analysis.normed_space.star.basic | 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

aa666983

(last sync)

feat(topology/algebra/module/star): continuity results for star_modules (#19037)

Notably this adds starL.

This also fixes some unnecessary typeclass arguments in star_linear_equiv.

Co-authored-by: ADedecker <anatolededecker@gmail.com>

Diff

@@ -10,6 +10,7 @@ import analysis.normed_space.linear_isometry
 import algebra.star.self_adjoint
 import algebra.star.unitary
 import topology.algebra.star_subalgebra
+import topology.algebra.module.star
 
 /-!
 # Normed star rings and algebras
@@ -257,6 +258,10 @@ variables {𝕜}
 
 lemma starₗᵢ_apply {x : E} : starₗᵢ 𝕜 x = star x := rfl
 
+@[simp] lemma starₗᵢ_to_continuous_linear_equiv :
+  (starₗᵢ 𝕜 : E ≃ₗᵢ⋆[𝕜] E).to_continuous_linear_equiv = (starL 𝕜 : E ≃L⋆[𝕜] E) :=
+continuous_linear_equiv.ext rfl
+
 end starₗᵢ
 
 namespace star_subalgebra

e6577119

(first ported)

Changes in mathlib3port

mathlib3

mathlib3port

aa666983

bump to nightly-2024-04-06-08

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

e34029c9

Diff

@@ -328,7 +328,7 @@ theorem IsSelfAdjoint.nnnorm_pow_two_pow [NormedRing E] [StarRing E] [CstarRing
   by
   induction' n with k hk
   · simp only [pow_zero, pow_one]
-  · rw [pow_succ, pow_mul', sq]
+  · rw [pow_succ', pow_mul', sq]
     nth_rw 1 [← self_adjoint.mem_iff.mp hx]
     rw [← star_pow, CstarRing.nnnorm_star_mul_self, ← sq, hk, pow_mul']
 #align is_self_adjoint.nnnorm_pow_two_pow IsSelfAdjoint.nnnorm_pow_two_pow

aa666983

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,13 +3,13 @@ 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.Analysis.Normed.Group.Hom
-import Mathbin.Analysis.NormedSpace.Basic
-import Mathbin.Analysis.NormedSpace.LinearIsometry
-import Mathbin.Algebra.Star.SelfAdjoint
-import Mathbin.Algebra.Star.Unitary
-import Mathbin.Topology.Algebra.StarSubalgebra
-import Mathbin.Topology.Algebra.Module.Star
+import Analysis.Normed.Group.Hom
+import Analysis.NormedSpace.Basic
+import Analysis.NormedSpace.LinearIsometry
+import Algebra.Star.SelfAdjoint
+import Algebra.Star.Unitary
+import Topology.Algebra.StarSubalgebra
+import Topology.Algebra.Module.Star
 
 #align_import analysis.normed_space.star.basic from "leanprover-community/mathlib"@"aa6669832974f87406a3d9d70fc5707a60546207"

aa666983

bump to nightly-2023-08-17-09

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

60285dcc

Diff

@@ -99,11 +99,11 @@ instance RingHomIsometric.starRingEnd [NormedCommRing E] [StarRing E] [NormedSta
 /-- A C*-ring is a normed star ring that satifies the stronger condition `‖x⋆ * x‖ = ‖x‖^2`
 for every `x`. -/
 class CstarRing (E : Type _) [NonUnitalNormedRing E] [StarRing E] : Prop where
-  norm_star_mul_self : ∀ {x : E}, ‖x⋆ * x‖ = ‖x‖ * ‖x‖
+  norm_star_hMul_self : ∀ {x : E}, ‖x⋆ * x‖ = ‖x‖ * ‖x‖
 #align cstar_ring CstarRing
 -/
 
-instance : CstarRing ℝ where norm_star_mul_self x := by simp only [star, id.def, norm_mul]
+instance : CstarRing ℝ where norm_star_hMul_self x := by simp only [star, id.def, norm_mul]
 
 namespace CstarRing
 
@@ -153,7 +153,7 @@ theorem nnnorm_self_mul_star {x : E} : ‖x * star x‖₊ = ‖x‖₊ * ‖x
 
 #print CstarRing.nnnorm_star_mul_self /-
 theorem nnnorm_star_mul_self {x : E} : ‖x⋆ * x‖₊ = ‖x‖₊ * ‖x‖₊ :=
-  Subtype.ext norm_star_mul_self
+  Subtype.ext norm_star_hMul_self
 #align cstar_ring.nnnorm_star_mul_self CstarRing.nnnorm_star_mul_self
 -/
 
@@ -207,7 +207,7 @@ variable [Fintype ι] [∀ i, CstarRing (R i)]
 
 #print Prod.cstarRing /-
 instance Prod.cstarRing : CstarRing (R₁ × R₂)
-    where norm_star_mul_self x := by
+    where norm_star_hMul_self x := by
     unfold norm
     simp only [Prod.fst_mul, Prod.fst_star, Prod.snd_mul, Prod.snd_star, norm_star_mul_self, ← sq]
     refine' le_antisymm _ _
@@ -221,7 +221,7 @@ instance Prod.cstarRing : CstarRing (R₁ × R₂)
 
 #print Pi.cstarRing /-
 instance Pi.cstarRing : CstarRing (∀ i, R i)
-    where norm_star_mul_self x :=
+    where norm_star_hMul_self x :=
     by
     simp only [norm, Pi.mul_apply, Pi.star_apply, nnnorm_star_mul_self, ← sq]
     norm_cast
@@ -258,7 +258,7 @@ instance (priority := 100) [Nontrivial E] : NormOneClass E :=
 
 #print CstarRing.norm_coe_unitary /-
 theorem norm_coe_unitary [Nontrivial E] (U : unitary E) : ‖(U : E)‖ = 1 := by
-  rw [← sq_eq_sq (norm_nonneg _) zero_le_one, one_pow 2, sq, ← CstarRing.norm_star_mul_self,
+  rw [← sq_eq_sq (norm_nonneg _) zero_le_one, one_pow 2, sq, ← CstarRing.norm_star_hMul_self,
     unitary.coe_star_mul_self, CstarRing.norm_one]
 #align cstar_ring.norm_coe_unitary CstarRing.norm_coe_unitary
 -/
@@ -397,7 +397,7 @@ instance toNormedAlgebra {𝕜 A : Type _} [NormedField 𝕜] [StarRing 𝕜] [S
 #print StarSubalgebra.to_cstarRing /-
 instance to_cstarRing {R A} [CommRing R] [StarRing R] [NormedRing A] [StarRing A] [CstarRing A]
     [Algebra R A] [StarModule R A] (S : StarSubalgebra R A) : CstarRing S
-    where norm_star_mul_self x := @CstarRing.norm_star_mul_self A _ _ _ x
+    where norm_star_hMul_self x := @CstarRing.norm_star_hMul_self A _ _ _ x
 #align star_subalgebra.to_cstar_ring StarSubalgebra.to_cstarRing
 -/

aa666983

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,11 +2,6 @@
 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 analysis.normed_space.star.basic
-! leanprover-community/mathlib commit aa6669832974f87406a3d9d70fc5707a60546207
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Analysis.Normed.Group.Hom
 import Mathbin.Analysis.NormedSpace.Basic
@@ -16,6 +11,8 @@ import Mathbin.Algebra.Star.Unitary
 import Mathbin.Topology.Algebra.StarSubalgebra
 import Mathbin.Topology.Algebra.Module.Star
 
+#align_import analysis.normed_space.star.basic from "leanprover-community/mathlib"@"aa6669832974f87406a3d9d70fc5707a60546207"
+
 /-!
 # Normed star rings and algebras

aa666983

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -42,7 +42,6 @@ To get a C⋆-algebra `E` over field `𝕜`, use
 
 open scoped Topology
 
--- mathport name: «expr ⋆»
 local postfix:max "⋆" => star
 
 #print NormedStarGroup /-
@@ -138,38 +137,54 @@ instance (priority := 100) to_normedStarGroup : NormedStarGroup E :=
 #align cstar_ring.to_normed_star_group CstarRing.to_normedStarGroup
 -/
 
+#print CstarRing.norm_self_mul_star /-
 theorem norm_self_mul_star {x : E} : ‖x * x⋆‖ = ‖x‖ * ‖x‖ := by nth_rw 1 [← star_star x];
   simp only [norm_star_mul_self, norm_star]
 #align cstar_ring.norm_self_mul_star CstarRing.norm_self_mul_star
+-/
 
+#print CstarRing.norm_star_mul_self' /-
 theorem norm_star_mul_self' {x : E} : ‖x⋆ * x‖ = ‖x⋆‖ * ‖x‖ := by rw [norm_star_mul_self, norm_star]
 #align cstar_ring.norm_star_mul_self' CstarRing.norm_star_mul_self'
+-/
 
+#print CstarRing.nnnorm_self_mul_star /-
 theorem nnnorm_self_mul_star {x : E} : ‖x * star x‖₊ = ‖x‖₊ * ‖x‖₊ :=
   Subtype.ext norm_self_mul_star
 #align cstar_ring.nnnorm_self_mul_star CstarRing.nnnorm_self_mul_star
+-/
 
+#print CstarRing.nnnorm_star_mul_self /-
 theorem nnnorm_star_mul_self {x : E} : ‖x⋆ * x‖₊ = ‖x‖₊ * ‖x‖₊ :=
   Subtype.ext norm_star_mul_self
 #align cstar_ring.nnnorm_star_mul_self CstarRing.nnnorm_star_mul_self
+-/
 
+#print CstarRing.star_mul_self_eq_zero_iff /-
 @[simp]
 theorem star_mul_self_eq_zero_iff (x : E) : star x * x = 0 ↔ x = 0 := by
   rw [← norm_eq_zero, norm_star_mul_self]; exact mul_self_eq_zero.trans norm_eq_zero
 #align cstar_ring.star_mul_self_eq_zero_iff CstarRing.star_mul_self_eq_zero_iff
+-/
 
+#print CstarRing.star_mul_self_ne_zero_iff /-
 theorem star_mul_self_ne_zero_iff (x : E) : star x * x ≠ 0 ↔ x ≠ 0 := by
   simp only [Ne.def, star_mul_self_eq_zero_iff]
 #align cstar_ring.star_mul_self_ne_zero_iff CstarRing.star_mul_self_ne_zero_iff
+-/
 
+#print CstarRing.mul_star_self_eq_zero_iff /-
 @[simp]
 theorem mul_star_self_eq_zero_iff (x : E) : x * star x = 0 ↔ x = 0 := by
   simpa only [star_eq_zero, star_star] using @star_mul_self_eq_zero_iff _ _ _ _ (star x)
 #align cstar_ring.mul_star_self_eq_zero_iff CstarRing.mul_star_self_eq_zero_iff
+-/
 
+#print CstarRing.mul_star_self_ne_zero_iff /-
 theorem mul_star_self_ne_zero_iff (x : E) : x * star x ≠ 0 ↔ x ≠ 0 := by
   simp only [Ne.def, mul_star_self_eq_zero_iff]
 #align cstar_ring.mul_star_self_ne_zero_iff CstarRing.mul_star_self_ne_zero_iff
+-/
 
 end NonUnital
 
@@ -193,6 +208,7 @@ instance Pi.starRing' : StarRing (∀ i, R i) :=
 
 variable [Fintype ι] [∀ i, CstarRing (R i)]
 
+#print Prod.cstarRing /-
 instance Prod.cstarRing : CstarRing (R₁ × R₂)
     where norm_star_mul_self x := by
     unfold norm
@@ -204,6 +220,7 @@ instance Prod.cstarRing : CstarRing (R₁ × R₂)
     · rw [le_sup_iff]
       rcases le_total ‖x.fst‖ ‖x.snd‖ with (h | h) <;> simp [h]
 #align prod.cstar_ring Prod.cstarRing
+-/
 
 #print Pi.cstarRing /-
 instance Pi.cstarRing : CstarRing (∀ i, R i)
@@ -229,27 +246,34 @@ section Unital
 
 variable [NormedRing E] [StarRing E] [CstarRing E]
 
+#print CstarRing.norm_one /-
 @[simp]
 theorem norm_one [Nontrivial E] : ‖(1 : E)‖ = 1 :=
   by
   have : 0 < ‖(1 : E)‖ := norm_pos_iff.mpr one_ne_zero
   rw [← mul_left_inj' this.ne', ← norm_star_mul_self, mul_one, star_one, one_mul]
 #align cstar_ring.norm_one CstarRing.norm_one
+-/
 
 -- see Note [lower instance priority]
 instance (priority := 100) [Nontrivial E] : NormOneClass E :=
   ⟨norm_one⟩
 
+#print CstarRing.norm_coe_unitary /-
 theorem norm_coe_unitary [Nontrivial E] (U : unitary E) : ‖(U : E)‖ = 1 := by
   rw [← sq_eq_sq (norm_nonneg _) zero_le_one, one_pow 2, sq, ← CstarRing.norm_star_mul_self,
     unitary.coe_star_mul_self, CstarRing.norm_one]
 #align cstar_ring.norm_coe_unitary CstarRing.norm_coe_unitary
+-/
 
+#print CstarRing.norm_of_mem_unitary /-
 @[simp]
 theorem norm_of_mem_unitary [Nontrivial E] {U : E} (hU : U ∈ unitary E) : ‖U‖ = 1 :=
   norm_coe_unitary ⟨U, hU⟩
 #align cstar_ring.norm_of_mem_unitary CstarRing.norm_of_mem_unitary
+-/
 
+#print CstarRing.norm_coe_unitary_mul /-
 @[simp]
 theorem norm_coe_unitary_mul (U : unitary E) (A : E) : ‖(U : E) * A‖ = ‖A‖ :=
   by
@@ -265,16 +289,22 @@ theorem norm_coe_unitary_mul (U : unitary E) (A : E) : ‖(U : E) * A‖ = ‖A
       _ ≤ ‖(U : E)⋆‖ * ‖(U : E) * A‖ := by rw [mul_assoc]; exact norm_mul_le _ _
       _ = ‖(U : E) * A‖ := by rw [norm_star, norm_coe_unitary, one_mul]
 #align cstar_ring.norm_coe_unitary_mul CstarRing.norm_coe_unitary_mul
+-/
 
+#print CstarRing.norm_unitary_smul /-
 @[simp]
 theorem norm_unitary_smul (U : unitary E) (A : E) : ‖U • A‖ = ‖A‖ :=
   norm_coe_unitary_mul U A
 #align cstar_ring.norm_unitary_smul CstarRing.norm_unitary_smul
+-/
 
+#print CstarRing.norm_mem_unitary_mul /-
 theorem norm_mem_unitary_mul {U : E} (A : E) (hU : U ∈ unitary E) : ‖U * A‖ = ‖A‖ :=
   norm_coe_unitary_mul ⟨U, hU⟩ A
 #align cstar_ring.norm_mem_unitary_mul CstarRing.norm_mem_unitary_mul
+-/
 
+#print CstarRing.norm_mul_coe_unitary /-
 @[simp]
 theorem norm_mul_coe_unitary (A : E) (U : unitary E) : ‖A * U‖ = ‖A‖ :=
   calc
@@ -283,15 +313,19 @@ theorem norm_mul_coe_unitary (A : E) (U : unitary E) : ‖A * U‖ = ‖A‖ :=
     _ = ‖A⋆‖ := (norm_mem_unitary_mul (star A) (unitary.star_mem U.Prop))
     _ = ‖A‖ := norm_star _
 #align cstar_ring.norm_mul_coe_unitary CstarRing.norm_mul_coe_unitary
+-/
 
+#print CstarRing.norm_mul_mem_unitary /-
 theorem norm_mul_mem_unitary (A : E) {U : E} (hU : U ∈ unitary E) : ‖A * U‖ = ‖A‖ :=
   norm_mul_coe_unitary A ⟨U, hU⟩
 #align cstar_ring.norm_mul_mem_unitary CstarRing.norm_mul_mem_unitary
+-/
 
 end Unital
 
 end CstarRing
 
+#print IsSelfAdjoint.nnnorm_pow_two_pow /-
 theorem IsSelfAdjoint.nnnorm_pow_two_pow [NormedRing E] [StarRing E] [CstarRing E] {x : E}
     (hx : IsSelfAdjoint x) (n : ℕ) : ‖x ^ 2 ^ n‖₊ = ‖x‖₊ ^ 2 ^ n :=
   by
@@ -301,11 +335,14 @@ theorem IsSelfAdjoint.nnnorm_pow_two_pow [NormedRing E] [StarRing E] [CstarRing
     nth_rw 1 [← self_adjoint.mem_iff.mp hx]
     rw [← star_pow, CstarRing.nnnorm_star_mul_self, ← sq, hk, pow_mul']
 #align is_self_adjoint.nnnorm_pow_two_pow IsSelfAdjoint.nnnorm_pow_two_pow
+-/
 
+#print selfAdjoint.nnnorm_pow_two_pow /-
 theorem selfAdjoint.nnnorm_pow_two_pow [NormedRing E] [StarRing E] [CstarRing E] (x : selfAdjoint E)
     (n : ℕ) : ‖x ^ 2 ^ n‖₊ = ‖x‖₊ ^ 2 ^ n :=
   x.Prop.nnnorm_pow_two_pow _
 #align self_adjoint.nnnorm_pow_two_pow selfAdjoint.nnnorm_pow_two_pow
+-/
 
 section starₗᵢ
 
@@ -328,14 +365,18 @@ def starₗᵢ : E ≃ₗᵢ⋆[𝕜] E :=
 
 variable {𝕜}
 
+#print coe_starₗᵢ /-
 @[simp]
 theorem coe_starₗᵢ : (starₗᵢ 𝕜 : E → E) = star :=
   rfl
 #align coe_starₗᵢ coe_starₗᵢ
+-/
 
+#print starₗᵢ_apply /-
 theorem starₗᵢ_apply {x : E} : starₗᵢ 𝕜 x = star x :=
   rfl
 #align starₗᵢ_apply starₗᵢ_apply
+-/
 
 #print starₗᵢ_toContinuousLinearEquiv /-
 @[simp]

aa666983

bump to nightly-2023-06-09-07

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

16afdc39

Diff

@@ -130,12 +130,10 @@ instance (priority := 100) to_normedStarGroup : NormedStarGroup E :=
         calc
           ‖x‖ * ‖x‖ = ‖x⋆ * x‖ := norm_star_mul_self.symm
           _ ≤ ‖x⋆‖ * ‖x‖ := norm_mul_le _ _
-          
       have h₂ :=
         calc
           ‖x⋆‖ * ‖x⋆‖ = ‖x * x⋆‖ := by rw [← norm_star_mul_self, star_star]
           _ ≤ ‖x‖ * ‖x⋆‖ := norm_mul_le _ _
-          
       exact le_antisymm (le_of_mul_le_mul_right h₂ hnt_star) (le_of_mul_le_mul_right h₁ hnt)⟩
 #align cstar_ring.to_normed_star_group CstarRing.to_normedStarGroup
 -/
@@ -261,13 +259,11 @@ theorem norm_coe_unitary_mul (U : unitary E) (A : E) : ‖(U : E) * A‖ = ‖A
     calc
       _ ≤ ‖(U : E)‖ * ‖A‖ := norm_mul_le _ _
       _ = ‖A‖ := by rw [norm_coe_unitary, one_mul]
-      
   ·
     calc
       _ = ‖(U : E)⋆ * U * A‖ := by rw [unitary.coe_star_mul_self U, one_mul]
       _ ≤ ‖(U : E)⋆‖ * ‖(U : E) * A‖ := by rw [mul_assoc]; exact norm_mul_le _ _
       _ = ‖(U : E) * A‖ := by rw [norm_star, norm_coe_unitary, one_mul]
-      
 #align cstar_ring.norm_coe_unitary_mul CstarRing.norm_coe_unitary_mul
 
 @[simp]
@@ -286,7 +282,6 @@ theorem norm_mul_coe_unitary (A : E) (U : unitary E) : ‖A * U‖ = ‖A‖ :=
     _ = ‖(U : E)⋆ * A⋆‖ := by rw [norm_star]
     _ = ‖A⋆‖ := (norm_mem_unitary_mul (star A) (unitary.star_mem U.Prop))
     _ = ‖A‖ := norm_star _
-    
 #align cstar_ring.norm_mul_coe_unitary CstarRing.norm_mul_coe_unitary
 
 theorem norm_mul_mem_unitary (A : E) {U : E} (hU : U ∈ unitary E) : ‖A * U‖ = ‖A‖ :=

aa666983

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -40,7 +40,7 @@ To get a C⋆-algebra `E` over field `𝕜`, use
 -/
 
 
-open Topology
+open scoped Topology
 
 -- mathport name: «expr ⋆»
 local postfix:max "⋆" => star

aa666983

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -140,83 +140,35 @@ instance (priority := 100) to_normedStarGroup : NormedStarGroup E :=
 #align cstar_ring.to_normed_star_group CstarRing.to_normedStarGroup
 -/
 
-/- warning: cstar_ring.norm_self_mul_star -> CstarRing.norm_self_mul_star is a dubious translation:
-lean 3 declaration is
-  forall {E : Type.{u1}} [_inst_1 : NonUnitalNormedRing.{u1} E] [_inst_2 : StarRing.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E _inst_1))] [_inst_3 : CstarRing.{u1} E _inst_1 _inst_2] {x : E}, Eq.{1} Real (Norm.norm.{u1} E (NonUnitalNormedRing.toHasNorm.{u1} E _inst_1) (HMul.hMul.{u1, u1, u1} E E E (instHMul.{u1} E (Distrib.toHasMul.{u1} E (NonUnitalNonAssocSemiring.toDistrib.{u1} E (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} E (NonUnitalRing.toNonUnitalNonAssocRing.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E _inst_1)))))) x (Star.star.{u1} E (InvolutiveStar.toHasStar.{u1} E (StarAddMonoid.toHasInvolutiveStar.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} E (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E _inst_1))))) (StarRing.toStarAddMonoid.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E _inst_1)) _inst_2))) x))) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Norm.norm.{u1} E (NonUnitalNormedRing.toHasNorm.{u1} E _inst_1) x) (Norm.norm.{u1} E (NonUnitalNormedRing.toHasNorm.{u1} E _inst_1) x))
-but is expected to have type
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 theorem norm_self_mul_star {x : E} : ‖x * x⋆‖ = ‖x‖ * ‖x‖ := by nth_rw 1 [← star_star x];
   simp only [norm_star_mul_self, norm_star]
 #align cstar_ring.norm_self_mul_star CstarRing.norm_self_mul_star
 
