) where
-  star_comm_self := by simpa only [star_zero] using Commute.refl 0
+/-- Scalar multiplication of a self-adjoint element by a skew-adjoint element produces a
+skew-adjoint element. -/
+theorem IsSelfAdjoint.smul_mem_skewAdjoint [Ring R] [AddCommGroup A] [Module R A] [StarAddMonoid R]
+    [StarAddMonoid A] [StarModule R A] {r : R} (hr : r ∈ skewAdjoint R) {a : A}
+    (ha : IsSelfAdjoint a) : r • a ∈ skewAdjoint A :=
+  (star_smul _ _).trans <| (congr_arg₂ _ hr ha).trans <| neg_smul _ _
+#align is_self_adjoint.smul_mem_skew_adjoint IsSelfAdjoint.smul_mem_skewAdjoint
+
+/-- Scalar multiplication of a skew-adjoint element by a skew-adjoint element produces a
+self-adjoint element. -/
+theorem isSelfAdjoint_smul_of_mem_skewAdjoint [Ring R] [AddCommGroup A] [Module R A]
+    [StarAddMonoid R] [StarAddMonoid A] [StarModule R A] {r : R} (hr : r ∈ skewAdjoint R) {a : A}
+    (ha : a ∈ skewAdjoint A) : IsSelfAdjoint (r • a) :=
+  (star_smul _ _).trans <| (congr_arg₂ _ hr ha).trans <| neg_smul_neg _ _
+#align is_self_adjoint_smul_of_mem_skew_adjoint isSelfAdjoint_smul_of_mem_skewAdjoint
+
+instance isStarNormal_zero [Semiring R] [StarRing R] : IsStarNormal (0 : R) :=
+  ⟨by simp only [Commute.refl, star_comm_self, star_zero]⟩
 #align is_star_normal_zero isStarNormal_zero
 
-instance isStarNormal_one [Monoid R] [StarSemigroup R] : IsStarNormal (1 : R) where
-  star_comm_self := by simpa only [star_one] using Commute.refl 1
+instance isStarNormal_one [Monoid R] [StarSemigroup R] : IsStarNormal (1 : R) :=
+  ⟨by simp only [Commute.refl, star_comm_self, star_one]⟩
 #align is_star_normal_one isStarNormal_one
 
 instance isStarNormal_star_self [Monoid R] [StarSemigroup R] {x : R} [IsStarNormal x] :

f93c1193

chore: forward-port leanprover-community/mathlib#18597 (#2926)

This is a forward-port of https://github.com/leanprover-community/mathlib/pull/18597

Some notes:

This doesn't forward-port the changes to algebra/star/self_adjoint; I plan to re-port this file from scratch after https://github.com/leanprover-community/mathlib/pull/18565 lands. For now, I just add some hacks to keep it compiling.
It seems that the changes to algebra/periodic were made during porting, see https://github.com/leanprover-community/mathlib4/pull/1963/files/2a6b385f555c37f3eb5e4dd9c113e0a1b5f6b958..[578a6252](https://github.com/leanprover-community/mathlib/commit/578a6252973bcdbd1a6ce4fc0fe2791295cf80e4)#r1140354814. So there is nothing to do other than update the SHA.

Co-authored-by: Jeremy Tan Jie Rui <reddeloostw@gmail.com>

5ea27f76

Diff

@@ -182,16 +182,22 @@ section Field
 
 variable [Field R] [StarRing R]
 
-theorem inv {x : R} (hx : IsSelfAdjoint x) : IsSelfAdjoint x⁻¹ := by
-  simp only [isSelfAdjoint_iff, star_inv', hx.star_eq]
+theorem inv {x : R} (hx : IsSelfAdjoint x) : IsSelfAdjoint x⁻¹ :=
+  -- porting note: hack for lean4#2074, remove after forward-porting other changes to this file
+  set_option synthInstance.etaExperiment true in by
+    simp only [isSelfAdjoint_iff, star_inv', hx.star_eq]
 #align is_self_adjoint.inv IsSelfAdjoint.inv
 
-theorem div {x y : R} (hx : IsSelfAdjoint x) (hy : IsSelfAdjoint y) : IsSelfAdjoint (x / y) := by
-  simp only [isSelfAdjoint_iff, star_div', hx.star_eq, hy.star_eq]
+theorem div {x y : R} (hx : IsSelfAdjoint x) (hy : IsSelfAdjoint y) : IsSelfAdjoint (x / y) :=
+  -- porting note: hack for lean4#2074, remove after forward-porting other changes to this file
+  set_option synthInstance.etaExperiment true in by
+    simp only [isSelfAdjoint_iff, star_div', hx.star_eq, hy.star_eq]
 #align is_self_adjoint.div IsSelfAdjoint.div
 
-theorem zpow {x : R} (hx : IsSelfAdjoint x) (n : ℤ) : IsSelfAdjoint (x ^ n) := by
-  simp only [isSelfAdjoint_iff, star_zpow₀, hx.star_eq]
+theorem zpow {x : R} (hx : IsSelfAdjoint x) (n : ℤ) : IsSelfAdjoint (x ^ n) :=
+  -- porting note: hack for lean4#2074, remove after forward-porting other changes to this file
+  set_option synthInstance.etaExperiment true in by
+    simp only [isSelfAdjoint_iff, star_zpow₀, hx.star_eq]
 #align is_self_adjoint.zpow IsSelfAdjoint.zpow
 
 end Field
@@ -341,12 +347,10 @@ theorem val_zpow (x : selfAdjoint R) (z : ℤ) : (x ^ z : R) = (x : R) ^ z :=
 #align self_adjoint.coe_zpow selfAdjoint.val_zpow
 
 theorem ratCast_mem : ∀ x : ℚ, IsSelfAdjoint (x : R)
-  | ⟨a, b, h1, h2⟩ => by
-    -- Porting note: added
-    let inst : StarRing R := ‹_›
-    rw [IsSelfAdjoint, Rat.cast_mk', star_mul', star_inv']
-    rw [@star_natCast _ _ inst]
-    rw [star_intCast]
+  | ⟨a, b, h1, h2⟩ =>
+    -- porting note: hack for lean4#2074, remove after forward-porting other changes to this file
+    set_option synthInstance.etaExperiment true in by
+      rw [IsSelfAdjoint, Rat.cast_mk', star_mul', star_inv', star_natCast, star_intCast]
 #align self_adjoint.rat_cast_mem selfAdjoint.ratCast_mem
 
 instance : RatCast (selfAdjoint R) :=

f93c1193

feat: port Algebra.Star.SelfAdjoint (#1860)

See the Zulip thread for issues I encountered.

Co-authored-by: ChrisHughes24 <chrishughes24@gmail.com> Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com> Co-authored-by: Lukas Miaskiwskyi <lukas.mias@gmail.com> Co-authored-by: Johan Commelin <johan@commelin.net>

f7001b11

`algebra.star.self_adjoint` ⟷ `Mathlib.Algebra.Star.SelfAdjoint`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Important changes

Remaining issues

Slower (failing) search

`simp` not firing sometimes

Missing instances due to unification failing

Workaround for issues

Dependencies 4 + 230

algebra.star.self_adjoint ⟷ Mathlib.Algebra.Star.SelfAdjoint

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Important changes

Remaining issues

Slower (failing) search

simp not firing sometimes

Missing instances due to unification failing

Workaround for issues

Dependencies 4 + 230

`algebra.star.self_adjoint` ⟷ `Mathlib.Algebra.Star.SelfAdjoint`

`simp` not firing sometimes