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 theorem norm_star_mul_self' {x : E} : ‖x⋆ * x‖ = ‖x⋆‖ * ‖x‖ := by rw [norm_star_mul_self, norm_star]
 #align cstar_ring.norm_star_mul_self' CstarRing.norm_star_mul_self'
 
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 theorem nnnorm_self_mul_star {x : E} : ‖x * star x‖₊ = ‖x‖₊ * ‖x‖₊ :=
   Subtype.ext norm_self_mul_star
 #align cstar_ring.nnnorm_self_mul_star CstarRing.nnnorm_self_mul_star
 
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 theorem nnnorm_star_mul_self {x : E} : ‖x⋆ * x‖₊ = ‖x‖₊ * ‖x‖₊ :=
   Subtype.ext norm_star_mul_self
 #align cstar_ring.nnnorm_star_mul_self CstarRing.nnnorm_star_mul_self
 
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 @[simp]
 theorem star_mul_self_eq_zero_iff (x : E) : star x * x = 0 ↔ x = 0 := by
   rw [← norm_eq_zero, norm_star_mul_self]; exact mul_self_eq_zero.trans norm_eq_zero
 #align cstar_ring.star_mul_self_eq_zero_iff CstarRing.star_mul_self_eq_zero_iff
 
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 theorem star_mul_self_ne_zero_iff (x : E) : star x * x ≠ 0 ↔ x ≠ 0 := by
   simp only [Ne.def, star_mul_self_eq_zero_iff]
 #align cstar_ring.star_mul_self_ne_zero_iff CstarRing.star_mul_self_ne_zero_iff
 
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 @[simp]
 theorem mul_star_self_eq_zero_iff (x : E) : x * star x = 0 ↔ x = 0 := by
   simpa only [star_eq_zero, star_star] using @star_mul_self_eq_zero_iff _ _ _ _ (star x)
 #align cstar_ring.mul_star_self_eq_zero_iff CstarRing.mul_star_self_eq_zero_iff
 
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 theorem mul_star_self_ne_zero_iff (x : E) : x * star x ≠ 0 ↔ x ≠ 0 := by
   simp only [Ne.def, mul_star_self_eq_zero_iff]
 #align cstar_ring.mul_star_self_ne_zero_iff CstarRing.mul_star_self_ne_zero_iff
@@ -243,12 +195,6 @@ instance Pi.starRing' : StarRing (∀ i, R i) :=
 
 variable [Fintype ι] [∀ i, CstarRing (R i)]
 
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 instance Prod.cstarRing : CstarRing (R₁ × R₂)
     where norm_star_mul_self x := by
     unfold norm
@@ -285,12 +231,6 @@ section Unital
 
 variable [NormedRing E] [StarRing E] [CstarRing E]
 
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 @[simp]
 theorem norm_one [Nontrivial E] : ‖(1 : E)‖ = 1 :=
   by
@@ -302,34 +242,16 @@ theorem norm_one [Nontrivial E] : ‖(1 : E)‖ = 1 :=
 instance (priority := 100) [Nontrivial E] : NormOneClass E :=
   ⟨norm_one⟩
 
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 theorem norm_coe_unitary [Nontrivial E] (U : unitary E) : ‖(U : E)‖ = 1 := by
   rw [← sq_eq_sq (norm_nonneg _) zero_le_one, one_pow 2, sq, ← CstarRing.norm_star_mul_self,
     unitary.coe_star_mul_self, CstarRing.norm_one]
 #align cstar_ring.norm_coe_unitary CstarRing.norm_coe_unitary
 
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 @[simp]
 theorem norm_of_mem_unitary [Nontrivial E] {U : E} (hU : U ∈ unitary E) : ‖U‖ = 1 :=
   norm_coe_unitary ⟨U, hU⟩
 #align cstar_ring.norm_of_mem_unitary CstarRing.norm_of_mem_unitary
 
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 @[simp]
 theorem norm_coe_unitary_mul (U : unitary E) (A : E) : ‖(U : E) * A‖ = ‖A‖ :=
   by
@@ -348,33 +270,15 @@ theorem norm_coe_unitary_mul (U : unitary E) (A : E) : ‖(U : E) * A‖ = ‖A
       
 #align cstar_ring.norm_coe_unitary_mul CstarRing.norm_coe_unitary_mul
 
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 @[simp]
 theorem norm_unitary_smul (U : unitary E) (A : E) : ‖U • A‖ = ‖A‖ :=
   norm_coe_unitary_mul U A
 #align cstar_ring.norm_unitary_smul CstarRing.norm_unitary_smul
 
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 theorem norm_mem_unitary_mul {U : E} (A : E) (hU : U ∈ unitary E) : ‖U * A‖ = ‖A‖ :=
   norm_coe_unitary_mul ⟨U, hU⟩ A
 #align cstar_ring.norm_mem_unitary_mul CstarRing.norm_mem_unitary_mul
 
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 @[simp]
 theorem norm_mul_coe_unitary (A : E) (U : unitary E) : ‖A * U‖ = ‖A‖ :=
   calc
@@ -385,12 +289,6 @@ theorem norm_mul_coe_unitary (A : E) (U : unitary E) : ‖A * U‖ = ‖A‖ :=
     
 #align cstar_ring.norm_mul_coe_unitary CstarRing.norm_mul_coe_unitary
 
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 theorem norm_mul_mem_unitary (A : E) {U : E} (hU : U ∈ unitary E) : ‖A * U‖ = ‖A‖ :=
   norm_mul_coe_unitary A ⟨U, hU⟩
 #align cstar_ring.norm_mul_mem_unitary CstarRing.norm_mul_mem_unitary
@@ -399,12 +297,6 @@ end Unital
 
 end CstarRing
 
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-  forall {E : Type.{u1}} [_inst_1 : NormedRing.{u1} E] [_inst_2 : StarRing.{u1} E (Semiring.toNonUnitalSemiring.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))] [_inst_3 : CstarRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1) _inst_2] {x : E}, (IsSelfAdjoint.{u1} E (InvolutiveStar.toStar.{u1} E (StarAddMonoid.toInvolutiveStar.{u1} E (AddMonoidWithOne.toAddMonoid.{u1} E (AddGroupWithOne.toAddMonoidWithOne.{u1} E (Ring.toAddGroupWithOne.{u1} E (NormedRing.toRing.{u1} E _inst_1)))) (StarRing.toStarAddMonoid.{u1} E (Semiring.toNonUnitalSemiring.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1))) _inst_2))) x) -> (forall (n : Nat), Eq.{1} NNReal (NNNorm.nnnorm.{u1} E (SeminormedAddGroup.toNNNorm.{u1} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} E (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} E (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))))) (HPow.hPow.{u1, 0, u1} E Nat E (instHPow.{u1, 0} E Nat (Monoid.Pow.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))))) x (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) n))) (HPow.hPow.{0, 0, 0} NNReal Nat NNReal (instHPow.{0, 0} NNReal Nat (Monoid.Pow.{0} NNReal (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal instNNRealSemiring)))) (NNNorm.nnnorm.{u1} E (SeminormedAddGroup.toNNNorm.{u1} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} E (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} E (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))))) x) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) n)))
-Case conversion may be inaccurate. Consider using '#align is_self_adjoint.nnnorm_pow_two_pow IsSelfAdjoint.nnnorm_pow_two_powₓ'. -/
 theorem IsSelfAdjoint.nnnorm_pow_two_pow [NormedRing E] [StarRing E] [CstarRing E] {x : E}
     (hx : IsSelfAdjoint x) (n : ℕ) : ‖x ^ 2 ^ n‖₊ = ‖x‖₊ ^ 2 ^ n :=
   by
@@ -415,9 +307,6 @@ theorem IsSelfAdjoint.nnnorm_pow_two_pow [NormedRing E] [StarRing E] [CstarRing
     rw [← star_pow, CstarRing.nnnorm_star_mul_self, ← sq, hk, pow_mul']
 #align is_self_adjoint.nnnorm_pow_two_pow IsSelfAdjoint.nnnorm_pow_two_pow
 
-/- warning: self_adjoint.nnnorm_pow_two_pow -> selfAdjoint.nnnorm_pow_two_pow is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align self_adjoint.nnnorm_pow_two_pow selfAdjoint.nnnorm_pow_two_powₓ'. -/
 theorem selfAdjoint.nnnorm_pow_two_pow [NormedRing E] [StarRing E] [CstarRing E] (x : selfAdjoint E)
     (n : ℕ) : ‖x ^ 2 ^ n‖₊ = ‖x‖₊ ^ 2 ^ n :=
   x.Prop.nnnorm_pow_two_pow _
@@ -444,17 +333,11 @@ def starₗᵢ : E ≃ₗᵢ⋆[𝕜] E :=
 
 variable {𝕜}
 
-/- warning: coe_starₗᵢ -> coe_starₗᵢ is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align coe_starₗᵢ coe_starₗᵢₓ'. -/
 @[simp]
 theorem coe_starₗᵢ : (starₗᵢ 𝕜 : E → E) = star :=
   rfl
 #align coe_starₗᵢ coe_starₗᵢ
 
-/- warning: starₗᵢ_apply -> starₗᵢ_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align starₗᵢ_apply starₗᵢ_applyₓ'. -/
 theorem starₗᵢ_apply {x : E} : starₗᵢ 𝕜 x = star x :=
   rfl
 #align starₗᵢ_apply starₗᵢ_apply

aa666983

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -146,9 +146,7 @@ lean 3 declaration is
 but is expected to have type
   forall {E : Type.{u1}} [_inst_1 : NonUnitalNormedRing.{u1} E] [_inst_2 : StarRing.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E _inst_1))] [_inst_3 : CstarRing.{u1} E _inst_1 _inst_2] {x : E}, Eq.{1} Real (Norm.norm.{u1} E (NonUnitalNormedRing.toNorm.{u1} E _inst_1) (HMul.hMul.{u1, u1, u1} E E E (instHMul.{u1} E (NonUnitalNonAssocRing.toMul.{u1} E (NonUnitalRing.toNonUnitalNonAssocRing.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E _inst_1)))) x (Star.star.{u1} E (InvolutiveStar.toStar.{u1} E (StarAddMonoid.toInvolutiveStar.{u1} E (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E (NonUnitalNormedRing.toNormedAddCommGroup.{u1} E _inst_1))))) (StarRing.toStarAddMonoid.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E _inst_1)) _inst_2))) x))) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Norm.norm.{u1} E (NonUnitalNormedRing.toNorm.{u1} E _inst_1) x) (Norm.norm.{u1} E (NonUnitalNormedRing.toNorm.{u1} E _inst_1) x))
 Case conversion may be inaccurate. Consider using '#align cstar_ring.norm_self_mul_star CstarRing.norm_self_mul_starₓ'. -/
-theorem norm_self_mul_star {x : E} : ‖x * x⋆‖ = ‖x‖ * ‖x‖ :=
-  by
-  nth_rw 1 [← star_star x]
+theorem norm_self_mul_star {x : E} : ‖x * x⋆‖ = ‖x‖ * ‖x‖ := by nth_rw 1 [← star_star x];
   simp only [norm_star_mul_self, norm_star]
 #align cstar_ring.norm_self_mul_star CstarRing.norm_self_mul_star
 
@@ -188,10 +186,8 @@ but is expected to have type
   forall {E : Type.{u1}} [_inst_1 : NonUnitalNormedRing.{u1} E] [_inst_2 : StarRing.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E _inst_1))] [_inst_3 : CstarRing.{u1} E _inst_1 _inst_2] (x : E), Iff (Eq.{succ u1} E (HMul.hMul.{u1, u1, u1} E E E (instHMul.{u1} E (NonUnitalNonAssocRing.toMul.{u1} E (NonUnitalRing.toNonUnitalNonAssocRing.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E _inst_1)))) (Star.star.{u1} E (InvolutiveStar.toStar.{u1} E (StarAddMonoid.toInvolutiveStar.{u1} E (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E (NonUnitalNormedRing.toNormedAddCommGroup.{u1} E _inst_1))))) (StarRing.toStarAddMonoid.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E _inst_1)) _inst_2))) x) x) (OfNat.ofNat.{u1} E 0 (Zero.toOfNat0.{u1} E (SemigroupWithZero.toZero.{u1} E (NonUnitalSemiring.toSemigroupWithZero.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E _inst_1))))))) (Eq.{succ u1} E x (OfNat.ofNat.{u1} E 0 (Zero.toOfNat0.{u1} E (SemigroupWithZero.toZero.{u1} E (NonUnitalSemiring.toSemigroupWithZero.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E _inst_1)))))))
 Case conversion may be inaccurate. Consider using '#align cstar_ring.star_mul_self_eq_zero_iff CstarRing.star_mul_self_eq_zero_iffₓ'. -/
 @[simp]
-theorem star_mul_self_eq_zero_iff (x : E) : star x * x = 0 ↔ x = 0 :=
-  by
-  rw [← norm_eq_zero, norm_star_mul_self]
-  exact mul_self_eq_zero.trans norm_eq_zero
+theorem star_mul_self_eq_zero_iff (x : E) : star x * x = 0 ↔ x = 0 := by
+  rw [← norm_eq_zero, norm_star_mul_self]; exact mul_self_eq_zero.trans norm_eq_zero
 #align cstar_ring.star_mul_self_eq_zero_iff CstarRing.star_mul_self_eq_zero_iff
 
 /- warning: cstar_ring.star_mul_self_ne_zero_iff -> CstarRing.star_mul_self_ne_zero_iff is a dubious translation:
@@ -347,9 +343,7 @@ theorem norm_coe_unitary_mul (U : unitary E) (A : E) : ‖(U : E) * A‖ = ‖A
   ·
     calc
       _ = ‖(U : E)⋆ * U * A‖ := by rw [unitary.coe_star_mul_self U, one_mul]
-      _ ≤ ‖(U : E)⋆‖ * ‖(U : E) * A‖ := by
-        rw [mul_assoc]
-        exact norm_mul_le _ _
+      _ ≤ ‖(U : E)⋆‖ * ‖(U : E) * A‖ := by rw [mul_assoc]; exact norm_mul_le _ _
       _ = ‖(U : E) * A‖ := by rw [norm_star, norm_coe_unitary, one_mul]
       
 #align cstar_ring.norm_coe_unitary_mul CstarRing.norm_coe_unitary_mul

aa666983

bump to nightly-2023-05-28-03

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

6c6011cf

Diff

@@ -422,10 +422,7 @@ theorem IsSelfAdjoint.nnnorm_pow_two_pow [NormedRing E] [StarRing E] [CstarRing
 #align is_self_adjoint.nnnorm_pow_two_pow IsSelfAdjoint.nnnorm_pow_two_pow
 
 /- warning: self_adjoint.nnnorm_pow_two_pow -> selfAdjoint.nnnorm_pow_two_pow is a dubious translation:
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(OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) n))
+<too large>
 Case conversion may be inaccurate. Consider using '#align self_adjoint.nnnorm_pow_two_pow selfAdjoint.nnnorm_pow_two_powₓ'. -/
 theorem selfAdjoint.nnnorm_pow_two_pow [NormedRing E] [StarRing E] [CstarRing E] (x : selfAdjoint E)
     (n : ℕ) : ‖x ^ 2 ^ n‖₊ = ‖x‖₊ ^ 2 ^ n :=
@@ -454,10 +451,7 @@ def starₗᵢ : E ≃ₗᵢ⋆[𝕜] E :=
 variable {𝕜}
 
 /- warning: coe_starₗᵢ -> coe_starₗᵢ is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : CommSemiring.{u1} 𝕜] [_inst_2 : StarRing.{u1} 𝕜 (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} 𝕜 (CommSemiring.toNonUnitalCommSemiring.{u1} 𝕜 _inst_1))] [_inst_3 : SeminormedAddCommGroup.{u2} E] [_inst_4 : StarAddMonoid.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_3))))] [_inst_5 : NormedStarGroup.{u2} E _inst_3 _inst_4] [_inst_6 : Module.{u1, u2} 𝕜 E (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_3))] [_inst_7 : StarModule.{u1, u2} 𝕜 E (InvolutiveStar.toHasStar.{u1} 𝕜 (StarAddMonoid.toHasInvolutiveStar.{u1} 𝕜 (AddCommMonoid.toAddMonoid.{u1} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} 𝕜 (CommSemiring.toNonUnitalCommSemiring.{u1} 𝕜 _inst_1))))) (StarRing.toStarAddMonoid.{u1} 𝕜 (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} 𝕜 (CommSemiring.toNonUnitalCommSemiring.{u1} 𝕜 _inst_1)) _inst_2))) (InvolutiveStar.toHasStar.{u2} E (StarAddMonoid.toHasInvolutiveStar.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_3)))) _inst_4)) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_3))))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_3))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_3)) _inst_6))))], Eq.{succ u2} ((fun (_x : LinearIsometryEquiv.{u1, u1, u2, u2} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (starRingEnd.{u1} 𝕜 _inst_1 _inst_2) (starRingEnd.{u1} 𝕜 _inst_1 _inst_2) (RingHomInvPair.StarRingEnd.ringHomInvPair.{u1} 𝕜 _inst_1 _inst_2) (RingHomInvPair.StarRingEnd.ringHomInvPair.{u1} 𝕜 _inst_1 _inst_2) E E _inst_3 _inst_3 _inst_6 _inst_6) => E -> E) (starₗᵢ.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7)) (coeFn.{succ u2, succ u2} (LinearIsometryEquiv.{u1, u1, u2, u2} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (starRingEnd.{u1} 𝕜 _inst_1 _inst_2) (starRingEnd.{u1} 𝕜 _inst_1 _inst_2) (RingHomInvPair.StarRingEnd.ringHomInvPair.{u1} 𝕜 _inst_1 _inst_2) (RingHomInvPair.StarRingEnd.ringHomInvPair.{u1} 𝕜 _inst_1 _inst_2) E E _inst_3 _inst_3 _inst_6 _inst_6) (fun (_x : LinearIsometryEquiv.{u1, u1, u2, u2} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (starRingEnd.{u1} 𝕜 _inst_1 _inst_2) (starRingEnd.{u1} 𝕜 _inst_1 _inst_2) (RingHomInvPair.StarRingEnd.ringHomInvPair.{u1} 𝕜 _inst_1 _inst_2) (RingHomInvPair.StarRingEnd.ringHomInvPair.{u1} 𝕜 _inst_1 _inst_2) E E _inst_3 _inst_3 _inst_6 _inst_6) => E -> E) (LinearIsometryEquiv.hasCoeToFun.{u1, u1, u2, u2} 𝕜 𝕜 E E (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (starRingEnd.{u1} 𝕜 _inst_1 _inst_2) (starRingEnd.{u1} 𝕜 _inst_1 _inst_2) (RingHomInvPair.StarRingEnd.ringHomInvPair.{u1} 𝕜 _inst_1 _inst_2) (RingHomInvPair.StarRingEnd.ringHomInvPair.{u1} 𝕜 _inst_1 _inst_2) _inst_3 _inst_3 _inst_6 _inst_6) (starₗᵢ.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7)) (Star.star.{u2} E (InvolutiveStar.toHasStar.{u2} E (StarAddMonoid.toHasInvolutiveStar.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_3)))) _inst_4)))
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : CommSemiring.{u1} 𝕜] [_inst_2 : StarRing.{u1} 𝕜 (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} 𝕜 (CommSemiring.toNonUnitalCommSemiring.{u1} 𝕜 _inst_1))] [_inst_3 : SeminormedAddCommGroup.{u2} E] [_inst_4 : StarAddMonoid.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_3))))] [_inst_5 : NormedStarGroup.{u2} E _inst_3 _inst_4] [_inst_6 : Module.{u1, u2} 𝕜 E (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_3))] [_inst_7 : StarModule.{u1, u2} 𝕜 E (InvolutiveStar.toStar.{u1} 𝕜 (StarAddMonoid.toInvolutiveStar.{u1} 𝕜 (AddMonoidWithOne.toAddMonoid.{u1} 𝕜 (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} 𝕜 (NonAssocSemiring.toAddCommMonoidWithOne.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 _inst_1))))) (StarRing.toStarAddMonoid.{u1} 𝕜 (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} 𝕜 (CommSemiring.toNonUnitalCommSemiring.{u1} 𝕜 _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u2} E (StarAddMonoid.toInvolutiveStar.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_3)))) _inst_4)) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_3)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 _inst_1)) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 _inst_1)) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_3)))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_3)) _inst_6))))], Eq.{succ u2} (forall (a : E), (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => E) a) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearIsometryEquiv.{u1, u1, u2, u2} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (starRingEnd.{u1} 𝕜 _inst_1 _inst_2) (starRingEnd.{u1} 𝕜 _inst_1 _inst_2) (RingHomInvPair.instRingHomInvPairToSemiringStarRingEnd.{u1} 𝕜 _inst_1 _inst_2) (RingHomInvPair.instRingHomInvPairToSemiringStarRingEnd.{u1} 𝕜 _inst_1 _inst_2) E E _inst_3 _inst_3 _inst_6 _inst_6) E (fun (_x : E) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => E) _x) (ContinuousMapClass.toFunLike.{u2, u2, u2} (LinearIsometryEquiv.{u1, u1, u2, u2} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (starRingEnd.{u1} 𝕜 _inst_1 _inst_2) (starRingEnd.{u1} 𝕜 _inst_1 _inst_2) (RingHomInvPair.instRingHomInvPairToSemiringStarRingEnd.{u1} 𝕜 _inst_1 _inst_2) (RingHomInvPair.instRingHomInvPairToSemiringStarRingEnd.{u1} 𝕜 _inst_1 _inst_2) E E _inst_3 _inst_3 _inst_6 _inst_6) E E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_3))) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_3))) (ContinuousSemilinearMapClass.toContinuousMapClass.{u2, u1, u1, u2, u2} (LinearIsometryEquiv.{u1, u1, u2, u2} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (starRingEnd.{u1} 𝕜 _inst_1 _inst_2) (starRingEnd.{u1} 𝕜 _inst_1 _inst_2) (RingHomInvPair.instRingHomInvPairToSemiringStarRingEnd.{u1} 𝕜 _inst_1 _inst_2) (RingHomInvPair.instRingHomInvPairToSemiringStarRingEnd.{u1} 𝕜 _inst_1 _inst_2) E E _inst_3 _inst_3 _inst_6 _inst_6) 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (starRingEnd.{u1} 𝕜 _inst_1 _inst_2) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_3)) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_3)) _inst_6 _inst_6 (SemilinearIsometryClass.instContinuousSemilinearMapClassToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToAddCommMonoidToAddCommGroupToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToAddCommMonoidToAddCommGroup.{u1, u1, u2, u2, u2} 𝕜 𝕜 E E (LinearIsometryEquiv.{u1, u1, u2, u2} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (starRingEnd.{u1} 𝕜 _inst_1 _inst_2) (starRingEnd.{u1} 𝕜 _inst_1 _inst_2) (RingHomInvPair.instRingHomInvPairToSemiringStarRingEnd.{u1} 𝕜 _inst_1 _inst_2) (RingHomInvPair.instRingHomInvPairToSemiringStarRingEnd.{u1} 𝕜 _inst_1 _inst_2) E E _inst_3 _inst_3 _inst_6 _inst_6) (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (starRingEnd.{u1} 𝕜 _inst_1 _inst_2) _inst_3 _inst_3 _inst_6 _inst_6 (SemilinearIsometryEquivClass.instSemilinearIsometryClass.{u1, u1, u2, u2, u2} 𝕜 𝕜 E E (LinearIsometryEquiv.{u1, u1, u2, u2} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (starRingEnd.{u1} 𝕜 _inst_1 _inst_2) (starRingEnd.{u1} 𝕜 _inst_1 _inst_2) (RingHomInvPair.instRingHomInvPairToSemiringStarRingEnd.{u1} 𝕜 _inst_1 _inst_2) (RingHomInvPair.instRingHomInvPairToSemiringStarRingEnd.{u1} 𝕜 _inst_1 _inst_2) E E _inst_3 _inst_3 _inst_6 _inst_6) (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (starRingEnd.{u1} 𝕜 _inst_1 _inst_2) (starRingEnd.{u1} 𝕜 _inst_1 _inst_2) (RingHomInvPair.instRingHomInvPairToSemiringStarRingEnd.{u1} 𝕜 _inst_1 _inst_2) (RingHomInvPair.instRingHomInvPairToSemiringStarRingEnd.{u1} 𝕜 _inst_1 _inst_2) _inst_3 _inst_3 _inst_6 _inst_6 (LinearIsometryEquiv.instSemilinearIsometryEquivClassLinearIsometryEquiv.{u1, u1, u2, u2} 𝕜 𝕜 E E (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (starRingEnd.{u1} 𝕜 _inst_1 _inst_2) (starRingEnd.{u1} 𝕜 _inst_1 _inst_2) (RingHomInvPair.instRingHomInvPairToSemiringStarRingEnd.{u1} 𝕜 _inst_1 _inst_2) (RingHomInvPair.instRingHomInvPairToSemiringStarRingEnd.{u1} 𝕜 _inst_1 _inst_2) _inst_3 _inst_3 _inst_6 _inst_6))))) (starₗᵢ.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7)) (Star.star.{u2} E (InvolutiveStar.toStar.{u2} E (StarAddMonoid.toInvolutiveStar.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_3)))) _inst_4)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align coe_starₗᵢ coe_starₗᵢₓ'. -/
 @[simp]
 theorem coe_starₗᵢ : (starₗᵢ 𝕜 : E → E) = star :=
@@ -465,10 +459,7 @@ theorem coe_starₗᵢ : (starₗᵢ 𝕜 : E → E) = star :=
 #align coe_starₗᵢ coe_starₗᵢ
 
 /- warning: starₗᵢ_apply -> starₗᵢ_apply is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : CommSemiring.{u1} 𝕜] [_inst_2 : StarRing.{u1} 𝕜 (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} 𝕜 (CommSemiring.toNonUnitalCommSemiring.{u1} 𝕜 _inst_1))] [_inst_3 : SeminormedAddCommGroup.{u2} E] [_inst_4 : StarAddMonoid.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_3))))] [_inst_5 : NormedStarGroup.{u2} E _inst_3 _inst_4] [_inst_6 : Module.{u1, u2} 𝕜 E (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_3))] [_inst_7 : StarModule.{u1, u2} 𝕜 E (InvolutiveStar.toHasStar.{u1} 𝕜 (StarAddMonoid.toHasInvolutiveStar.{u1} 𝕜 (AddCommMonoid.toAddMonoid.{u1} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} 𝕜 (CommSemiring.toNonUnitalCommSemiring.{u1} 𝕜 _inst_1))))) (StarRing.toStarAddMonoid.{u1} 𝕜 (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} 𝕜 (CommSemiring.toNonUnitalCommSemiring.{u1} 𝕜 _inst_1)) _inst_2))) (InvolutiveStar.toHasStar.{u2} E (StarAddMonoid.toHasInvolutiveStar.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_3)))) _inst_4)) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_3))))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_3))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_3)) _inst_6))))] {x : E}, Eq.{succ u2} E (coeFn.{succ u2, succ u2} (LinearIsometryEquiv.{u1, u1, u2, u2} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (starRingEnd.{u1} 𝕜 _inst_1 _inst_2) (starRingEnd.{u1} 𝕜 _inst_1 _inst_2) (RingHomInvPair.StarRingEnd.ringHomInvPair.{u1} 𝕜 _inst_1 _inst_2) (RingHomInvPair.StarRingEnd.ringHomInvPair.{u1} 𝕜 _inst_1 _inst_2) E E _inst_3 _inst_3 _inst_6 _inst_6) (fun (_x : LinearIsometryEquiv.{u1, u1, u2, u2} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (starRingEnd.{u1} 𝕜 _inst_1 _inst_2) (starRingEnd.{u1} 𝕜 _inst_1 _inst_2) (RingHomInvPair.StarRingEnd.ringHomInvPair.{u1} 𝕜 _inst_1 _inst_2) (RingHomInvPair.StarRingEnd.ringHomInvPair.{u1} 𝕜 _inst_1 _inst_2) E E _inst_3 _inst_3 _inst_6 _inst_6) => E -> E) (LinearIsometryEquiv.hasCoeToFun.{u1, u1, u2, u2} 𝕜 𝕜 E E (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (starRingEnd.{u1} 𝕜 _inst_1 _inst_2) (starRingEnd.{u1} 𝕜 _inst_1 _inst_2) (RingHomInvPair.StarRingEnd.ringHomInvPair.{u1} 𝕜 _inst_1 _inst_2) (RingHomInvPair.StarRingEnd.ringHomInvPair.{u1} 𝕜 _inst_1 _inst_2) _inst_3 _inst_3 _inst_6 _inst_6) (starₗᵢ.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) x) (Star.star.{u2} E (InvolutiveStar.toHasStar.{u2} E (StarAddMonoid.toHasInvolutiveStar.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_3)))) _inst_4)) x)
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : CommSemiring.{u1} 𝕜] [_inst_2 : StarRing.{u1} 𝕜 (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} 𝕜 (CommSemiring.toNonUnitalCommSemiring.{u1} 𝕜 _inst_1))] [_inst_3 : SeminormedAddCommGroup.{u2} E] [_inst_4 : StarAddMonoid.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_3))))] [_inst_5 : NormedStarGroup.{u2} E _inst_3 _inst_4] [_inst_6 : Module.{u1, u2} 𝕜 E (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_3))] [_inst_7 : StarModule.{u1, u2} 𝕜 E (InvolutiveStar.toStar.{u1} 𝕜 (StarAddMonoid.toInvolutiveStar.{u1} 𝕜 (AddMonoidWithOne.toAddMonoid.{u1} 𝕜 (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} 𝕜 (NonAssocSemiring.toAddCommMonoidWithOne.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 _inst_1))))) (StarRing.toStarAddMonoid.{u1} 𝕜 (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} 𝕜 (CommSemiring.toNonUnitalCommSemiring.{u1} 𝕜 _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u2} E (StarAddMonoid.toInvolutiveStar.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_3)))) _inst_4)) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_3)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 _inst_1)) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 _inst_1)) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_3)))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_3)) _inst_6))))] {x : E}, Eq.{succ u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => E) x) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearIsometryEquiv.{u1, u1, u2, u2} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (starRingEnd.{u1} 𝕜 _inst_1 _inst_2) (starRingEnd.{u1} 𝕜 _inst_1 _inst_2) (RingHomInvPair.instRingHomInvPairToSemiringStarRingEnd.{u1} 𝕜 _inst_1 _inst_2) (RingHomInvPair.instRingHomInvPairToSemiringStarRingEnd.{u1} 𝕜 _inst_1 _inst_2) E E _inst_3 _inst_3 _inst_6 _inst_6) E (fun (_x : E) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => E) _x) (ContinuousMapClass.toFunLike.{u2, u2, u2} (LinearIsometryEquiv.{u1, u1, u2, u2} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (starRingEnd.{u1} 𝕜 _inst_1 _inst_2) (starRingEnd.{u1} 𝕜 _inst_1 _inst_2) (RingHomInvPair.instRingHomInvPairToSemiringStarRingEnd.{u1} 𝕜 _inst_1 _inst_2) (RingHomInvPair.instRingHomInvPairToSemiringStarRingEnd.{u1} 𝕜 _inst_1 _inst_2) E E _inst_3 _inst_3 _inst_6 _inst_6) E E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_3))) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_3))) (ContinuousSemilinearMapClass.toContinuousMapClass.{u2, u1, u1, u2, u2} (LinearIsometryEquiv.{u1, u1, u2, u2} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (starRingEnd.{u1} 𝕜 _inst_1 _inst_2) (starRingEnd.{u1} 𝕜 _inst_1 _inst_2) (RingHomInvPair.instRingHomInvPairToSemiringStarRingEnd.{u1} 𝕜 _inst_1 _inst_2) (RingHomInvPair.instRingHomInvPairToSemiringStarRingEnd.{u1} 𝕜 _inst_1 _inst_2) E E _inst_3 _inst_3 _inst_6 _inst_6) 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (starRingEnd.{u1} 𝕜 _inst_1 _inst_2) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_3)) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_3)) _inst_6 _inst_6 (SemilinearIsometryClass.instContinuousSemilinearMapClassToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToAddCommMonoidToAddCommGroupToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToAddCommMonoidToAddCommGroup.{u1, u1, u2, u2, u2} 𝕜 𝕜 E E (LinearIsometryEquiv.{u1, u1, u2, u2} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (starRingEnd.{u1} 𝕜 _inst_1 _inst_2) (starRingEnd.{u1} 𝕜 _inst_1 _inst_2) (RingHomInvPair.instRingHomInvPairToSemiringStarRingEnd.{u1} 𝕜 _inst_1 _inst_2) (RingHomInvPair.instRingHomInvPairToSemiringStarRingEnd.{u1} 𝕜 _inst_1 _inst_2) E E _inst_3 _inst_3 _inst_6 _inst_6) (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (starRingEnd.{u1} 𝕜 _inst_1 _inst_2) _inst_3 _inst_3 _inst_6 _inst_6 (SemilinearIsometryEquivClass.instSemilinearIsometryClass.{u1, u1, u2, u2, u2} 𝕜 𝕜 E E (LinearIsometryEquiv.{u1, u1, u2, u2} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (starRingEnd.{u1} 𝕜 _inst_1 _inst_2) (starRingEnd.{u1} 𝕜 _inst_1 _inst_2) (RingHomInvPair.instRingHomInvPairToSemiringStarRingEnd.{u1} 𝕜 _inst_1 _inst_2) (RingHomInvPair.instRingHomInvPairToSemiringStarRingEnd.{u1} 𝕜 _inst_1 _inst_2) E E _inst_3 _inst_3 _inst_6 _inst_6) (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (starRingEnd.{u1} 𝕜 _inst_1 _inst_2) (starRingEnd.{u1} 𝕜 _inst_1 _inst_2) (RingHomInvPair.instRingHomInvPairToSemiringStarRingEnd.{u1} 𝕜 _inst_1 _inst_2) (RingHomInvPair.instRingHomInvPairToSemiringStarRingEnd.{u1} 𝕜 _inst_1 _inst_2) _inst_3 _inst_3 _inst_6 _inst_6 (LinearIsometryEquiv.instSemilinearIsometryEquivClassLinearIsometryEquiv.{u1, u1, u2, u2} 𝕜 𝕜 E E (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (starRingEnd.{u1} 𝕜 _inst_1 _inst_2) (starRingEnd.{u1} 𝕜 _inst_1 _inst_2) (RingHomInvPair.instRingHomInvPairToSemiringStarRingEnd.{u1} 𝕜 _inst_1 _inst_2) (RingHomInvPair.instRingHomInvPairToSemiringStarRingEnd.{u1} 𝕜 _inst_1 _inst_2) _inst_3 _inst_3 _inst_6 _inst_6))))) (starₗᵢ.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) x) (Star.star.{u2} E (InvolutiveStar.toStar.{u2} E (StarAddMonoid.toInvolutiveStar.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_3)))) _inst_4)) x)
+<too large>
 Case conversion may be inaccurate. Consider using '#align starₗᵢ_apply starₗᵢ_applyₓ'. -/
 theorem starₗᵢ_apply {x : E} : starₗᵢ 𝕜 x = star x :=
   rfl

aa666983

bump to nightly-2023-05-21-11

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

edafec7f

Diff

@@ -474,11 +474,13 @@ theorem starₗᵢ_apply {x : E} : starₗᵢ 𝕜 x = star x :=
   rfl
 #align starₗᵢ_apply starₗᵢ_apply
 
+#print starₗᵢ_toContinuousLinearEquiv /-
 @[simp]
 theorem starₗᵢ_toContinuousLinearEquiv :
     (starₗᵢ 𝕜 : E ≃ₗᵢ⋆[𝕜] E).toContinuousLinearEquiv = (starL 𝕜 : E ≃L⋆[𝕜] E) :=
   ContinuousLinearEquiv.ext rfl
 #align starₗᵢ_to_continuous_linear_equiv starₗᵢ_toContinuousLinearEquiv
+-/
 
 end starₗᵢ

aa666983

bump to nightly-2023-05-20-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/f51de8769c34652d82d1c8e5f8f18f8374782bed

0efc566e

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 analysis.normed_space.star.basic
-! leanprover-community/mathlib commit 9d2f0748e6c50d7a2657c564b1ff2c695b39148d
+! leanprover-community/mathlib commit aa6669832974f87406a3d9d70fc5707a60546207
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,7 @@ import Mathbin.Analysis.NormedSpace.LinearIsometry
 import Mathbin.Algebra.Star.SelfAdjoint
 import Mathbin.Algebra.Star.Unitary
 import Mathbin.Topology.Algebra.StarSubalgebra
+import Mathbin.Topology.Algebra.Module.Star
 
 /-!
 # Normed star rings and algebras
@@ -473,6 +474,12 @@ theorem starₗᵢ_apply {x : E} : starₗᵢ 𝕜 x = star x :=
   rfl
 #align starₗᵢ_apply starₗᵢ_apply
 
+@[simp]
+theorem starₗᵢ_toContinuousLinearEquiv :
+    (starₗᵢ 𝕜 : E ≃ₗᵢ⋆[𝕜] E).toContinuousLinearEquiv = (starL 𝕜 : E ≃L⋆[𝕜] E) :=
+  ContinuousLinearEquiv.ext rfl
+#align starₗᵢ_to_continuous_linear_equiv starₗᵢ_toContinuousLinearEquiv
+
 end starₗᵢ
 
 namespace StarSubalgebra

9d2f0748

bump to nightly-2023-05-08-22

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

63e712c6

Diff

@@ -292,7 +292,7 @@ variable [NormedRing E] [StarRing E] [CstarRing E]
 lean 3 declaration is
   forall {E : Type.{u1}} [_inst_1 : NormedRing.{u1} E] [_inst_2 : StarRing.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1)))] [_inst_3 : CstarRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1) _inst_2] [_inst_4 : Nontrivial.{u1} E], Eq.{1} Real (Norm.norm.{u1} E (NormedRing.toHasNorm.{u1} E _inst_1) (OfNat.ofNat.{u1} E 1 (OfNat.mk.{u1} E 1 (One.one.{u1} E (AddMonoidWithOne.toOne.{u1} E (AddGroupWithOne.toAddMonoidWithOne.{u1} E (AddCommGroupWithOne.toAddGroupWithOne.{u1} E (Ring.toAddCommGroupWithOne.{u1} E (NormedRing.toRing.{u1} E _inst_1))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))
 but is expected to have type
-  forall {E : Type.{u1}} [_inst_1 : NormedRing.{u1} E] [_inst_2 : StarRing.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1)))] [_inst_3 : CstarRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1) _inst_2] [_inst_4 : Nontrivial.{u1} E], Eq.{1} Real (Norm.norm.{u1} E (NormedRing.toNorm.{u1} E _inst_1) (OfNat.ofNat.{u1} E 1 (One.toOfNat1.{u1} E (NonAssocRing.toOne.{u1} E (Ring.toNonAssocRing.{u1} E (NormedRing.toRing.{u1} E _inst_1)))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))
+  forall {E : Type.{u1}} [_inst_1 : NormedRing.{u1} E] [_inst_2 : StarRing.{u1} E (Semiring.toNonUnitalSemiring.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))] [_inst_3 : CstarRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1) _inst_2] [_inst_4 : Nontrivial.{u1} E], Eq.{1} Real (Norm.norm.{u1} E (NormedRing.toNorm.{u1} E _inst_1) (OfNat.ofNat.{u1} E 1 (One.toOfNat1.{u1} E (Semiring.toOne.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))
 Case conversion may be inaccurate. Consider using '#align cstar_ring.norm_one CstarRing.norm_oneₓ'. -/
 @[simp]
 theorem norm_one [Nontrivial E] : ‖(1 : E)‖ = 1 :=
@@ -309,7 +309,7 @@ instance (priority := 100) [Nontrivial E] : NormOneClass E :=
 lean 3 declaration is
   forall {E : Type.{u1}} [_inst_1 : NormedRing.{u1} E] [_inst_2 : StarRing.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1)))] [_inst_3 : CstarRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1) _inst_2] [_inst_4 : Nontrivial.{u1} E] (U : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} E (Monoid.toMulOneClass.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1)))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} E (Monoid.toMulOneClass.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1)))) E (Submonoid.setLike.{u1} E (Monoid.toMulOneClass.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1))))) (unitary.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1)) (StarRing.toStarSemigroup.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))) _inst_2))), Eq.{1} Real (Norm.norm.{u1} E (NormedRing.toHasNorm.{u1} E _inst_1) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} E (Monoid.toMulOneClass.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1)))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} E (Monoid.toMulOneClass.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1)))) E (Submonoid.setLike.{u1} E (Monoid.toMulOneClass.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1))))) (unitary.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1)) (StarRing.toStarSemigroup.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))) _inst_2))) E (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} E (Monoid.toMulOneClass.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1)))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} E (Monoid.toMulOneClass.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1)))) E (Submonoid.setLike.{u1} E (Monoid.toMulOneClass.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1))))) (unitary.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1)) (StarRing.toStarSemigroup.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))) _inst_2))) E (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} E (Monoid.toMulOneClass.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1)))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} E (Monoid.toMulOneClass.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1)))) E (Submonoid.setLike.{u1} E (Monoid.toMulOneClass.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1))))) (unitary.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1)) (StarRing.toStarSemigroup.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))) _inst_2))) E (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} E (Monoid.toMulOneClass.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1)))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} E (Monoid.toMulOneClass.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1)))) E (Submonoid.setLike.{u1} E (Monoid.toMulOneClass.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1))))) (unitary.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1)) (StarRing.toStarSemigroup.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))) _inst_2))) E (coeSubtype.{succ u1} E (fun (x : E) => Membership.Mem.{u1, u1} E (Submonoid.{u1} E (Monoid.toMulOneClass.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1)))) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} E (Monoid.toMulOneClass.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1)))) E (Submonoid.setLike.{u1} E (Monoid.toMulOneClass.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1))))) x (unitary.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1)) (StarRing.toStarSemigroup.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))) _inst_2))))))) U)) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))
 but is expected to have type
-  forall {E : Type.{u1}} [_inst_1 : NormedRing.{u1} E] [_inst_2 : StarRing.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1)))] [_inst_3 : CstarRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1) _inst_2] [_inst_4 : Nontrivial.{u1} E] (U : Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submonoid.{u1} E (Monoid.toMulOneClass.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} E (Monoid.toMulOneClass.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))))) E (Submonoid.instSetLikeSubmonoid.{u1} E (Monoid.toMulOneClass.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1))))))) x (unitary.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))) (StarRing.toStarSemigroup.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))) _inst_2)))), Eq.{1} Real (Norm.norm.{u1} E (NormedRing.toNorm.{u1} E _inst_1) (Subtype.val.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) x (SetLike.coe.{u1, u1} (Submonoid.{u1} E (Monoid.toMulOneClass.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))))) E (Submonoid.instSetLikeSubmonoid.{u1} E (Monoid.toMulOneClass.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))))) (unitary.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))) (StarRing.toStarSemigroup.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))) _inst_2)))) U)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))
+  forall {E : Type.{u1}} [_inst_1 : NormedRing.{u1} E] [_inst_2 : StarRing.{u1} E (Semiring.toNonUnitalSemiring.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))] [_inst_3 : CstarRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1) _inst_2] [_inst_4 : Nontrivial.{u1} E] (U : Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submonoid.{u1} E (Monoid.toMulOneClass.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} E (Monoid.toMulOneClass.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))))) E (Submonoid.instSetLikeSubmonoid.{u1} E (Monoid.toMulOneClass.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1))))))) x (unitary.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))) (StarRing.toStarSemigroup.{u1} E (Semiring.toNonUnitalSemiring.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1))) _inst_2)))), Eq.{1} Real (Norm.norm.{u1} E (NormedRing.toNorm.{u1} E _inst_1) (Subtype.val.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) x (SetLike.coe.{u1, u1} (Submonoid.{u1} E (Monoid.toMulOneClass.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))))) E (Submonoid.instSetLikeSubmonoid.{u1} E (Monoid.toMulOneClass.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))))) (unitary.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))) (StarRing.toStarSemigroup.{u1} E (Semiring.toNonUnitalSemiring.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1))) _inst_2)))) U)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))
 Case conversion may be inaccurate. Consider using '#align cstar_ring.norm_coe_unitary CstarRing.norm_coe_unitaryₓ'. -/
 theorem norm_coe_unitary [Nontrivial E] (U : unitary E) : ‖(U : E)‖ = 1 := by
   rw [← sq_eq_sq (norm_nonneg _) zero_le_one, one_pow 2, sq, ← CstarRing.norm_star_mul_self,
@@ -320,7 +320,7 @@ theorem norm_coe_unitary [Nontrivial E] (U : unitary E) : ‖(U : E)‖ = 1 := b
 lean 3 declaration is
   forall {E : Type.{u1}} [_inst_1 : NormedRing.{u1} E] [_inst_2 : StarRing.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1)))] [_inst_3 : CstarRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1) _inst_2] [_inst_4 : Nontrivial.{u1} E] {U : E}, (Membership.Mem.{u1, u1} E (Submonoid.{u1} E (Monoid.toMulOneClass.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1)))) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} E (Monoid.toMulOneClass.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1)))) E (Submonoid.setLike.{u1} E (Monoid.toMulOneClass.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1))))) U (unitary.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1)) (StarRing.toStarSemigroup.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))) _inst_2))) -> (Eq.{1} Real (Norm.norm.{u1} E (NormedRing.toHasNorm.{u1} E _inst_1) U) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))
 but is expected to have type
-  forall {E : Type.{u1}} [_inst_1 : NormedRing.{u1} E] [_inst_2 : StarRing.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1)))] [_inst_3 : CstarRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1) _inst_2] [_inst_4 : Nontrivial.{u1} E] {U : E}, (Membership.mem.{u1, u1} E (Submonoid.{u1} E (Monoid.toMulOneClass.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} E (Monoid.toMulOneClass.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))))) E (Submonoid.instSetLikeSubmonoid.{u1} E (Monoid.toMulOneClass.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1))))))) U (unitary.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))) (StarRing.toStarSemigroup.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))) _inst_2))) -> (Eq.{1} Real (Norm.norm.{u1} E (NormedRing.toNorm.{u1} E _inst_1) U) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))
+  forall {E : Type.{u1}} [_inst_1 : NormedRing.{u1} E] [_inst_2 : StarRing.{u1} E (Semiring.toNonUnitalSemiring.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))] [_inst_3 : CstarRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1) _inst_2] [_inst_4 : Nontrivial.{u1} E] {U : E}, (Membership.mem.{u1, u1} E (Submonoid.{u1} E (Monoid.toMulOneClass.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} E (Monoid.toMulOneClass.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))))) E (Submonoid.instSetLikeSubmonoid.{u1} E (Monoid.toMulOneClass.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1))))))) U (unitary.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))) (StarRing.toStarSemigroup.{u1} E (Semiring.toNonUnitalSemiring.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1))) _inst_2))) -> (Eq.{1} Real (Norm.norm.{u1} E (NormedRing.toNorm.{u1} E _inst_1) U) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))
 Case conversion may be inaccurate. Consider using '#align cstar_ring.norm_of_mem_unitary CstarRing.norm_of_mem_unitaryₓ'. -/
 @[simp]
 theorem norm_of_mem_unitary [Nontrivial E] {U : E} (hU : U ∈ unitary E) : ‖U‖ = 1 :=
@@ -331,7 +331,7 @@ theorem norm_of_mem_unitary [Nontrivial E] {U : E} (hU : U ∈ unitary E) : ‖U
 lean 3 declaration is
   forall {E : Type.{u1}} [_inst_1 : NormedRing.{u1} E] [_inst_2 : StarRing.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1)))] [_inst_3 : CstarRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1) _inst_2] (U : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} E (Monoid.toMulOneClass.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1)))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} E (Monoid.toMulOneClass.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1)))) E (Submonoid.setLike.{u1} E (Monoid.toMulOneClass.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1))))) (unitary.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1)) (StarRing.toStarSemigroup.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))) _inst_2))) (A : E), Eq.{1} Real (Norm.norm.{u1} E (NormedRing.toHasNorm.{u1} E _inst_1) (HMul.hMul.{u1, u1, u1} E E E (instHMul.{u1} E (Distrib.toHasMul.{u1} E (Ring.toDistrib.{u1} E (NormedRing.toRing.{u1} E _inst_1)))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} E (Monoid.toMulOneClass.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1)))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} E (Monoid.toMulOneClass.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1)))) E (Submonoid.setLike.{u1} E (Monoid.toMulOneClass.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1))))) (unitary.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1)) (StarRing.toStarSemigroup.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))) _inst_2))) E (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} E (Monoid.toMulOneClass.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1)))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} E (Monoid.toMulOneClass.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1)))) E (Submonoid.setLike.{u1} E (Monoid.toMulOneClass.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1))))) (unitary.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1)) (StarRing.toStarSemigroup.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))) _inst_2))) E (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} E (Monoid.toMulOneClass.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1)))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} E (Monoid.toMulOneClass.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1)))) E (Submonoid.setLike.{u1} E (Monoid.toMulOneClass.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1))))) (unitary.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1)) (StarRing.toStarSemigroup.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))) _inst_2))) E (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} E (Monoid.toMulOneClass.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1)))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} E (Monoid.toMulOneClass.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1)))) E (Submonoid.setLike.{u1} E (Monoid.toMulOneClass.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1))))) (unitary.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1)) (StarRing.toStarSemigroup.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))) _inst_2))) E (coeSubtype.{succ u1} E (fun (x : E) => Membership.Mem.{u1, u1} E (Submonoid.{u1} E (Monoid.toMulOneClass.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1)))) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} E (Monoid.toMulOneClass.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1)))) E (Submonoid.setLike.{u1} E (Monoid.toMulOneClass.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1))))) x (unitary.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1)) (StarRing.toStarSemigroup.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))) _inst_2))))))) U) A)) (Norm.norm.{u1} E (NormedRing.toHasNorm.{u1} E _inst_1) A)
 but is expected to have type
-  forall {E : Type.{u1}} [_inst_1 : NormedRing.{u1} E] [_inst_2 : StarRing.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1)))] [_inst_3 : CstarRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1) _inst_2] (U : Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submonoid.{u1} E (Monoid.toMulOneClass.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} E (Monoid.toMulOneClass.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))))) E (Submonoid.instSetLikeSubmonoid.{u1} E (Monoid.toMulOneClass.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1))))))) x (unitary.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))) (StarRing.toStarSemigroup.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))) _inst_2)))) (A : E), Eq.{1} Real (Norm.norm.{u1} E (NormedRing.toNorm.{u1} E _inst_1) (HMul.hMul.{u1, u1, u1} E E E (instHMul.{u1} E (NonUnitalNonAssocRing.toMul.{u1} E (NonAssocRing.toNonUnitalNonAssocRing.{u1} E (Ring.toNonAssocRing.{u1} E (NormedRing.toRing.{u1} E _inst_1))))) (Subtype.val.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) x (SetLike.coe.{u1, u1} (Submonoid.{u1} E (Monoid.toMulOneClass.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))))) E (Submonoid.instSetLikeSubmonoid.{u1} E (Monoid.toMulOneClass.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))))) (unitary.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))) (StarRing.toStarSemigroup.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))) _inst_2)))) U) A)) (Norm.norm.{u1} E (NormedRing.toNorm.{u1} E _inst_1) A)
+  forall {E : Type.{u1}} [_inst_1 : NormedRing.{u1} E] [_inst_2 : StarRing.{u1} E (Semiring.toNonUnitalSemiring.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))] [_inst_3 : CstarRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1) _inst_2] (U : Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submonoid.{u1} E (Monoid.toMulOneClass.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} E (Monoid.toMulOneClass.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))))) E (Submonoid.instSetLikeSubmonoid.{u1} E (Monoid.toMulOneClass.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1))))))) x (unitary.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))) (StarRing.toStarSemigroup.{u1} E (Semiring.toNonUnitalSemiring.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1))) _inst_2)))) (A : E), Eq.{1} Real (Norm.norm.{u1} E (NormedRing.toNorm.{u1} E _inst_1) (HMul.hMul.{u1, u1, u1} E E E (instHMul.{u1} E (NonUnitalNonAssocRing.toMul.{u1} E (NonAssocRing.toNonUnitalNonAssocRing.{u1} E (Ring.toNonAssocRing.{u1} E (NormedRing.toRing.{u1} E _inst_1))))) (Subtype.val.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) x (SetLike.coe.{u1, u1} (Submonoid.{u1} E (Monoid.toMulOneClass.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))))) E (Submonoid.instSetLikeSubmonoid.{u1} E (Monoid.toMulOneClass.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))))) (unitary.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))) (StarRing.toStarSemigroup.{u1} E (Semiring.toNonUnitalSemiring.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1))) _inst_2)))) U) A)) (Norm.norm.{u1} E (NormedRing.toNorm.{u1} E _inst_1) A)
 Case conversion may be inaccurate. Consider using '#align cstar_ring.norm_coe_unitary_mul CstarRing.norm_coe_unitary_mulₓ'. -/
 @[simp]
 theorem norm_coe_unitary_mul (U : unitary E) (A : E) : ‖(U : E) * A‖ = ‖A‖ :=
@@ -357,7 +357,7 @@ theorem norm_coe_unitary_mul (U : unitary E) (A : E) : ‖(U : E) * A‖ = ‖A
 lean 3 declaration is
   forall {E : Type.{u1}} [_inst_1 : NormedRing.{u1} E] [_inst_2 : StarRing.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1)))] [_inst_3 : CstarRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1) _inst_2] (U : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} E (Monoid.toMulOneClass.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1)))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} E (Monoid.toMulOneClass.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1)))) E (Submonoid.setLike.{u1} E (Monoid.toMulOneClass.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1))))) (unitary.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1)) (StarRing.toStarSemigroup.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))) _inst_2))) (A : E), Eq.{1} Real (Norm.norm.{u1} E (NormedRing.toHasNorm.{u1} E _inst_1) (SMul.smul.{u1, u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} E (Monoid.toMulOneClass.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1)))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} E (Monoid.toMulOneClass.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1)))) E (Submonoid.setLike.{u1} E (Monoid.toMulOneClass.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1))))) (unitary.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1)) (StarRing.toStarSemigroup.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))) _inst_2))) E (Submonoid.hasSmul.{u1, u1} E E (Monoid.toMulOneClass.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1))) (Mul.toSMul.{u1} E (Distrib.toHasMul.{u1} E (Ring.toDistrib.{u1} E (NormedRing.toRing.{u1} E _inst_1)))) (unitary.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1)) (StarRing.toStarSemigroup.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))) _inst_2))) U A)) (Norm.norm.{u1} E (NormedRing.toHasNorm.{u1} E _inst_1) A)
 but is expected to have type
-  forall {E : Type.{u1}} [_inst_1 : NormedRing.{u1} E] [_inst_2 : StarRing.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1)))] [_inst_3 : CstarRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1) _inst_2] (U : Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submonoid.{u1} E (Monoid.toMulOneClass.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} E (Monoid.toMulOneClass.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))))) E (Submonoid.instSetLikeSubmonoid.{u1} E (Monoid.toMulOneClass.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1))))))) x (unitary.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))) (StarRing.toStarSemigroup.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))) _inst_2)))) (A : E), Eq.{1} Real (Norm.norm.{u1} E (NormedRing.toNorm.{u1} E _inst_1) (HSMul.hSMul.{u1, u1, u1} (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submonoid.{u1} E (Monoid.toMulOneClass.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} E (Monoid.toMulOneClass.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))))) E (Submonoid.instSetLikeSubmonoid.{u1} E (Monoid.toMulOneClass.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1))))))) x (unitary.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))) (StarRing.toStarSemigroup.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))) _inst_2)))) E E (instHSMul.{u1, u1} (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submonoid.{u1} E (Monoid.toMulOneClass.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} E (Monoid.toMulOneClass.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))))) E (Submonoid.instSetLikeSubmonoid.{u1} E (Monoid.toMulOneClass.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1))))))) x (unitary.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))) (StarRing.toStarSemigroup.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))) _inst_2)))) E (Submonoid.smul.{u1, u1} E E (Monoid.toMulOneClass.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} E E (MonoidWithZero.toZero.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))) (SMulWithZero.toSMulZeroClass.{u1, u1} E E (MonoidWithZero.toZero.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))) (MonoidWithZero.toZero.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))) (MulZeroClass.toSMulWithZero.{u1} E (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} E (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} E (NonAssocRing.toNonUnitalNonAssocRing.{u1} E (Ring.toNonAssocRing.{u1} E (NormedRing.toRing.{u1} E _inst_1)))))))) (unitary.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))) (StarRing.toStarSemigroup.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))) _inst_2)))) U A)) (Norm.norm.{u1} E (NormedRing.toNorm.{u1} E _inst_1) A)
+  forall {E : Type.{u1}} [_inst_1 : NormedRing.{u1} E] [_inst_2 : StarRing.{u1} E (Semiring.toNonUnitalSemiring.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))] [_inst_3 : CstarRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1) _inst_2] (U : Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submonoid.{u1} E (Monoid.toMulOneClass.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} E (Monoid.toMulOneClass.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))))) E (Submonoid.instSetLikeSubmonoid.{u1} E (Monoid.toMulOneClass.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1))))))) x (unitary.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))) (StarRing.toStarSemigroup.{u1} E (Semiring.toNonUnitalSemiring.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1))) _inst_2)))) (A : E), Eq.{1} Real (Norm.norm.{u1} E (NormedRing.toNorm.{u1} E _inst_1) (HSMul.hSMul.{u1, u1, u1} (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submonoid.{u1} E (Monoid.toMulOneClass.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} E (Monoid.toMulOneClass.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))))) E (Submonoid.instSetLikeSubmonoid.{u1} E (Monoid.toMulOneClass.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1))))))) x (unitary.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))) (StarRing.toStarSemigroup.{u1} E (Semiring.toNonUnitalSemiring.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1))) _inst_2)))) E E (instHSMul.{u1, u1} (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submonoid.{u1} E (Monoid.toMulOneClass.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} E (Monoid.toMulOneClass.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))))) E (Submonoid.instSetLikeSubmonoid.{u1} E (Monoid.toMulOneClass.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1))))))) x (unitary.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))) (StarRing.toStarSemigroup.{u1} E (Semiring.toNonUnitalSemiring.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1))) _inst_2)))) E (Submonoid.smul.{u1, u1} E E (Monoid.toMulOneClass.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1))))) (SMulZeroClass.toSMul.{u1, u1} E E (MonoidWithZero.toZero.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))) (SMulWithZero.toSMulZeroClass.{u1, u1} E E (MonoidWithZero.toZero.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))) (MonoidWithZero.toZero.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))) (MulZeroClass.toSMulWithZero.{u1} E (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} E (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} E (NonAssocRing.toNonUnitalNonAssocRing.{u1} E (Ring.toNonAssocRing.{u1} E (NormedRing.toRing.{u1} E _inst_1)))))))) (unitary.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))) (StarRing.toStarSemigroup.{u1} E (Semiring.toNonUnitalSemiring.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1))) _inst_2)))) U A)) (Norm.norm.{u1} E (NormedRing.toNorm.{u1} E _inst_1) A)
 Case conversion may be inaccurate. Consider using '#align cstar_ring.norm_unitary_smul CstarRing.norm_unitary_smulₓ'. -/
 @[simp]
 theorem norm_unitary_smul (U : unitary E) (A : E) : ‖U • A‖ = ‖A‖ :=
@@ -368,7 +368,7 @@ theorem norm_unitary_smul (U : unitary E) (A : E) : ‖U • A‖ = ‖A‖ :=
 lean 3 declaration is
   forall {E : Type.{u1}} [_inst_1 : NormedRing.{u1} E] [_inst_2 : StarRing.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1)))] [_inst_3 : CstarRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1) _inst_2] {U : E} (A : E), (Membership.Mem.{u1, u1} E (Submonoid.{u1} E (Monoid.toMulOneClass.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1)))) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} E (Monoid.toMulOneClass.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1)))) E (Submonoid.setLike.{u1} E (Monoid.toMulOneClass.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1))))) U (unitary.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1)) (StarRing.toStarSemigroup.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))) _inst_2))) -> (Eq.{1} Real (Norm.norm.{u1} E (NormedRing.toHasNorm.{u1} E _inst_1) (HMul.hMul.{u1, u1, u1} E E E (instHMul.{u1} E (Distrib.toHasMul.{u1} E (Ring.toDistrib.{u1} E (NormedRing.toRing.{u1} E _inst_1)))) U A)) (Norm.norm.{u1} E (NormedRing.toHasNorm.{u1} E _inst_1) A))
 but is expected to have type
-  forall {E : Type.{u1}} [_inst_1 : NormedRing.{u1} E] [_inst_2 : StarRing.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1)))] [_inst_3 : CstarRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1) _inst_2] {U : E} (A : E), (Membership.mem.{u1, u1} E (Submonoid.{u1} E (Monoid.toMulOneClass.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} E (Monoid.toMulOneClass.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))))) E (Submonoid.instSetLikeSubmonoid.{u1} E (Monoid.toMulOneClass.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1))))))) U (unitary.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))) (StarRing.toStarSemigroup.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))) _inst_2))) -> (Eq.{1} Real (Norm.norm.{u1} E (NormedRing.toNorm.{u1} E _inst_1) (HMul.hMul.{u1, u1, u1} E E E (instHMul.{u1} E (NonUnitalNonAssocRing.toMul.{u1} E (NonAssocRing.toNonUnitalNonAssocRing.{u1} E (Ring.toNonAssocRing.{u1} E (NormedRing.toRing.{u1} E _inst_1))))) U A)) (Norm.norm.{u1} E (NormedRing.toNorm.{u1} E _inst_1) A))
+  forall {E : Type.{u1}} [_inst_1 : NormedRing.{u1} E] [_inst_2 : StarRing.{u1} E (Semiring.toNonUnitalSemiring.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))] [_inst_3 : CstarRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1) _inst_2] {U : E} (A : E), (Membership.mem.{u1, u1} E (Submonoid.{u1} E (Monoid.toMulOneClass.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} E (Monoid.toMulOneClass.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))))) E (Submonoid.instSetLikeSubmonoid.{u1} E (Monoid.toMulOneClass.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1))))))) U (unitary.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))) (StarRing.toStarSemigroup.{u1} E (Semiring.toNonUnitalSemiring.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1))) _inst_2))) -> (Eq.{1} Real (Norm.norm.{u1} E (NormedRing.toNorm.{u1} E _inst_1) (HMul.hMul.{u1, u1, u1} E E E (instHMul.{u1} E (NonUnitalNonAssocRing.toMul.{u1} E (NonAssocRing.toNonUnitalNonAssocRing.{u1} E (Ring.toNonAssocRing.{u1} E (NormedRing.toRing.{u1} E _inst_1))))) U A)) (Norm.norm.{u1} E (NormedRing.toNorm.{u1} E _inst_1) A))
 Case conversion may be inaccurate. Consider using '#align cstar_ring.norm_mem_unitary_mul CstarRing.norm_mem_unitary_mulₓ'. -/
 theorem norm_mem_unitary_mul {U : E} (A : E) (hU : U ∈ unitary E) : ‖U * A‖ = ‖A‖ :=
   norm_coe_unitary_mul ⟨U, hU⟩ A
@@ -378,7 +378,7 @@ theorem norm_mem_unitary_mul {U : E} (A : E) (hU : U ∈ unitary E) : ‖U * A
 lean 3 declaration is
   forall {E : Type.{u1}} [_inst_1 : NormedRing.{u1} E] [_inst_2 : StarRing.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1)))] [_inst_3 : CstarRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1) _inst_2] (A : E) (U : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} E (Monoid.toMulOneClass.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1)))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} E (Monoid.toMulOneClass.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1)))) E (Submonoid.setLike.{u1} E (Monoid.toMulOneClass.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1))))) (unitary.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1)) (StarRing.toStarSemigroup.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))) _inst_2))), Eq.{1} Real (Norm.norm.{u1} E (NormedRing.toHasNorm.{u1} E _inst_1) (HMul.hMul.{u1, u1, u1} E E E (instHMul.{u1} E (Distrib.toHasMul.{u1} E (Ring.toDistrib.{u1} E (NormedRing.toRing.{u1} E _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)} (Submonoid.{u1} E (Monoid.toMulOneClass.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1)))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} E (Monoid.toMulOneClass.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1)))) E (Submonoid.setLike.{u1} E (Monoid.toMulOneClass.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1))))) (unitary.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1)) (StarRing.toStarSemigroup.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))) _inst_2))) E (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} E (Monoid.toMulOneClass.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1)))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} E (Monoid.toMulOneClass.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1)))) E (Submonoid.setLike.{u1} E (Monoid.toMulOneClass.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1))))) (unitary.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1)) (StarRing.toStarSemigroup.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))) _inst_2))) E (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} E (Monoid.toMulOneClass.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1)))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} E (Monoid.toMulOneClass.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1)))) E (Submonoid.setLike.{u1} E (Monoid.toMulOneClass.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1))))) (unitary.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1)) (StarRing.toStarSemigroup.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))) _inst_2))) E (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} E (Monoid.toMulOneClass.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1)))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} E (Monoid.toMulOneClass.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1)))) E (Submonoid.setLike.{u1} E (Monoid.toMulOneClass.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1))))) (unitary.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1)) (StarRing.toStarSemigroup.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))) _inst_2))) E (coeSubtype.{succ u1} E (fun (x : E) => Membership.Mem.{u1, u1} E (Submonoid.{u1} E (Monoid.toMulOneClass.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1)))) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} E (Monoid.toMulOneClass.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1)))) E (Submonoid.setLike.{u1} E (Monoid.toMulOneClass.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1))))) x (unitary.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1)) (StarRing.toStarSemigroup.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))) _inst_2))))))) U))) (Norm.norm.{u1} E (NormedRing.toHasNorm.{u1} E _inst_1) A)
 but is expected to have type
-  forall {E : Type.{u1}} [_inst_1 : NormedRing.{u1} E] [_inst_2 : StarRing.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1)))] [_inst_3 : CstarRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1) _inst_2] (A : E) (U : Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submonoid.{u1} E (Monoid.toMulOneClass.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} E (Monoid.toMulOneClass.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))))) E (Submonoid.instSetLikeSubmonoid.{u1} E (Monoid.toMulOneClass.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1))))))) x (unitary.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))) (StarRing.toStarSemigroup.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))) _inst_2)))), Eq.{1} Real (Norm.norm.{u1} E (NormedRing.toNorm.{u1} E _inst_1) (HMul.hMul.{u1, u1, u1} E E E (instHMul.{u1} E (NonUnitalNonAssocRing.toMul.{u1} E (NonAssocRing.toNonUnitalNonAssocRing.{u1} E (Ring.toNonAssocRing.{u1} E (NormedRing.toRing.{u1} E _inst_1))))) A (Subtype.val.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) x (SetLike.coe.{u1, u1} (Submonoid.{u1} E (Monoid.toMulOneClass.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))))) E (Submonoid.instSetLikeSubmonoid.{u1} E (Monoid.toMulOneClass.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))))) (unitary.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))) (StarRing.toStarSemigroup.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))) _inst_2)))) U))) (Norm.norm.{u1} E (NormedRing.toNorm.{u1} E _inst_1) A)
+  forall {E : Type.{u1}} [_inst_1 : NormedRing.{u1} E] [_inst_2 : StarRing.{u1} E (Semiring.toNonUnitalSemiring.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))] [_inst_3 : CstarRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1) _inst_2] (A : E) (U : Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submonoid.{u1} E (Monoid.toMulOneClass.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} E (Monoid.toMulOneClass.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))))) E (Submonoid.instSetLikeSubmonoid.{u1} E (Monoid.toMulOneClass.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1))))))) x (unitary.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))) (StarRing.toStarSemigroup.{u1} E (Semiring.toNonUnitalSemiring.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1))) _inst_2)))), Eq.{1} Real (Norm.norm.{u1} E (NormedRing.toNorm.{u1} E _inst_1) (HMul.hMul.{u1, u1, u1} E E E (instHMul.{u1} E (NonUnitalNonAssocRing.toMul.{u1} E (NonAssocRing.toNonUnitalNonAssocRing.{u1} E (Ring.toNonAssocRing.{u1} E (NormedRing.toRing.{u1} E _inst_1))))) A (Subtype.val.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) x (SetLike.coe.{u1, u1} (Submonoid.{u1} E (Monoid.toMulOneClass.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))))) E (Submonoid.instSetLikeSubmonoid.{u1} E (Monoid.toMulOneClass.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))))) (unitary.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))) (StarRing.toStarSemigroup.{u1} E (Semiring.toNonUnitalSemiring.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1))) _inst_2)))) U))) (Norm.norm.{u1} E (NormedRing.toNorm.{u1} E _inst_1) A)
 Case conversion may be inaccurate. Consider using '#align cstar_ring.norm_mul_coe_unitary CstarRing.norm_mul_coe_unitaryₓ'. -/
 @[simp]
 theorem norm_mul_coe_unitary (A : E) (U : unitary E) : ‖A * U‖ = ‖A‖ :=
@@ -394,7 +394,7 @@ theorem norm_mul_coe_unitary (A : E) (U : unitary E) : ‖A * U‖ = ‖A‖ :=
 lean 3 declaration is
   forall {E : Type.{u1}} [_inst_1 : NormedRing.{u1} E] [_inst_2 : StarRing.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1)))] [_inst_3 : CstarRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1) _inst_2] (A : E) {U : E}, (Membership.Mem.{u1, u1} E (Submonoid.{u1} E (Monoid.toMulOneClass.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1)))) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} E (Monoid.toMulOneClass.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1)))) E (Submonoid.setLike.{u1} E (Monoid.toMulOneClass.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1))))) U (unitary.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1)) (StarRing.toStarSemigroup.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))) _inst_2))) -> (Eq.{1} Real (Norm.norm.{u1} E (NormedRing.toHasNorm.{u1} E _inst_1) (HMul.hMul.{u1, u1, u1} E E E (instHMul.{u1} E (Distrib.toHasMul.{u1} E (Ring.toDistrib.{u1} E (NormedRing.toRing.{u1} E _inst_1)))) A U)) (Norm.norm.{u1} E (NormedRing.toHasNorm.{u1} E _inst_1) A))
 but is expected to have type
-  forall {E : Type.{u1}} [_inst_1 : NormedRing.{u1} E] [_inst_2 : StarRing.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1)))] [_inst_3 : CstarRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1) _inst_2] (A : E) {U : E}, (Membership.mem.{u1, u1} E (Submonoid.{u1} E (Monoid.toMulOneClass.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} E (Monoid.toMulOneClass.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))))) E (Submonoid.instSetLikeSubmonoid.{u1} E (Monoid.toMulOneClass.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1))))))) U (unitary.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))) (StarRing.toStarSemigroup.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))) _inst_2))) -> (Eq.{1} Real (Norm.norm.{u1} E (NormedRing.toNorm.{u1} E _inst_1) (HMul.hMul.{u1, u1, u1} E E E (instHMul.{u1} E (NonUnitalNonAssocRing.toMul.{u1} E (NonAssocRing.toNonUnitalNonAssocRing.{u1} E (Ring.toNonAssocRing.{u1} E (NormedRing.toRing.{u1} E _inst_1))))) A U)) (Norm.norm.{u1} E (NormedRing.toNorm.{u1} E _inst_1) A))
+  forall {E : Type.{u1}} [_inst_1 : NormedRing.{u1} E] [_inst_2 : StarRing.{u1} E (Semiring.toNonUnitalSemiring.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))] [_inst_3 : CstarRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1) _inst_2] (A : E) {U : E}, (Membership.mem.{u1, u1} E (Submonoid.{u1} E (Monoid.toMulOneClass.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} E (Monoid.toMulOneClass.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))))) E (Submonoid.instSetLikeSubmonoid.{u1} E (Monoid.toMulOneClass.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1))))))) U (unitary.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))) (StarRing.toStarSemigroup.{u1} E (Semiring.toNonUnitalSemiring.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1))) _inst_2))) -> (Eq.{1} Real (Norm.norm.{u1} E (NormedRing.toNorm.{u1} E _inst_1) (HMul.hMul.{u1, u1, u1} E E E (instHMul.{u1} E (NonUnitalNonAssocRing.toMul.{u1} E (NonAssocRing.toNonUnitalNonAssocRing.{u1} E (Ring.toNonAssocRing.{u1} E (NormedRing.toRing.{u1} E _inst_1))))) A U)) (Norm.norm.{u1} E (NormedRing.toNorm.{u1} E _inst_1) A))
 Case conversion may be inaccurate. Consider using '#align cstar_ring.norm_mul_mem_unitary CstarRing.norm_mul_mem_unitaryₓ'. -/
 theorem norm_mul_mem_unitary (A : E) {U : E} (hU : U ∈ unitary E) : ‖A * U‖ = ‖A‖ :=
   norm_mul_coe_unitary A ⟨U, hU⟩
@@ -408,7 +408,7 @@ end CstarRing
 lean 3 declaration is
   forall {E : Type.{u1}} [_inst_1 : NormedRing.{u1} E] [_inst_2 : StarRing.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1)))] [_inst_3 : CstarRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1) _inst_2] {x : E}, (IsSelfAdjoint.{u1} E (InvolutiveStar.toHasStar.{u1} E (StarAddMonoid.toHasInvolutiveStar.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} E (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1)))))) (StarRing.toStarAddMonoid.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))) _inst_2))) x) -> (forall (n : Nat), Eq.{1} NNReal (NNNorm.nnnorm.{u1} E (SeminormedAddGroup.toNNNorm.{u1} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} E (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} E (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))))) (HPow.hPow.{u1, 0, u1} E Nat E (instHPow.{u1, 0} E Nat (Monoid.Pow.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1)))) x (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) n))) (HPow.hPow.{0, 0, 0} NNReal Nat NNReal (instHPow.{0, 0} NNReal Nat (Monoid.Pow.{0} NNReal (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal NNReal.semiring)))) (NNNorm.nnnorm.{u1} E (SeminormedAddGroup.toNNNorm.{u1} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} E (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} E (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))))) x) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) n)))
 but is expected to have type
-  forall {E : Type.{u1}} [_inst_1 : NormedRing.{u1} E] [_inst_2 : StarRing.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1)))] [_inst_3 : CstarRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1) _inst_2] {x : E}, (IsSelfAdjoint.{u1} E (InvolutiveStar.toStar.{u1} E (StarAddMonoid.toInvolutiveStar.{u1} E (AddMonoidWithOne.toAddMonoid.{u1} E (AddGroupWithOne.toAddMonoidWithOne.{u1} E (Ring.toAddGroupWithOne.{u1} E (NormedRing.toRing.{u1} E _inst_1)))) (StarRing.toStarAddMonoid.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))) _inst_2))) x) -> (forall (n : Nat), Eq.{1} NNReal (NNNorm.nnnorm.{u1} E (SeminormedAddGroup.toNNNorm.{u1} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} E (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} E (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))))) (HPow.hPow.{u1, 0, u1} E Nat E (instHPow.{u1, 0} E Nat (Monoid.Pow.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))))) x (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) n))) (HPow.hPow.{0, 0, 0} NNReal Nat NNReal (instHPow.{0, 0} NNReal Nat (Monoid.Pow.{0} NNReal (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal instNNRealSemiring)))) (NNNorm.nnnorm.{u1} E (SeminormedAddGroup.toNNNorm.{u1} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} E (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} E (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))))) x) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) n)))
+  forall {E : Type.{u1}} [_inst_1 : NormedRing.{u1} E] [_inst_2 : StarRing.{u1} E (Semiring.toNonUnitalSemiring.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))] [_inst_3 : CstarRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1) _inst_2] {x : E}, (IsSelfAdjoint.{u1} E (InvolutiveStar.toStar.{u1} E (StarAddMonoid.toInvolutiveStar.{u1} E (AddMonoidWithOne.toAddMonoid.{u1} E (AddGroupWithOne.toAddMonoidWithOne.{u1} E (Ring.toAddGroupWithOne.{u1} E (NormedRing.toRing.{u1} E _inst_1)))) (StarRing.toStarAddMonoid.{u1} E (Semiring.toNonUnitalSemiring.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1))) _inst_2))) x) -> (forall (n : Nat), Eq.{1} NNReal (NNNorm.nnnorm.{u1} E (SeminormedAddGroup.toNNNorm.{u1} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} E (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} E (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))))) (HPow.hPow.{u1, 0, u1} E Nat E (instHPow.{u1, 0} E Nat (Monoid.Pow.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))))) x (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) n))) (HPow.hPow.{0, 0, 0} NNReal Nat NNReal (instHPow.{0, 0} NNReal Nat (Monoid.Pow.{0} NNReal (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal instNNRealSemiring)))) (NNNorm.nnnorm.{u1} E (SeminormedAddGroup.toNNNorm.{u1} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} E (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} E (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))))) x) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) n)))
 Case conversion may be inaccurate. Consider using '#align is_self_adjoint.nnnorm_pow_two_pow IsSelfAdjoint.nnnorm_pow_two_powₓ'. -/
 theorem IsSelfAdjoint.nnnorm_pow_two_pow [NormedRing E] [StarRing E] [CstarRing E] {x : E}
     (hx : IsSelfAdjoint x) (n : ℕ) : ‖x ^ 2 ^ n‖₊ = ‖x‖₊ ^ 2 ^ n :=
@@ -424,7 +424,7 @@ theorem IsSelfAdjoint.nnnorm_pow_two_pow [NormedRing E] [StarRing E] [CstarRing
 lean 3 declaration is
   forall {E : Type.{u1}} [_inst_1 : NormedRing.{u1} E] [_inst_2 : StarRing.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1)))] [_inst_3 : CstarRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1) _inst_2] (x : coeSort.{succ u1, succ (succ u1)} (AddSubgroup.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E (NonUnitalNormedRing.toNormedAddCommGroup.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (AddSubgroup.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E (NonUnitalNormedRing.toNormedAddCommGroup.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))))) E (AddSubgroup.setLike.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E (NonUnitalNormedRing.toNormedAddCommGroup.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1)))))) (selfAdjoint.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E (NonUnitalNormedRing.toNormedAddCommGroup.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1)))) (StarRing.toStarAddMonoid.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))) _inst_2))) (n : Nat), Eq.{1} NNReal (NNNorm.nnnorm.{u1} (coeSort.{succ u1, succ (succ u1)} (AddSubgroup.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E (NonUnitalNormedRing.toNormedAddCommGroup.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (AddSubgroup.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E (NonUnitalNormedRing.toNormedAddCommGroup.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))))) E (AddSubgroup.setLike.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E (NonUnitalNormedRing.toNormedAddCommGroup.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1)))))) (selfAdjoint.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E (NonUnitalNormedRing.toNormedAddCommGroup.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1)))) (StarRing.toStarAddMonoid.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))) _inst_2))) (SeminormedAddGroup.toNNNorm.{u1} (coeSort.{succ u1, succ (succ u1)} (AddSubgroup.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E (NonUnitalNormedRing.toNormedAddCommGroup.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (AddSubgroup.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E (NonUnitalNormedRing.toNormedAddCommGroup.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))))) E (AddSubgroup.setLike.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E (NonUnitalNormedRing.toNormedAddCommGroup.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1)))))) (selfAdjoint.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E (NonUnitalNormedRing.toNormedAddCommGroup.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1)))) (StarRing.toStarAddMonoid.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))) _inst_2))) (AddSubgroup.seminormedAddGroup.{u1} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} E (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} E (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1)))) (selfAdjoint.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E (NonUnitalNormedRing.toNormedAddCommGroup.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1)))) (StarRing.toStarAddMonoid.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))) _inst_2)))) (HPow.hPow.{u1, 0, u1} (coeSort.{succ u1, succ (succ u1)} (AddSubgroup.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E (NonUnitalNormedRing.toNormedAddCommGroup.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (AddSubgroup.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E (NonUnitalNormedRing.toNormedAddCommGroup.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))))) E (AddSubgroup.setLike.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E (NonUnitalNormedRing.toNormedAddCommGroup.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1)))))) (selfAdjoint.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E (NonUnitalNormedRing.toNormedAddCommGroup.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1)))) (StarRing.toStarAddMonoid.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))) _inst_2))) Nat (coeSort.{succ u1, succ (succ u1)} (AddSubgroup.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E (NonUnitalNormedRing.toNormedAddCommGroup.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (AddSubgroup.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E (NonUnitalNormedRing.toNormedAddCommGroup.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))))) E (AddSubgroup.setLike.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E (NonUnitalNormedRing.toNormedAddCommGroup.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1)))))) (selfAdjoint.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E (NonUnitalNormedRing.toNormedAddCommGroup.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1)))) (StarRing.toStarAddMonoid.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))) _inst_2))) (instHPow.{u1, 0} (coeSort.{succ u1, succ (succ u1)} (AddSubgroup.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E (NonUnitalNormedRing.toNormedAddCommGroup.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (AddSubgroup.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E (NonUnitalNormedRing.toNormedAddCommGroup.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))))) E (AddSubgroup.setLike.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E (NonUnitalNormedRing.toNormedAddCommGroup.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1)))))) (selfAdjoint.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E (NonUnitalNormedRing.toNormedAddCommGroup.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1)))) (StarRing.toStarAddMonoid.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))) _inst_2))) Nat (selfAdjoint.Nat.hasPow.{u1} E (NormedRing.toRing.{u1} E _inst_1) _inst_2)) x (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) n))) (HPow.hPow.{0, 0, 0} NNReal Nat NNReal (instHPow.{0, 0} NNReal Nat (Monoid.Pow.{0} NNReal (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal NNReal.semiring)))) (NNNorm.nnnorm.{u1} (coeSort.{succ u1, succ (succ u1)} (AddSubgroup.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E (NonUnitalNormedRing.toNormedAddCommGroup.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (AddSubgroup.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E (NonUnitalNormedRing.toNormedAddCommGroup.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))))) E (AddSubgroup.setLike.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E (NonUnitalNormedRing.toNormedAddCommGroup.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1)))))) (selfAdjoint.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E (NonUnitalNormedRing.toNormedAddCommGroup.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1)))) (StarRing.toStarAddMonoid.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))) _inst_2))) (SeminormedAddGroup.toNNNorm.{u1} (coeSort.{succ u1, succ (succ u1)} (AddSubgroup.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E (NonUnitalNormedRing.toNormedAddCommGroup.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (AddSubgroup.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E (NonUnitalNormedRing.toNormedAddCommGroup.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))))) E (AddSubgroup.setLike.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E (NonUnitalNormedRing.toNormedAddCommGroup.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1)))))) (selfAdjoint.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E (NonUnitalNormedRing.toNormedAddCommGroup.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1)))) (StarRing.toStarAddMonoid.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))) _inst_2))) (AddSubgroup.seminormedAddGroup.{u1} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} E (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} E (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1)))) (selfAdjoint.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E (NonUnitalNormedRing.toNormedAddCommGroup.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1)))) (StarRing.toStarAddMonoid.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))) _inst_2)))) x) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) n))
 but is expected to have type
-  forall {E : Type.{u1}} [_inst_1 : NormedRing.{u1} E] [_inst_2 : StarRing.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1)))] [_inst_3 : CstarRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1) _inst_2] (x : Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (AddSubgroup.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E (NonUnitalNormedRing.toNormedAddCommGroup.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))))) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E (NonUnitalNormedRing.toNormedAddCommGroup.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))))) E (AddSubgroup.instSetLikeAddSubgroup.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E (NonUnitalNormedRing.toNormedAddCommGroup.{u1} E 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+  forall {E : Type.{u1}} [_inst_1 : NormedRing.{u1} E] [_inst_2 : StarRing.{u1} E (Semiring.toNonUnitalSemiring.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))] [_inst_3 : CstarRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1) _inst_2] (x : Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (AddSubgroup.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E (NonUnitalNormedRing.toNormedAddCommGroup.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))))) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E (NonUnitalNormedRing.toNormedAddCommGroup.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))))) E (AddSubgroup.instSetLikeAddSubgroup.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E (NonUnitalNormedRing.toNormedAddCommGroup.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1)))))) x (selfAdjoint.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E (NonUnitalNormedRing.toNormedAddCommGroup.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1)))) (StarRing.toStarAddMonoid.{u1} E (Semiring.toNonUnitalSemiring.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1))) _inst_2)))) (n : Nat), Eq.{1} NNReal (NNNorm.nnnorm.{u1} (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (AddSubgroup.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E (NonUnitalNormedRing.toNormedAddCommGroup.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))))) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E (NonUnitalNormedRing.toNormedAddCommGroup.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))))) E (AddSubgroup.instSetLikeAddSubgroup.{u1} E (NormedAddGroup.toAddGroup.{u1} E 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(selfAdjoint.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E (NonUnitalNormedRing.toNormedAddCommGroup.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1)))) (StarRing.toStarAddMonoid.{u1} E (Semiring.toNonUnitalSemiring.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1))) _inst_2)))) Nat (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (AddSubgroup.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E (NonUnitalNormedRing.toNormedAddCommGroup.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))))) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E (NonUnitalNormedRing.toNormedAddCommGroup.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))))) E (AddSubgroup.instSetLikeAddSubgroup.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E (NonUnitalNormedRing.toNormedAddCommGroup.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1)))))) x (selfAdjoint.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E (NonUnitalNormedRing.toNormedAddCommGroup.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1)))) (StarRing.toStarAddMonoid.{u1} E (Semiring.toNonUnitalSemiring.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1))) _inst_2)))) (instHPow.{u1, 0} (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (AddSubgroup.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E (NonUnitalNormedRing.toNormedAddCommGroup.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))))) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E (NonUnitalNormedRing.toNormedAddCommGroup.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))))) E (AddSubgroup.instSetLikeAddSubgroup.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E (NonUnitalNormedRing.toNormedAddCommGroup.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1)))))) x (selfAdjoint.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E (NonUnitalNormedRing.toNormedAddCommGroup.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1)))) (StarRing.toStarAddMonoid.{u1} E (Semiring.toNonUnitalSemiring.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1))) _inst_2)))) Nat (selfAdjoint.instPowSubtypeMemAddSubgroupToAddGroupToAddGroupWithOneInstMembershipInstSetLikeAddSubgroupSelfAdjointToStarAddMonoidToNonUnitalSemiringToSemiringNat.{u1} E (NormedRing.toRing.{u1} E _inst_1) _inst_2)) x (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) n))) (HPow.hPow.{0, 0, 0} NNReal Nat NNReal (instHPow.{0, 0} NNReal Nat (Monoid.Pow.{0} NNReal (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal instNNRealSemiring)))) (NNNorm.nnnorm.{u1} (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (AddSubgroup.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E (NonUnitalNormedRing.toNormedAddCommGroup.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))))) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E (NonUnitalNormedRing.toNormedAddCommGroup.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))))) E (AddSubgroup.instSetLikeAddSubgroup.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E (NonUnitalNormedRing.toNormedAddCommGroup.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1)))))) x (selfAdjoint.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E (NonUnitalNormedRing.toNormedAddCommGroup.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1)))) (StarRing.toStarAddMonoid.{u1} E (Semiring.toNonUnitalSemiring.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1))) _inst_2)))) (SeminormedAddGroup.toNNNorm.{u1} (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (AddSubgroup.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E (NonUnitalNormedRing.toNormedAddCommGroup.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))))) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E (NonUnitalNormedRing.toNormedAddCommGroup.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))))) E (AddSubgroup.instSetLikeAddSubgroup.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E (NonUnitalNormedRing.toNormedAddCommGroup.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1)))))) x (selfAdjoint.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E (NonUnitalNormedRing.toNormedAddCommGroup.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1)))) (StarRing.toStarAddMonoid.{u1} E (Semiring.toNonUnitalSemiring.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1))) _inst_2)))) (AddSubgroup.seminormedAddGroup.{u1} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} E (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} E (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1)))) (selfAdjoint.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E (NonUnitalNormedRing.toNormedAddCommGroup.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1)))) (StarRing.toStarAddMonoid.{u1} E (Semiring.toNonUnitalSemiring.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1))) _inst_2)))) x) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) n))
 Case conversion may be inaccurate. Consider using '#align self_adjoint.nnnorm_pow_two_pow selfAdjoint.nnnorm_pow_two_powₓ'. -/
 theorem selfAdjoint.nnnorm_pow_two_pow [NormedRing E] [StarRing E] [CstarRing E] (x : selfAdjoint E)
     (n : ℕ) : ‖x ^ 2 ^ n‖₊ = ‖x‖₊ ^ 2 ^ n :=

9d2f0748

bump to nightly-2023-05-05-14

mathlib commit https://github.com/leanprover-community/mathlib/commit/738054fa93d43512da144ec45ce799d18fd44248

fdd4022f

Diff

@@ -276,10 +276,10 @@ instance Pi.cstarRing : CstarRing (∀ i, R i)
 #align pi.cstar_ring Pi.cstarRing
 -/
 
-#print Pi.cstar_ring' /-
-instance Pi.cstar_ring' : CstarRing (ι → R₁) :=
+#print Pi.cstarRing' /-
+instance Pi.cstarRing' : CstarRing (ι → R₁) :=
   Pi.cstarRing
-#align pi.cstar_ring' Pi.cstar_ring'
+#align pi.cstar_ring' Pi.cstarRing'
 -/
 
 end ProdPi

9d2f0748

bump to nightly-2023-04-28-02

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

473bb540

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 analysis.normed_space.star.basic
-! leanprover-community/mathlib commit e65771194f9e923a70dfb49b6ca7be6e400d8b6f
+! leanprover-community/mathlib commit 9d2f0748e6c50d7a2657c564b1ff2c695b39148d
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -18,6 +18,9 @@ import Mathbin.Topology.Algebra.StarSubalgebra
 /-!
 # Normed star rings and algebras
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 A normed star group is a normed group with a compatible `star` which is isometric.
 
 A C⋆-ring is a normed star group that is also a ring and that verifies the stronger

e6577119

bump to nightly-2023-04-25-22

mathlib commit https://github.com/leanprover-community/mathlib/commit/2651125b48fc5c170ab1111afd0817c903b1fc6c

ed327085

Diff

@@ -41,10 +41,12 @@ open Topology
 -- mathport name: «expr ⋆»
 local postfix:max "⋆" => star
 
+#print NormedStarGroup /-
 /-- A normed star group is a normed group with a compatible `star` which is isometric. -/
 class NormedStarGroup (E : Type _) [SeminormedAddCommGroup E] [StarAddMonoid E] : Prop where
   norm_star : ∀ x : E, ‖x⋆‖ = ‖x‖
 #align normed_star_group NormedStarGroup
+-/
 
 export NormedStarGroup (norm_star)
 
@@ -56,38 +58,50 @@ section NormedStarGroup
 
 variable [SeminormedAddCommGroup E] [StarAddMonoid E] [NormedStarGroup E]
 
+#print nnnorm_star /-
 @[simp]
 theorem nnnorm_star (x : E) : ‖star x‖₊ = ‖x‖₊ :=
   Subtype.ext <| norm_star _
 #align nnnorm_star nnnorm_star
+-/
 
+#print starNormedAddGroupHom /-
 /-- The `star` map in a normed star group is a normed group homomorphism. -/
 def starNormedAddGroupHom : NormedAddGroupHom E E :=
   { starAddEquiv with bound' := ⟨1, fun v => le_trans (norm_star _).le (one_mul _).symm.le⟩ }
 #align star_normed_add_group_hom starNormedAddGroupHom
+-/
 
+#print star_isometry /-
 /-- The `star` map in a normed star group is an isometry -/
 theorem star_isometry : Isometry (star : E → E) :=
   show Isometry starAddEquiv from
     AddMonoidHomClass.isometry_of_norm starAddEquiv (show ∀ x, ‖x⋆‖ = ‖x‖ from norm_star)
 #align star_isometry star_isometry
+-/
 
+#print NormedStarGroup.to_continuousStar /-
 instance (priority := 100) NormedStarGroup.to_continuousStar : ContinuousStar E :=
   ⟨star_isometry.Continuous⟩
 #align normed_star_group.to_has_continuous_star NormedStarGroup.to_continuousStar
+-/
 
 end NormedStarGroup
 
+#print RingHomIsometric.starRingEnd /-
 instance RingHomIsometric.starRingEnd [NormedCommRing E] [StarRing E] [NormedStarGroup E] :
     RingHomIsometric (starRingEnd E) :=
   ⟨norm_star⟩
 #align ring_hom_isometric.star_ring_end RingHomIsometric.starRingEnd
+-/
 
+#print CstarRing /-
 /-- A C*-ring is a normed star ring that satifies the stronger condition `‖x⋆ * x‖ = ‖x‖^2`
 for every `x`. -/
 class CstarRing (E : Type _) [NonUnitalNormedRing E] [StarRing E] : Prop where
   norm_star_mul_self : ∀ {x : E}, ‖x⋆ * x‖ = ‖x‖ * ‖x‖
 #align cstar_ring CstarRing
+-/
 
 instance : CstarRing ℝ where norm_star_mul_self x := by simp only [star, id.def, norm_mul]
 
@@ -97,6 +111,7 @@ section NonUnital
 
 variable [NonUnitalNormedRing E] [StarRing E] [CstarRing E]
 
+#print CstarRing.to_normedStarGroup /-
 -- see Note [lower instance priority]
 /-- In a C*-ring, star preserves the norm. -/
 instance (priority := 100) to_normedStarGroup : NormedStarGroup E :=
@@ -119,24 +134,55 @@ instance (priority := 100) to_normedStarGroup : NormedStarGroup E :=
           
       exact le_antisymm (le_of_mul_le_mul_right h₂ hnt_star) (le_of_mul_le_mul_right h₁ hnt)⟩
 #align cstar_ring.to_normed_star_group CstarRing.to_normedStarGroup
+-/
 
+/- warning: cstar_ring.norm_self_mul_star -> CstarRing.norm_self_mul_star is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {E : Type.{u1}} [_inst_1 : NonUnitalNormedRing.{u1} E] [_inst_2 : StarRing.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E _inst_1))] [_inst_3 : CstarRing.{u1} E _inst_1 _inst_2] {x : E}, Eq.{1} Real (Norm.norm.{u1} E (NonUnitalNormedRing.toNorm.{u1} E _inst_1) (HMul.hMul.{u1, u1, u1} E E E (instHMul.{u1} E (NonUnitalNonAssocRing.toMul.{u1} E (NonUnitalRing.toNonUnitalNonAssocRing.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E _inst_1)))) x (Star.star.{u1} E (InvolutiveStar.toStar.{u1} E (StarAddMonoid.toInvolutiveStar.{u1} E (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E (NonUnitalNormedRing.toNormedAddCommGroup.{u1} E _inst_1))))) (StarRing.toStarAddMonoid.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E _inst_1)) _inst_2))) x))) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Norm.norm.{u1} E (NonUnitalNormedRing.toNorm.{u1} E _inst_1) x) (Norm.norm.{u1} E (NonUnitalNormedRing.toNorm.{u1} E _inst_1) x))
+Case conversion may be inaccurate. Consider using '#align cstar_ring.norm_self_mul_star CstarRing.norm_self_mul_starₓ'. -/
 theorem norm_self_mul_star {x : E} : ‖x * x⋆‖ = ‖x‖ * ‖x‖ :=
   by
   nth_rw 1 [← star_star x]
   simp only [norm_star_mul_self, norm_star]
 #align cstar_ring.norm_self_mul_star CstarRing.norm_self_mul_star
 
+/- warning: cstar_ring.norm_star_mul_self' -> CstarRing.norm_star_mul_self' is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {E : Type.{u1}} [_inst_1 : NonUnitalNormedRing.{u1} E] [_inst_2 : StarRing.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E _inst_1))] [_inst_3 : CstarRing.{u1} E _inst_1 _inst_2] {x : E}, Eq.{1} Real (Norm.norm.{u1} E (NonUnitalNormedRing.toNorm.{u1} E _inst_1) (HMul.hMul.{u1, u1, u1} E E E (instHMul.{u1} E (NonUnitalNonAssocRing.toMul.{u1} E (NonUnitalRing.toNonUnitalNonAssocRing.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E _inst_1)))) (Star.star.{u1} E (InvolutiveStar.toStar.{u1} E (StarAddMonoid.toInvolutiveStar.{u1} E (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E (NonUnitalNormedRing.toNormedAddCommGroup.{u1} E _inst_1))))) (StarRing.toStarAddMonoid.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E _inst_1)) _inst_2))) x) x)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Norm.norm.{u1} E (NonUnitalNormedRing.toNorm.{u1} E _inst_1) (Star.star.{u1} E (InvolutiveStar.toStar.{u1} E (StarAddMonoid.toInvolutiveStar.{u1} E (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E (NonUnitalNormedRing.toNormedAddCommGroup.{u1} E _inst_1))))) (StarRing.toStarAddMonoid.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E _inst_1)) _inst_2))) x)) (Norm.norm.{u1} E (NonUnitalNormedRing.toNorm.{u1} E _inst_1) x))
+Case conversion may be inaccurate. Consider using '#align cstar_ring.norm_star_mul_self' CstarRing.norm_star_mul_self'ₓ'. -/
 theorem norm_star_mul_self' {x : E} : ‖x⋆ * x‖ = ‖x⋆‖ * ‖x‖ := by rw [norm_star_mul_self, norm_star]
 #align cstar_ring.norm_star_mul_self' CstarRing.norm_star_mul_self'
 
+/- warning: cstar_ring.nnnorm_self_mul_star -> CstarRing.nnnorm_self_mul_star is a dubious translation:
+lean 3 declaration is
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+  forall {E : Type.{u1}} [_inst_1 : NonUnitalNormedRing.{u1} E] [_inst_2 : StarRing.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E _inst_1))] [_inst_3 : CstarRing.{u1} E _inst_1 _inst_2] {x : E}, Eq.{1} NNReal (NNNorm.nnnorm.{u1} E (SeminormedAddGroup.toNNNorm.{u1} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} E (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} E (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} E _inst_1)))) (HMul.hMul.{u1, u1, u1} E E E (instHMul.{u1} E (NonUnitalNonAssocRing.toMul.{u1} E (NonUnitalRing.toNonUnitalNonAssocRing.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E _inst_1)))) x (Star.star.{u1} E (InvolutiveStar.toStar.{u1} E (StarAddMonoid.toInvolutiveStar.{u1} E (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E (NonUnitalNormedRing.toNormedAddCommGroup.{u1} E _inst_1))))) (StarRing.toStarAddMonoid.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E _inst_1)) _inst_2))) x))) (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) (NNNorm.nnnorm.{u1} E (SeminormedAddGroup.toNNNorm.{u1} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} E (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} E (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} E _inst_1)))) x) (NNNorm.nnnorm.{u1} E (SeminormedAddGroup.toNNNorm.{u1} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} E (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} E (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} E _inst_1)))) x))
+Case conversion may be inaccurate. Consider using '#align cstar_ring.nnnorm_self_mul_star CstarRing.nnnorm_self_mul_starₓ'. -/
 theorem nnnorm_self_mul_star {x : E} : ‖x * star x‖₊ = ‖x‖₊ * ‖x‖₊ :=
   Subtype.ext norm_self_mul_star
 #align cstar_ring.nnnorm_self_mul_star CstarRing.nnnorm_self_mul_star
 
+/- warning: cstar_ring.nnnorm_star_mul_self -> CstarRing.nnnorm_star_mul_self is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {E : Type.{u1}} [_inst_1 : NonUnitalNormedRing.{u1} E] [_inst_2 : StarRing.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E _inst_1))] [_inst_3 : CstarRing.{u1} E _inst_1 _inst_2] {x : E}, Eq.{1} NNReal (NNNorm.nnnorm.{u1} E (SeminormedAddGroup.toNNNorm.{u1} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} E (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} E (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} E _inst_1)))) (HMul.hMul.{u1, u1, u1} E E E (instHMul.{u1} E (NonUnitalNonAssocRing.toMul.{u1} E (NonUnitalRing.toNonUnitalNonAssocRing.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E _inst_1)))) (Star.star.{u1} E (InvolutiveStar.toStar.{u1} E (StarAddMonoid.toInvolutiveStar.{u1} E (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E (NonUnitalNormedRing.toNormedAddCommGroup.{u1} E _inst_1))))) (StarRing.toStarAddMonoid.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E _inst_1)) _inst_2))) x) x)) (HMul.hMul.{0, 0, 0} NNReal NNReal NNReal (instHMul.{0} NNReal (CanonicallyOrderedCommSemiring.toMul.{0} NNReal instNNRealCanonicallyOrderedCommSemiring)) (NNNorm.nnnorm.{u1} E (SeminormedAddGroup.toNNNorm.{u1} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} E (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} E (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} E _inst_1)))) x) (NNNorm.nnnorm.{u1} E (SeminormedAddGroup.toNNNorm.{u1} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} E (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} E (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} E _inst_1)))) x))
+Case conversion may be inaccurate. Consider using '#align cstar_ring.nnnorm_star_mul_self CstarRing.nnnorm_star_mul_selfₓ'. -/
 theorem nnnorm_star_mul_self {x : E} : ‖x⋆ * x‖₊ = ‖x‖₊ * ‖x‖₊ :=
   Subtype.ext norm_star_mul_self
 #align cstar_ring.nnnorm_star_mul_self CstarRing.nnnorm_star_mul_self
 
+/- warning: cstar_ring.star_mul_self_eq_zero_iff -> CstarRing.star_mul_self_eq_zero_iff is a dubious translation:
+lean 3 declaration is
+  forall {E : Type.{u1}} [_inst_1 : NonUnitalNormedRing.{u1} E] [_inst_2 : StarRing.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E _inst_1))] [_inst_3 : CstarRing.{u1} E _inst_1 _inst_2] (x : E), Iff (Eq.{succ u1} E (HMul.hMul.{u1, u1, u1} E E E (instHMul.{u1} E (Distrib.toHasMul.{u1} E (NonUnitalNonAssocSemiring.toDistrib.{u1} E (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} E (NonUnitalRing.toNonUnitalNonAssocRing.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E _inst_1)))))) (Star.star.{u1} E (InvolutiveStar.toHasStar.{u1} E (StarAddMonoid.toHasInvolutiveStar.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} E (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E _inst_1))))) (StarRing.toStarAddMonoid.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E _inst_1)) _inst_2))) x) x) (OfNat.ofNat.{u1} E 0 (OfNat.mk.{u1} E 0 (Zero.zero.{u1} E (MulZeroClass.toHasZero.{u1} E (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} E (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} E (NonUnitalRing.toNonUnitalNonAssocRing.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E _inst_1))))))))) (Eq.{succ u1} E x (OfNat.ofNat.{u1} E 0 (OfNat.mk.{u1} E 0 (Zero.zero.{u1} E (MulZeroClass.toHasZero.{u1} E (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} E (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} E (NonUnitalRing.toNonUnitalNonAssocRing.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E _inst_1)))))))))
+but is expected to have type
+  forall {E : Type.{u1}} [_inst_1 : NonUnitalNormedRing.{u1} E] [_inst_2 : StarRing.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E _inst_1))] [_inst_3 : CstarRing.{u1} E _inst_1 _inst_2] (x : E), Iff (Eq.{succ u1} E (HMul.hMul.{u1, u1, u1} E E E (instHMul.{u1} E (NonUnitalNonAssocRing.toMul.{u1} E (NonUnitalRing.toNonUnitalNonAssocRing.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E _inst_1)))) (Star.star.{u1} E (InvolutiveStar.toStar.{u1} E (StarAddMonoid.toInvolutiveStar.{u1} E (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E (NonUnitalNormedRing.toNormedAddCommGroup.{u1} E _inst_1))))) (StarRing.toStarAddMonoid.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E _inst_1)) _inst_2))) x) x) (OfNat.ofNat.{u1} E 0 (Zero.toOfNat0.{u1} E (SemigroupWithZero.toZero.{u1} E (NonUnitalSemiring.toSemigroupWithZero.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E _inst_1))))))) (Eq.{succ u1} E x (OfNat.ofNat.{u1} E 0 (Zero.toOfNat0.{u1} E (SemigroupWithZero.toZero.{u1} E (NonUnitalSemiring.toSemigroupWithZero.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E _inst_1)))))))
+Case conversion may be inaccurate. Consider using '#align cstar_ring.star_mul_self_eq_zero_iff CstarRing.star_mul_self_eq_zero_iffₓ'. -/
 @[simp]
 theorem star_mul_self_eq_zero_iff (x : E) : star x * x = 0 ↔ x = 0 :=
   by
@@ -144,15 +190,33 @@ theorem star_mul_self_eq_zero_iff (x : E) : star x * x = 0 ↔ x = 0 :=
   exact mul_self_eq_zero.trans norm_eq_zero
 #align cstar_ring.star_mul_self_eq_zero_iff CstarRing.star_mul_self_eq_zero_iff
 
+/- warning: cstar_ring.star_mul_self_ne_zero_iff -> CstarRing.star_mul_self_ne_zero_iff is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align cstar_ring.star_mul_self_ne_zero_iff CstarRing.star_mul_self_ne_zero_iffₓ'. -/
 theorem star_mul_self_ne_zero_iff (x : E) : star x * x ≠ 0 ↔ x ≠ 0 := by
   simp only [Ne.def, star_mul_self_eq_zero_iff]
 #align cstar_ring.star_mul_self_ne_zero_iff CstarRing.star_mul_self_ne_zero_iff
 
+/- warning: cstar_ring.mul_star_self_eq_zero_iff -> CstarRing.mul_star_self_eq_zero_iff is a dubious translation:
+lean 3 declaration is
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+  forall {E : Type.{u1}} [_inst_1 : NonUnitalNormedRing.{u1} E] [_inst_2 : StarRing.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E _inst_1))] [_inst_3 : CstarRing.{u1} E _inst_1 _inst_2] (x : E), Iff (Eq.{succ u1} E (HMul.hMul.{u1, u1, u1} E E E (instHMul.{u1} E (NonUnitalNonAssocRing.toMul.{u1} E (NonUnitalRing.toNonUnitalNonAssocRing.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E _inst_1)))) x (Star.star.{u1} E (InvolutiveStar.toStar.{u1} E (StarAddMonoid.toInvolutiveStar.{u1} E (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E (NonUnitalNormedRing.toNormedAddCommGroup.{u1} E _inst_1))))) (StarRing.toStarAddMonoid.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E _inst_1)) _inst_2))) x)) (OfNat.ofNat.{u1} E 0 (Zero.toOfNat0.{u1} E (SemigroupWithZero.toZero.{u1} E (NonUnitalSemiring.toSemigroupWithZero.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E _inst_1))))))) (Eq.{succ u1} E x (OfNat.ofNat.{u1} E 0 (Zero.toOfNat0.{u1} E (SemigroupWithZero.toZero.{u1} E (NonUnitalSemiring.toSemigroupWithZero.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E _inst_1)))))))
+Case conversion may be inaccurate. Consider using '#align cstar_ring.mul_star_self_eq_zero_iff CstarRing.mul_star_self_eq_zero_iffₓ'. -/
 @[simp]
 theorem mul_star_self_eq_zero_iff (x : E) : x * star x = 0 ↔ x = 0 := by
   simpa only [star_eq_zero, star_star] using @star_mul_self_eq_zero_iff _ _ _ _ (star x)
 #align cstar_ring.mul_star_self_eq_zero_iff CstarRing.mul_star_self_eq_zero_iff
 
+/- warning: cstar_ring.mul_star_self_ne_zero_iff -> CstarRing.mul_star_self_ne_zero_iff is a dubious translation:
+lean 3 declaration is
+  forall {E : Type.{u1}} [_inst_1 : NonUnitalNormedRing.{u1} E] [_inst_2 : StarRing.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E _inst_1))] [_inst_3 : CstarRing.{u1} E _inst_1 _inst_2] (x : E), Iff (Ne.{succ u1} E (HMul.hMul.{u1, u1, u1} E E E (instHMul.{u1} E (Distrib.toHasMul.{u1} E (NonUnitalNonAssocSemiring.toDistrib.{u1} E (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} E (NonUnitalRing.toNonUnitalNonAssocRing.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E _inst_1)))))) x (Star.star.{u1} E (InvolutiveStar.toHasStar.{u1} E (StarAddMonoid.toHasInvolutiveStar.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} E (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E _inst_1))))) (StarRing.toStarAddMonoid.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E _inst_1)) _inst_2))) x)) (OfNat.ofNat.{u1} E 0 (OfNat.mk.{u1} E 0 (Zero.zero.{u1} E (MulZeroClass.toHasZero.{u1} E (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} E (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} E (NonUnitalRing.toNonUnitalNonAssocRing.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E _inst_1))))))))) (Ne.{succ u1} E x (OfNat.ofNat.{u1} E 0 (OfNat.mk.{u1} E 0 (Zero.zero.{u1} E (MulZeroClass.toHasZero.{u1} E (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} E (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} E (NonUnitalRing.toNonUnitalNonAssocRing.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E _inst_1)))))))))
+but is expected to have type
+  forall {E : Type.{u1}} [_inst_1 : NonUnitalNormedRing.{u1} E] [_inst_2 : StarRing.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E _inst_1))] [_inst_3 : CstarRing.{u1} E _inst_1 _inst_2] (x : E), Iff (Ne.{succ u1} E (HMul.hMul.{u1, u1, u1} E E E (instHMul.{u1} E (NonUnitalNonAssocRing.toMul.{u1} E (NonUnitalRing.toNonUnitalNonAssocRing.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E _inst_1)))) x (Star.star.{u1} E (InvolutiveStar.toStar.{u1} E (StarAddMonoid.toInvolutiveStar.{u1} E (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E (NonUnitalNormedRing.toNormedAddCommGroup.{u1} E _inst_1))))) (StarRing.toStarAddMonoid.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E _inst_1)) _inst_2))) x)) (OfNat.ofNat.{u1} E 0 (Zero.toOfNat0.{u1} E (SemigroupWithZero.toZero.{u1} E (NonUnitalSemiring.toSemigroupWithZero.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E _inst_1))))))) (Ne.{succ u1} E x (OfNat.ofNat.{u1} E 0 (Zero.toOfNat0.{u1} E (SemigroupWithZero.toZero.{u1} E (NonUnitalSemiring.toSemigroupWithZero.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E _inst_1)))))))
+Case conversion may be inaccurate. Consider using '#align cstar_ring.mul_star_self_ne_zero_iff CstarRing.mul_star_self_ne_zero_iffₓ'. -/
 theorem mul_star_self_ne_zero_iff (x : E) : x * star x ≠ 0 ↔ x ≠ 0 := by
   simp only [Ne.def, mul_star_self_eq_zero_iff]
 #align cstar_ring.mul_star_self_ne_zero_iff CstarRing.mul_star_self_ne_zero_iff
@@ -169,14 +233,22 @@ variable [NonUnitalNormedRing R₂] [StarRing R₂] [CstarRing R₂]
 
 variable [∀ i, NonUnitalNormedRing (R i)] [∀ i, StarRing (R i)]
 
+#print Pi.starRing' /-
 /-- This instance exists to short circuit type class resolution because of problems with
 inference involving Π-types. -/
 instance Pi.starRing' : StarRing (∀ i, R i) :=
   inferInstance
 #align pi.star_ring' Pi.starRing'
+-/
 
 variable [Fintype ι] [∀ i, CstarRing (R i)]
 
+/- warning: prod.cstar_ring -> Prod.cstarRing is a dubious translation:
+lean 3 declaration is
+  forall {R₁ : Type.{u1}} {R₂ : Type.{u2}} [_inst_1 : NonUnitalNormedRing.{u1} R₁] [_inst_2 : StarRing.{u1} R₁ (NonUnitalRing.toNonUnitalSemiring.{u1} R₁ (NonUnitalNormedRing.toNonUnitalRing.{u1} R₁ _inst_1))] [_inst_3 : CstarRing.{u1} R₁ _inst_1 _inst_2] [_inst_4 : NonUnitalNormedRing.{u2} R₂] [_inst_5 : StarRing.{u2} R₂ (NonUnitalRing.toNonUnitalSemiring.{u2} R₂ (NonUnitalNormedRing.toNonUnitalRing.{u2} R₂ _inst_4))] [_inst_6 : CstarRing.{u2} R₂ _inst_4 _inst_5], CstarRing.{max u1 u2} (Prod.{u1, u2} R₁ R₂) (Prod.nonUnitalNormedRing.{u1, u2} R₁ R₂ _inst_1 _inst_4) (Prod.starRing.{u1, u2} R₁ R₂ (NonUnitalRing.toNonUnitalSemiring.{u1} R₁ (NonUnitalNormedRing.toNonUnitalRing.{u1} R₁ _inst_1)) (NonUnitalRing.toNonUnitalSemiring.{u2} R₂ (NonUnitalNormedRing.toNonUnitalRing.{u2} R₂ _inst_4)) _inst_2 _inst_5)
+but is expected to have type
+  forall {R₁ : Type.{u1}} {R₂ : Type.{u2}} [_inst_1 : NonUnitalNormedRing.{u1} R₁] [_inst_2 : StarRing.{u1} R₁ (NonUnitalRing.toNonUnitalSemiring.{u1} R₁ (NonUnitalNormedRing.toNonUnitalRing.{u1} R₁ _inst_1))] [_inst_3 : CstarRing.{u1} R₁ _inst_1 _inst_2] [_inst_4 : NonUnitalNormedRing.{u2} R₂] [_inst_5 : StarRing.{u2} R₂ (NonUnitalRing.toNonUnitalSemiring.{u2} R₂ (NonUnitalNormedRing.toNonUnitalRing.{u2} R₂ _inst_4))] [_inst_6 : CstarRing.{u2} R₂ _inst_4 _inst_5], CstarRing.{max u2 u1} (Prod.{u1, u2} R₁ R₂) (Prod.nonUnitalNormedRing.{u1, u2} R₁ R₂ _inst_1 _inst_4) (Prod.instStarRingProdInstNonUnitalSemiringProd.{u1, u2} R₁ R₂ (NonUnitalRing.toNonUnitalSemiring.{u1} R₁ (NonUnitalNormedRing.toNonUnitalRing.{u1} R₁ _inst_1)) (NonUnitalRing.toNonUnitalSemiring.{u2} R₂ (NonUnitalNormedRing.toNonUnitalRing.{u2} R₂ _inst_4)) _inst_2 _inst_5)
+Case conversion may be inaccurate. Consider using '#align prod.cstar_ring Prod.cstarRingₓ'. -/
 instance Prod.cstarRing : CstarRing (R₁ × R₂)
     where norm_star_mul_self x := by
     unfold norm
@@ -189,6 +261,7 @@ instance Prod.cstarRing : CstarRing (R₁ × R₂)
       rcases le_total ‖x.fst‖ ‖x.snd‖ with (h | h) <;> simp [h]
 #align prod.cstar_ring Prod.cstarRing
 
+#print Pi.cstarRing /-
 instance Pi.cstarRing : CstarRing (∀ i, R i)
     where norm_star_mul_self x :=
     by
@@ -198,10 +271,13 @@ instance Pi.cstarRing : CstarRing (∀ i, R i)
       (Finset.comp_sup_eq_sup_comp_of_is_total (fun x : NNReal => x ^ 2)
           (fun x y h => by simpa only [sq] using mul_le_mul' h h) (by simp)).symm
 #align pi.cstar_ring Pi.cstarRing
+-/
 
+#print Pi.cstar_ring' /-
 instance Pi.cstar_ring' : CstarRing (ι → R₁) :=
   Pi.cstarRing
 #align pi.cstar_ring' Pi.cstar_ring'
+-/
 
 end ProdPi
 
@@ -209,6 +285,12 @@ section Unital
 
 variable [NormedRing E] [StarRing E] [CstarRing E]
 
+/- warning: cstar_ring.norm_one -> CstarRing.norm_one is a dubious translation:
+lean 3 declaration is
+  forall {E : Type.{u1}} [_inst_1 : NormedRing.{u1} E] [_inst_2 : StarRing.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1)))] [_inst_3 : CstarRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1) _inst_2] [_inst_4 : Nontrivial.{u1} E], Eq.{1} Real (Norm.norm.{u1} E (NormedRing.toHasNorm.{u1} E _inst_1) (OfNat.ofNat.{u1} E 1 (OfNat.mk.{u1} E 1 (One.one.{u1} E (AddMonoidWithOne.toOne.{u1} E (AddGroupWithOne.toAddMonoidWithOne.{u1} E (AddCommGroupWithOne.toAddGroupWithOne.{u1} E (Ring.toAddCommGroupWithOne.{u1} E (NormedRing.toRing.{u1} E _inst_1))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))
+but is expected to have type
+  forall {E : Type.{u1}} [_inst_1 : NormedRing.{u1} E] [_inst_2 : StarRing.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1)))] [_inst_3 : CstarRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1) _inst_2] [_inst_4 : Nontrivial.{u1} E], Eq.{1} Real (Norm.norm.{u1} E (NormedRing.toNorm.{u1} E _inst_1) (OfNat.ofNat.{u1} E 1 (One.toOfNat1.{u1} E (NonAssocRing.toOne.{u1} E (Ring.toNonAssocRing.{u1} E (NormedRing.toRing.{u1} E _inst_1)))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))
+Case conversion may be inaccurate. Consider using '#align cstar_ring.norm_one CstarRing.norm_oneₓ'. -/
 @[simp]
 theorem norm_one [Nontrivial E] : ‖(1 : E)‖ = 1 :=
   by
@@ -220,16 +302,34 @@ theorem norm_one [Nontrivial E] : ‖(1 : E)‖ = 1 :=
 instance (priority := 100) [Nontrivial E] : NormOneClass E :=
   ⟨norm_one⟩
 
+/- warning: cstar_ring.norm_coe_unitary -> CstarRing.norm_coe_unitary is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align cstar_ring.norm_coe_unitary CstarRing.norm_coe_unitaryₓ'. -/
 theorem norm_coe_unitary [Nontrivial E] (U : unitary E) : ‖(U : E)‖ = 1 := by
   rw [← sq_eq_sq (norm_nonneg _) zero_le_one, one_pow 2, sq, ← CstarRing.norm_star_mul_self,
     unitary.coe_star_mul_self, CstarRing.norm_one]
 #align cstar_ring.norm_coe_unitary CstarRing.norm_coe_unitary
 
+/- warning: cstar_ring.norm_of_mem_unitary -> CstarRing.norm_of_mem_unitary is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align cstar_ring.norm_of_mem_unitary CstarRing.norm_of_mem_unitaryₓ'. -/
 @[simp]
 theorem norm_of_mem_unitary [Nontrivial E] {U : E} (hU : U ∈ unitary E) : ‖U‖ = 1 :=
   norm_coe_unitary ⟨U, hU⟩
 #align cstar_ring.norm_of_mem_unitary CstarRing.norm_of_mem_unitary
 
+/- warning: cstar_ring.norm_coe_unitary_mul -> CstarRing.norm_coe_unitary_mul is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align cstar_ring.norm_coe_unitary_mul CstarRing.norm_coe_unitary_mulₓ'. -/
 @[simp]
 theorem norm_coe_unitary_mul (U : unitary E) (A : E) : ‖(U : E) * A‖ = ‖A‖ :=
   by
@@ -250,15 +350,33 @@ theorem norm_coe_unitary_mul (U : unitary E) (A : E) : ‖(U : E) * A‖ = ‖A
       
 #align cstar_ring.norm_coe_unitary_mul CstarRing.norm_coe_unitary_mul
 
+/- warning: cstar_ring.norm_unitary_smul -> CstarRing.norm_unitary_smul is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align cstar_ring.norm_unitary_smul CstarRing.norm_unitary_smulₓ'. -/
 @[simp]
 theorem norm_unitary_smul (U : unitary E) (A : E) : ‖U • A‖ = ‖A‖ :=
   norm_coe_unitary_mul U A
 #align cstar_ring.norm_unitary_smul CstarRing.norm_unitary_smul
 
+/- warning: cstar_ring.norm_mem_unitary_mul -> CstarRing.norm_mem_unitary_mul is a dubious translation:
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+but is expected to have type
+  forall {E : Type.{u1}} [_inst_1 : NormedRing.{u1} E] [_inst_2 : StarRing.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1)))] [_inst_3 : CstarRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1) _inst_2] {U : E} (A : E), (Membership.mem.{u1, u1} E (Submonoid.{u1} E (Monoid.toMulOneClass.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} E (Monoid.toMulOneClass.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))))) E (Submonoid.instSetLikeSubmonoid.{u1} E (Monoid.toMulOneClass.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1))))))) U (unitary.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))) (StarRing.toStarSemigroup.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))) _inst_2))) -> (Eq.{1} Real (Norm.norm.{u1} E (NormedRing.toNorm.{u1} E _inst_1) (HMul.hMul.{u1, u1, u1} E E E (instHMul.{u1} E (NonUnitalNonAssocRing.toMul.{u1} E (NonAssocRing.toNonUnitalNonAssocRing.{u1} E (Ring.toNonAssocRing.{u1} E (NormedRing.toRing.{u1} E _inst_1))))) U A)) (Norm.norm.{u1} E (NormedRing.toNorm.{u1} E _inst_1) A))
+Case conversion may be inaccurate. Consider using '#align cstar_ring.norm_mem_unitary_mul CstarRing.norm_mem_unitary_mulₓ'. -/
 theorem norm_mem_unitary_mul {U : E} (A : E) (hU : U ∈ unitary E) : ‖U * A‖ = ‖A‖ :=
   norm_coe_unitary_mul ⟨U, hU⟩ A
 #align cstar_ring.norm_mem_unitary_mul CstarRing.norm_mem_unitary_mul
 
+/- warning: cstar_ring.norm_mul_coe_unitary -> CstarRing.norm_mul_coe_unitary is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align cstar_ring.norm_mul_coe_unitary CstarRing.norm_mul_coe_unitaryₓ'. -/
 @[simp]
 theorem norm_mul_coe_unitary (A : E) (U : unitary E) : ‖A * U‖ = ‖A‖ :=
   calc
@@ -269,6 +387,12 @@ theorem norm_mul_coe_unitary (A : E) (U : unitary E) : ‖A * U‖ = ‖A‖ :=
     
 #align cstar_ring.norm_mul_coe_unitary CstarRing.norm_mul_coe_unitary
 
+/- warning: cstar_ring.norm_mul_mem_unitary -> CstarRing.norm_mul_mem_unitary is a dubious translation:
+lean 3 declaration is
+  forall {E : Type.{u1}} [_inst_1 : NormedRing.{u1} E] [_inst_2 : StarRing.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1)))] [_inst_3 : CstarRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1) _inst_2] (A : E) {U : E}, (Membership.Mem.{u1, u1} E (Submonoid.{u1} E (Monoid.toMulOneClass.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1)))) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} E (Monoid.toMulOneClass.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1)))) E (Submonoid.setLike.{u1} E (Monoid.toMulOneClass.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1))))) U (unitary.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1)) (StarRing.toStarSemigroup.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))) _inst_2))) -> (Eq.{1} Real (Norm.norm.{u1} E (NormedRing.toHasNorm.{u1} E _inst_1) (HMul.hMul.{u1, u1, u1} E E E (instHMul.{u1} E (Distrib.toHasMul.{u1} E (Ring.toDistrib.{u1} E (NormedRing.toRing.{u1} E _inst_1)))) A U)) (Norm.norm.{u1} E (NormedRing.toHasNorm.{u1} E _inst_1) A))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align cstar_ring.norm_mul_mem_unitary CstarRing.norm_mul_mem_unitaryₓ'. -/
 theorem norm_mul_mem_unitary (A : E) {U : E} (hU : U ∈ unitary E) : ‖A * U‖ = ‖A‖ :=
   norm_mul_coe_unitary A ⟨U, hU⟩
 #align cstar_ring.norm_mul_mem_unitary CstarRing.norm_mul_mem_unitary
@@ -277,6 +401,12 @@ end Unital
 
 end CstarRing
 
+/- warning: is_self_adjoint.nnnorm_pow_two_pow -> IsSelfAdjoint.nnnorm_pow_two_pow is a dubious translation:
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+  forall {E : Type.{u1}} [_inst_1 : NormedRing.{u1} E] [_inst_2 : StarRing.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1)))] [_inst_3 : CstarRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1) _inst_2] {x : E}, (IsSelfAdjoint.{u1} E (InvolutiveStar.toHasStar.{u1} E (StarAddMonoid.toHasInvolutiveStar.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} E (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1)))))) (StarRing.toStarAddMonoid.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))) _inst_2))) x) -> (forall (n : Nat), Eq.{1} NNReal (NNNorm.nnnorm.{u1} E (SeminormedAddGroup.toNNNorm.{u1} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} E (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} E (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))))) (HPow.hPow.{u1, 0, u1} E Nat E (instHPow.{u1, 0} E Nat (Monoid.Pow.{u1} E (Ring.toMonoid.{u1} E (NormedRing.toRing.{u1} E _inst_1)))) x (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) n))) (HPow.hPow.{0, 0, 0} NNReal Nat NNReal (instHPow.{0, 0} NNReal Nat (Monoid.Pow.{0} NNReal (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal NNReal.semiring)))) (NNNorm.nnnorm.{u1} E (SeminormedAddGroup.toNNNorm.{u1} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} E (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} E (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))))) x) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) n)))
+but is expected to have type
+  forall {E : Type.{u1}} [_inst_1 : NormedRing.{u1} E] [_inst_2 : StarRing.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1)))] [_inst_3 : CstarRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1) _inst_2] {x : E}, (IsSelfAdjoint.{u1} E (InvolutiveStar.toStar.{u1} E (StarAddMonoid.toInvolutiveStar.{u1} E (AddMonoidWithOne.toAddMonoid.{u1} E (AddGroupWithOne.toAddMonoidWithOne.{u1} E (Ring.toAddGroupWithOne.{u1} E (NormedRing.toRing.{u1} E _inst_1)))) (StarRing.toStarAddMonoid.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))) _inst_2))) x) -> (forall (n : Nat), Eq.{1} NNReal (NNNorm.nnnorm.{u1} E (SeminormedAddGroup.toNNNorm.{u1} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} E (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} E (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))))) (HPow.hPow.{u1, 0, u1} E Nat E (instHPow.{u1, 0} E Nat (Monoid.Pow.{u1} E (MonoidWithZero.toMonoid.{u1} E (Semiring.toMonoidWithZero.{u1} E (Ring.toSemiring.{u1} E (NormedRing.toRing.{u1} E _inst_1)))))) x (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) n))) (HPow.hPow.{0, 0, 0} NNReal Nat NNReal (instHPow.{0, 0} NNReal Nat (Monoid.Pow.{0} NNReal (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal instNNRealSemiring)))) (NNNorm.nnnorm.{u1} E (SeminormedAddGroup.toNNNorm.{u1} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} E (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} E (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))))) x) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) n)))
+Case conversion may be inaccurate. Consider using '#align is_self_adjoint.nnnorm_pow_two_pow IsSelfAdjoint.nnnorm_pow_two_powₓ'. -/
 theorem IsSelfAdjoint.nnnorm_pow_two_pow [NormedRing E] [StarRing E] [CstarRing E] {x : E}
     (hx : IsSelfAdjoint x) (n : ℕ) : ‖x ^ 2 ^ n‖₊ = ‖x‖₊ ^ 2 ^ n :=
   by
@@ -287,6 +417,12 @@ theorem IsSelfAdjoint.nnnorm_pow_two_pow [NormedRing E] [StarRing E] [CstarRing
     rw [← star_pow, CstarRing.nnnorm_star_mul_self, ← sq, hk, pow_mul']
 #align is_self_adjoint.nnnorm_pow_two_pow IsSelfAdjoint.nnnorm_pow_two_pow
 
+/- warning: self_adjoint.nnnorm_pow_two_pow -> selfAdjoint.nnnorm_pow_two_pow is a dubious translation:
+lean 3 declaration is
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+  forall {E : Type.{u1}} [_inst_1 : NormedRing.{u1} E] [_inst_2 : StarRing.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1)))] [_inst_3 : CstarRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1) _inst_2] (x : Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (AddSubgroup.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E (NonUnitalNormedRing.toNormedAddCommGroup.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))))) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E (NonUnitalNormedRing.toNormedAddCommGroup.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))))) E (AddSubgroup.instSetLikeAddSubgroup.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E (NonUnitalNormedRing.toNormedAddCommGroup.{u1} E 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(AddSubgroup.instSetLikeAddSubgroup.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E (NonUnitalNormedRing.toNormedAddCommGroup.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1)))))) x (selfAdjoint.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E (NonUnitalNormedRing.toNormedAddCommGroup.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1)))) (StarRing.toStarAddMonoid.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))) _inst_2)))) (SeminormedAddGroup.toNNNorm.{u1} (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (AddSubgroup.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E (NonUnitalNormedRing.toNormedAddCommGroup.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))))) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E (NonUnitalNormedRing.toNormedAddCommGroup.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))))) E (AddSubgroup.instSetLikeAddSubgroup.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E (NonUnitalNormedRing.toNormedAddCommGroup.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1)))))) x (selfAdjoint.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E (NonUnitalNormedRing.toNormedAddCommGroup.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1)))) (StarRing.toStarAddMonoid.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))) _inst_2)))) (AddSubgroup.seminormedAddGroup.{u1} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} E (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} E (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} 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(NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E (NonUnitalNormedRing.toNormedAddCommGroup.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))))) E (AddSubgroup.instSetLikeAddSubgroup.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E (NonUnitalNormedRing.toNormedAddCommGroup.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1)))))) x (selfAdjoint.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E (NonUnitalNormedRing.toNormedAddCommGroup.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1)))) (StarRing.toStarAddMonoid.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))) _inst_2)))) Nat (selfAdjoint.instPowSubtypeMemAddSubgroupToAddGroupToAddGroupWithOneInstMembershipInstSetLikeAddSubgroupSelfAdjointToStarAddMonoidToNonUnitalSemiringToNonUnitalRingNat.{u1} E (NormedRing.toRing.{u1} E _inst_1) _inst_2)) x (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) n))) (HPow.hPow.{0, 0, 0} NNReal Nat NNReal (instHPow.{0, 0} NNReal Nat (Monoid.Pow.{0} NNReal (MonoidWithZero.toMonoid.{0} NNReal (Semiring.toMonoidWithZero.{0} NNReal instNNRealSemiring)))) (NNNorm.nnnorm.{u1} (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (AddSubgroup.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E (NonUnitalNormedRing.toNormedAddCommGroup.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))))) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E (NonUnitalNormedRing.toNormedAddCommGroup.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))))) E (AddSubgroup.instSetLikeAddSubgroup.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E (NonUnitalNormedRing.toNormedAddCommGroup.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1)))))) x (selfAdjoint.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E (NonUnitalNormedRing.toNormedAddCommGroup.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1)))) (StarRing.toStarAddMonoid.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))) _inst_2)))) (SeminormedAddGroup.toNNNorm.{u1} (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (AddSubgroup.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E (NonUnitalNormedRing.toNormedAddCommGroup.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))))) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E (NonUnitalNormedRing.toNormedAddCommGroup.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))))) E (AddSubgroup.instSetLikeAddSubgroup.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E (NonUnitalNormedRing.toNormedAddCommGroup.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1)))))) x (selfAdjoint.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E (NonUnitalNormedRing.toNormedAddCommGroup.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1)))) (StarRing.toStarAddMonoid.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))) _inst_2)))) (AddSubgroup.seminormedAddGroup.{u1} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} E (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} E (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1)))) (selfAdjoint.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E (NonUnitalNormedRing.toNormedAddCommGroup.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1)))) (StarRing.toStarAddMonoid.{u1} E (NonUnitalRing.toNonUnitalSemiring.{u1} E (NonUnitalNormedRing.toNonUnitalRing.{u1} E (NormedRing.toNonUnitalNormedRing.{u1} E _inst_1))) _inst_2)))) x) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) n))
+Case conversion may be inaccurate. Consider using '#align self_adjoint.nnnorm_pow_two_pow selfAdjoint.nnnorm_pow_two_powₓ'. -/
 theorem selfAdjoint.nnnorm_pow_two_pow [NormedRing E] [StarRing E] [CstarRing E] (x : selfAdjoint E)
     (n : ℕ) : ‖x ^ 2 ^ n‖₊ = ‖x‖₊ ^ 2 ^ n :=
   x.Prop.nnnorm_pow_two_pow _
@@ -302,20 +438,34 @@ variable [Module 𝕜 E] [StarModule 𝕜 E]
 
 variable (𝕜)
 
+#print starₗᵢ /-
 /-- `star` bundled as a linear isometric equivalence -/
 def starₗᵢ : E ≃ₗᵢ⋆[𝕜] E :=
   { starAddEquiv with
     map_smul' := star_smul
     norm_map' := norm_star }
 #align starₗᵢ starₗᵢ
+-/
 
 variable {𝕜}
 
+/- warning: coe_starₗᵢ -> coe_starₗᵢ is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : CommSemiring.{u1} 𝕜] [_inst_2 : StarRing.{u1} 𝕜 (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} 𝕜 (CommSemiring.toNonUnitalCommSemiring.{u1} 𝕜 _inst_1))] [_inst_3 : SeminormedAddCommGroup.{u2} E] [_inst_4 : StarAddMonoid.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_3))))] [_inst_5 : NormedStarGroup.{u2} E _inst_3 _inst_4] [_inst_6 : Module.{u1, u2} 𝕜 E (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_3))] [_inst_7 : StarModule.{u1, u2} 𝕜 E (InvolutiveStar.toHasStar.{u1} 𝕜 (StarAddMonoid.toHasInvolutiveStar.{u1} 𝕜 (AddCommMonoid.toAddMonoid.{u1} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} 𝕜 (CommSemiring.toNonUnitalCommSemiring.{u1} 𝕜 _inst_1))))) (StarRing.toStarAddMonoid.{u1} 𝕜 (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} 𝕜 (CommSemiring.toNonUnitalCommSemiring.{u1} 𝕜 _inst_1)) _inst_2))) (InvolutiveStar.toHasStar.{u2} E (StarAddMonoid.toHasInvolutiveStar.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_3)))) _inst_4)) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_3))))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_3))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_3)) _inst_6))))], Eq.{succ u2} ((fun (_x : LinearIsometryEquiv.{u1, u1, u2, u2} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (starRingEnd.{u1} 𝕜 _inst_1 _inst_2) (starRingEnd.{u1} 𝕜 _inst_1 _inst_2) (RingHomInvPair.StarRingEnd.ringHomInvPair.{u1} 𝕜 _inst_1 _inst_2) (RingHomInvPair.StarRingEnd.ringHomInvPair.{u1} 𝕜 _inst_1 _inst_2) E E _inst_3 _inst_3 _inst_6 _inst_6) => E -> E) (starₗᵢ.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7)) (coeFn.{succ u2, succ u2} (LinearIsometryEquiv.{u1, u1, u2, u2} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (starRingEnd.{u1} 𝕜 _inst_1 _inst_2) (starRingEnd.{u1} 𝕜 _inst_1 _inst_2) (RingHomInvPair.StarRingEnd.ringHomInvPair.{u1} 𝕜 _inst_1 _inst_2) (RingHomInvPair.StarRingEnd.ringHomInvPair.{u1} 𝕜 _inst_1 _inst_2) E E _inst_3 _inst_3 _inst_6 _inst_6) (fun (_x : LinearIsometryEquiv.{u1, u1, u2, u2} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (starRingEnd.{u1} 𝕜 _inst_1 _inst_2) (starRingEnd.{u1} 𝕜 _inst_1 _inst_2) (RingHomInvPair.StarRingEnd.ringHomInvPair.{u1} 𝕜 _inst_1 _inst_2) (RingHomInvPair.StarRingEnd.ringHomInvPair.{u1} 𝕜 _inst_1 _inst_2) E E _inst_3 _inst_3 _inst_6 _inst_6) => E -> E) (LinearIsometryEquiv.hasCoeToFun.{u1, u1, u2, u2} 𝕜 𝕜 E E (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (starRingEnd.{u1} 𝕜 _inst_1 _inst_2) (starRingEnd.{u1} 𝕜 _inst_1 _inst_2) (RingHomInvPair.StarRingEnd.ringHomInvPair.{u1} 𝕜 _inst_1 _inst_2) (RingHomInvPair.StarRingEnd.ringHomInvPair.{u1} 𝕜 _inst_1 _inst_2) _inst_3 _inst_3 _inst_6 _inst_6) (starₗᵢ.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7)) (Star.star.{u2} E (InvolutiveStar.toHasStar.{u2} E (StarAddMonoid.toHasInvolutiveStar.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_3)))) _inst_4)))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : CommSemiring.{u1} 𝕜] [_inst_2 : StarRing.{u1} 𝕜 (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} 𝕜 (CommSemiring.toNonUnitalCommSemiring.{u1} 𝕜 _inst_1))] [_inst_3 : SeminormedAddCommGroup.{u2} E] [_inst_4 : StarAddMonoid.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_3))))] [_inst_5 : NormedStarGroup.{u2} E _inst_3 _inst_4] [_inst_6 : Module.{u1, u2} 𝕜 E (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_3))] [_inst_7 : StarModule.{u1, u2} 𝕜 E (InvolutiveStar.toStar.{u1} 𝕜 (StarAddMonoid.toInvolutiveStar.{u1} 𝕜 (AddMonoidWithOne.toAddMonoid.{u1} 𝕜 (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} 𝕜 (NonAssocSemiring.toAddCommMonoidWithOne.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 _inst_1))))) (StarRing.toStarAddMonoid.{u1} 𝕜 (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} 𝕜 (CommSemiring.toNonUnitalCommSemiring.{u1} 𝕜 _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u2} E (StarAddMonoid.toInvolutiveStar.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_3)))) _inst_4)) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_3)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 _inst_1)) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 _inst_1)) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_3)))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_3)) _inst_6))))], Eq.{succ u2} (forall (a : E), (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => E) a) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearIsometryEquiv.{u1, u1, u2, u2} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (starRingEnd.{u1} 𝕜 _inst_1 _inst_2) (starRingEnd.{u1} 𝕜 _inst_1 _inst_2) (RingHomInvPair.instRingHomInvPairToSemiringStarRingEnd.{u1} 𝕜 _inst_1 _inst_2) (RingHomInvPair.instRingHomInvPairToSemiringStarRingEnd.{u1} 𝕜 _inst_1 _inst_2) E E _inst_3 _inst_3 _inst_6 _inst_6) E (fun (_x : E) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => E) _x) (ContinuousMapClass.toFunLike.{u2, u2, u2} (LinearIsometryEquiv.{u1, u1, u2, u2} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (starRingEnd.{u1} 𝕜 _inst_1 _inst_2) (starRingEnd.{u1} 𝕜 _inst_1 _inst_2) (RingHomInvPair.instRingHomInvPairToSemiringStarRingEnd.{u1} 𝕜 _inst_1 _inst_2) (RingHomInvPair.instRingHomInvPairToSemiringStarRingEnd.{u1} 𝕜 _inst_1 _inst_2) E E _inst_3 _inst_3 _inst_6 _inst_6) E E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_3))) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_3))) (ContinuousSemilinearMapClass.toContinuousMapClass.{u2, u1, u1, u2, u2} (LinearIsometryEquiv.{u1, u1, u2, u2} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (starRingEnd.{u1} 𝕜 _inst_1 _inst_2) (starRingEnd.{u1} 𝕜 _inst_1 _inst_2) (RingHomInvPair.instRingHomInvPairToSemiringStarRingEnd.{u1} 𝕜 _inst_1 _inst_2) (RingHomInvPair.instRingHomInvPairToSemiringStarRingEnd.{u1} 𝕜 _inst_1 _inst_2) E E _inst_3 _inst_3 _inst_6 _inst_6) 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (starRingEnd.{u1} 𝕜 _inst_1 _inst_2) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_3)) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_3)) _inst_6 _inst_6 (SemilinearIsometryClass.instContinuousSemilinearMapClassToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToAddCommMonoidToAddCommGroupToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToAddCommMonoidToAddCommGroup.{u1, u1, u2, u2, u2} 𝕜 𝕜 E E (LinearIsometryEquiv.{u1, u1, u2, u2} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (starRingEnd.{u1} 𝕜 _inst_1 _inst_2) (starRingEnd.{u1} 𝕜 _inst_1 _inst_2) (RingHomInvPair.instRingHomInvPairToSemiringStarRingEnd.{u1} 𝕜 _inst_1 _inst_2) (RingHomInvPair.instRingHomInvPairToSemiringStarRingEnd.{u1} 𝕜 _inst_1 _inst_2) E E _inst_3 _inst_3 _inst_6 _inst_6) (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (starRingEnd.{u1} 𝕜 _inst_1 _inst_2) _inst_3 _inst_3 _inst_6 _inst_6 (SemilinearIsometryEquivClass.instSemilinearIsometryClass.{u1, u1, u2, u2, u2} 𝕜 𝕜 E E (LinearIsometryEquiv.{u1, u1, u2, u2} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (starRingEnd.{u1} 𝕜 _inst_1 _inst_2) (starRingEnd.{u1} 𝕜 _inst_1 _inst_2) (RingHomInvPair.instRingHomInvPairToSemiringStarRingEnd.{u1} 𝕜 _inst_1 _inst_2) (RingHomInvPair.instRingHomInvPairToSemiringStarRingEnd.{u1} 𝕜 _inst_1 _inst_2) E E _inst_3 _inst_3 _inst_6 _inst_6) (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (starRingEnd.{u1} 𝕜 _inst_1 _inst_2) (starRingEnd.{u1} 𝕜 _inst_1 _inst_2) (RingHomInvPair.instRingHomInvPairToSemiringStarRingEnd.{u1} 𝕜 _inst_1 _inst_2) (RingHomInvPair.instRingHomInvPairToSemiringStarRingEnd.{u1} 𝕜 _inst_1 _inst_2) _inst_3 _inst_3 _inst_6 _inst_6 (LinearIsometryEquiv.instSemilinearIsometryEquivClassLinearIsometryEquiv.{u1, u1, u2, u2} 𝕜 𝕜 E E (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (starRingEnd.{u1} 𝕜 _inst_1 _inst_2) (starRingEnd.{u1} 𝕜 _inst_1 _inst_2) (RingHomInvPair.instRingHomInvPairToSemiringStarRingEnd.{u1} 𝕜 _inst_1 _inst_2) (RingHomInvPair.instRingHomInvPairToSemiringStarRingEnd.{u1} 𝕜 _inst_1 _inst_2) _inst_3 _inst_3 _inst_6 _inst_6))))) (starₗᵢ.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7)) (Star.star.{u2} E (InvolutiveStar.toStar.{u2} E (StarAddMonoid.toInvolutiveStar.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_3)))) _inst_4)))
+Case conversion may be inaccurate. Consider using '#align coe_starₗᵢ coe_starₗᵢₓ'. -/
 @[simp]
 theorem coe_starₗᵢ : (starₗᵢ 𝕜 : E → E) = star :=
   rfl
 #align coe_starₗᵢ coe_starₗᵢ
 
+/- warning: starₗᵢ_apply -> starₗᵢ_apply is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : CommSemiring.{u1} 𝕜] [_inst_2 : StarRing.{u1} 𝕜 (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} 𝕜 (CommSemiring.toNonUnitalCommSemiring.{u1} 𝕜 _inst_1))] [_inst_3 : SeminormedAddCommGroup.{u2} E] [_inst_4 : StarAddMonoid.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_3))))] [_inst_5 : NormedStarGroup.{u2} E _inst_3 _inst_4] [_inst_6 : Module.{u1, u2} 𝕜 E (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_3))] [_inst_7 : StarModule.{u1, u2} 𝕜 E (InvolutiveStar.toHasStar.{u1} 𝕜 (StarAddMonoid.toHasInvolutiveStar.{u1} 𝕜 (AddCommMonoid.toAddMonoid.{u1} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} 𝕜 (CommSemiring.toNonUnitalCommSemiring.{u1} 𝕜 _inst_1))))) (StarRing.toStarAddMonoid.{u1} 𝕜 (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} 𝕜 (CommSemiring.toNonUnitalCommSemiring.{u1} 𝕜 _inst_1)) _inst_2))) (InvolutiveStar.toHasStar.{u2} E (StarAddMonoid.toHasInvolutiveStar.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_3)))) _inst_4)) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_3))))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_3))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_3)) _inst_6))))] {x : E}, Eq.{succ u2} E (coeFn.{succ u2, succ u2} (LinearIsometryEquiv.{u1, u1, u2, u2} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (starRingEnd.{u1} 𝕜 _inst_1 _inst_2) (starRingEnd.{u1} 𝕜 _inst_1 _inst_2) (RingHomInvPair.StarRingEnd.ringHomInvPair.{u1} 𝕜 _inst_1 _inst_2) (RingHomInvPair.StarRingEnd.ringHomInvPair.{u1} 𝕜 _inst_1 _inst_2) E E _inst_3 _inst_3 _inst_6 _inst_6) (fun (_x : LinearIsometryEquiv.{u1, u1, u2, u2} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (starRingEnd.{u1} 𝕜 _inst_1 _inst_2) (starRingEnd.{u1} 𝕜 _inst_1 _inst_2) (RingHomInvPair.StarRingEnd.ringHomInvPair.{u1} 𝕜 _inst_1 _inst_2) (RingHomInvPair.StarRingEnd.ringHomInvPair.{u1} 𝕜 _inst_1 _inst_2) E E _inst_3 _inst_3 _inst_6 _inst_6) => E -> E) (LinearIsometryEquiv.hasCoeToFun.{u1, u1, u2, u2} 𝕜 𝕜 E E (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (starRingEnd.{u1} 𝕜 _inst_1 _inst_2) (starRingEnd.{u1} 𝕜 _inst_1 _inst_2) (RingHomInvPair.StarRingEnd.ringHomInvPair.{u1} 𝕜 _inst_1 _inst_2) (RingHomInvPair.StarRingEnd.ringHomInvPair.{u1} 𝕜 _inst_1 _inst_2) _inst_3 _inst_3 _inst_6 _inst_6) (starₗᵢ.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) x) (Star.star.{u2} E (InvolutiveStar.toHasStar.{u2} E (StarAddMonoid.toHasInvolutiveStar.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_3)))) _inst_4)) x)
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : CommSemiring.{u1} 𝕜] [_inst_2 : StarRing.{u1} 𝕜 (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} 𝕜 (CommSemiring.toNonUnitalCommSemiring.{u1} 𝕜 _inst_1))] [_inst_3 : SeminormedAddCommGroup.{u2} E] [_inst_4 : StarAddMonoid.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_3))))] [_inst_5 : NormedStarGroup.{u2} E _inst_3 _inst_4] [_inst_6 : Module.{u1, u2} 𝕜 E (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_3))] [_inst_7 : StarModule.{u1, u2} 𝕜 E (InvolutiveStar.toStar.{u1} 𝕜 (StarAddMonoid.toInvolutiveStar.{u1} 𝕜 (AddMonoidWithOne.toAddMonoid.{u1} 𝕜 (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} 𝕜 (NonAssocSemiring.toAddCommMonoidWithOne.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 _inst_1))))) (StarRing.toStarAddMonoid.{u1} 𝕜 (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} 𝕜 (CommSemiring.toNonUnitalCommSemiring.{u1} 𝕜 _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u2} E (StarAddMonoid.toInvolutiveStar.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_3)))) _inst_4)) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_3)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 _inst_1)) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 _inst_1)) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_3)))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_3)) _inst_6))))] {x : E}, Eq.{succ u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => E) x) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearIsometryEquiv.{u1, u1, u2, u2} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (starRingEnd.{u1} 𝕜 _inst_1 _inst_2) (starRingEnd.{u1} 𝕜 _inst_1 _inst_2) (RingHomInvPair.instRingHomInvPairToSemiringStarRingEnd.{u1} 𝕜 _inst_1 _inst_2) (RingHomInvPair.instRingHomInvPairToSemiringStarRingEnd.{u1} 𝕜 _inst_1 _inst_2) E E _inst_3 _inst_3 _inst_6 _inst_6) E (fun (_x : E) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => E) _x) (ContinuousMapClass.toFunLike.{u2, u2, u2} (LinearIsometryEquiv.{u1, u1, u2, u2} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (starRingEnd.{u1} 𝕜 _inst_1 _inst_2) (starRingEnd.{u1} 𝕜 _inst_1 _inst_2) (RingHomInvPair.instRingHomInvPairToSemiringStarRingEnd.{u1} 𝕜 _inst_1 _inst_2) (RingHomInvPair.instRingHomInvPairToSemiringStarRingEnd.{u1} 𝕜 _inst_1 _inst_2) E E _inst_3 _inst_3 _inst_6 _inst_6) E E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_3))) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_3))) (ContinuousSemilinearMapClass.toContinuousMapClass.{u2, u1, u1, u2, u2} (LinearIsometryEquiv.{u1, u1, u2, u2} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (starRingEnd.{u1} 𝕜 _inst_1 _inst_2) (starRingEnd.{u1} 𝕜 _inst_1 _inst_2) (RingHomInvPair.instRingHomInvPairToSemiringStarRingEnd.{u1} 𝕜 _inst_1 _inst_2) (RingHomInvPair.instRingHomInvPairToSemiringStarRingEnd.{u1} 𝕜 _inst_1 _inst_2) E E _inst_3 _inst_3 _inst_6 _inst_6) 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (starRingEnd.{u1} 𝕜 _inst_1 _inst_2) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_3)) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_3)) _inst_6 _inst_6 (SemilinearIsometryClass.instContinuousSemilinearMapClassToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToAddCommMonoidToAddCommGroupToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToAddCommMonoidToAddCommGroup.{u1, u1, u2, u2, u2} 𝕜 𝕜 E E (LinearIsometryEquiv.{u1, u1, u2, u2} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (starRingEnd.{u1} 𝕜 _inst_1 _inst_2) (starRingEnd.{u1} 𝕜 _inst_1 _inst_2) (RingHomInvPair.instRingHomInvPairToSemiringStarRingEnd.{u1} 𝕜 _inst_1 _inst_2) (RingHomInvPair.instRingHomInvPairToSemiringStarRingEnd.{u1} 𝕜 _inst_1 _inst_2) E E _inst_3 _inst_3 _inst_6 _inst_6) (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (starRingEnd.{u1} 𝕜 _inst_1 _inst_2) _inst_3 _inst_3 _inst_6 _inst_6 (SemilinearIsometryEquivClass.instSemilinearIsometryClass.{u1, u1, u2, u2, u2} 𝕜 𝕜 E E (LinearIsometryEquiv.{u1, u1, u2, u2} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (starRingEnd.{u1} 𝕜 _inst_1 _inst_2) (starRingEnd.{u1} 𝕜 _inst_1 _inst_2) (RingHomInvPair.instRingHomInvPairToSemiringStarRingEnd.{u1} 𝕜 _inst_1 _inst_2) (RingHomInvPair.instRingHomInvPairToSemiringStarRingEnd.{u1} 𝕜 _inst_1 _inst_2) E E _inst_3 _inst_3 _inst_6 _inst_6) (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (starRingEnd.{u1} 𝕜 _inst_1 _inst_2) (starRingEnd.{u1} 𝕜 _inst_1 _inst_2) (RingHomInvPair.instRingHomInvPairToSemiringStarRingEnd.{u1} 𝕜 _inst_1 _inst_2) (RingHomInvPair.instRingHomInvPairToSemiringStarRingEnd.{u1} 𝕜 _inst_1 _inst_2) _inst_3 _inst_3 _inst_6 _inst_6 (LinearIsometryEquiv.instSemilinearIsometryEquivClassLinearIsometryEquiv.{u1, u1, u2, u2} 𝕜 𝕜 E E (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (CommSemiring.toSemiring.{u1} 𝕜 _inst_1) (starRingEnd.{u1} 𝕜 _inst_1 _inst_2) (starRingEnd.{u1} 𝕜 _inst_1 _inst_2) (RingHomInvPair.instRingHomInvPairToSemiringStarRingEnd.{u1} 𝕜 _inst_1 _inst_2) (RingHomInvPair.instRingHomInvPairToSemiringStarRingEnd.{u1} 𝕜 _inst_1 _inst_2) _inst_3 _inst_3 _inst_6 _inst_6))))) (starₗᵢ.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) x) (Star.star.{u2} E (InvolutiveStar.toStar.{u2} E (StarAddMonoid.toInvolutiveStar.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_3)))) _inst_4)) x)
+Case conversion may be inaccurate. Consider using '#align starₗᵢ_apply starₗᵢ_applyₓ'. -/
 theorem starₗᵢ_apply {x : E} : starₗᵢ 𝕜 x = star x :=
   rfl
 #align starₗᵢ_apply starₗᵢ_apply
@@ -324,15 +474,19 @@ end starₗᵢ
 
 namespace StarSubalgebra
 
+#print StarSubalgebra.toNormedAlgebra /-
 instance toNormedAlgebra {𝕜 A : Type _} [NormedField 𝕜] [StarRing 𝕜] [SeminormedRing A] [StarRing A]
     [NormedAlgebra 𝕜 A] [StarModule 𝕜 A] (S : StarSubalgebra 𝕜 A) : NormedAlgebra 𝕜 S :=
   @NormedAlgebra.induced _ 𝕜 S A _ (SubringClass.toRing S) S.Algebra _ _ _ S.Subtype
 #align star_subalgebra.to_normed_algebra StarSubalgebra.toNormedAlgebra
+-/
 
+#print StarSubalgebra.to_cstarRing /-
 instance to_cstarRing {R A} [CommRing R] [StarRing R] [NormedRing A] [StarRing A] [CstarRing A]
     [Algebra R A] [StarModule R A] (S : StarSubalgebra R A) : CstarRing S
     where norm_star_mul_self x := @CstarRing.norm_star_mul_self A _ _ _ x
 #align star_subalgebra.to_cstar_ring StarSubalgebra.to_cstarRing
+-/
 
 end StarSubalgebra

e6577119

bump to nightly-2023-03-13-18

mathlib commit https://github.com/leanprover-community/mathlib/commit/2af0836443b4cfb5feda0df0051acdb398304931

66e1e587

Diff

@@ -324,7 +324,7 @@ end starₗᵢ
 
 namespace StarSubalgebra
 
-instance toNormedAlgebra {𝕜 A : Type _} [NormedField 𝕜] [StarRing 𝕜] [SemiNormedRing A] [StarRing A]
+instance toNormedAlgebra {𝕜 A : Type _} [NormedField 𝕜] [StarRing 𝕜] [SeminormedRing A] [StarRing A]
     [NormedAlgebra 𝕜 A] [StarModule 𝕜 A] (S : StarSubalgebra 𝕜 A) : NormedAlgebra 𝕜 S :=
   @NormedAlgebra.induced _ 𝕜 S A _ (SubringClass.toRing S) S.Algebra _ _ _ S.Subtype
 #align star_subalgebra.to_normed_algebra StarSubalgebra.toNormedAlgebra

e6577119

bump to nightly-2023-03-01-20

mathlib commit https://github.com/leanprover-community/mathlib/commit/4c586d291f189eecb9d00581aeb3dd998ac34442

20cadee0

Diff

@@ -264,7 +264,7 @@ theorem norm_mul_coe_unitary (A : E) (U : unitary E) : ‖A * U‖ = ‖A‖ :=
   calc
     _ = ‖((U : E)⋆ * A⋆)⋆‖ := by simp only [star_star, star_mul]
     _ = ‖(U : E)⋆ * A⋆‖ := by rw [norm_star]
-    _ = ‖A⋆‖ := norm_mem_unitary_mul (star A) (unitary.star_mem U.Prop)
+    _ = ‖A⋆‖ := (norm_mem_unitary_mul (star A) (unitary.star_mem U.Prop))
     _ = ‖A‖ := norm_star _
     
 #align cstar_ring.norm_mul_coe_unitary CstarRing.norm_mul_coe_unitary

e6577119

bump to nightly-2023-03-01-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/4c586d291f189eecb9d00581aeb3dd998ac34442

d0348377

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 analysis.normed_space.star.basic
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
+! leanprover-community/mathlib commit e65771194f9e923a70dfb49b6ca7be6e400d8b6f
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -13,6 +13,7 @@ import Mathbin.Analysis.NormedSpace.Basic
 import Mathbin.Analysis.NormedSpace.LinearIsometry
 import Mathbin.Algebra.Star.SelfAdjoint
 import Mathbin.Algebra.Star.Unitary
+import Mathbin.Topology.Algebra.StarSubalgebra
 
 /-!
 # Normed star rings and algebras
@@ -321,3 +322,17 @@ theorem starₗᵢ_apply {x : E} : starₗᵢ 𝕜 x = star x :=
 
 end starₗᵢ
 
+namespace StarSubalgebra
+
+instance toNormedAlgebra {𝕜 A : Type _} [NormedField 𝕜] [StarRing 𝕜] [SemiNormedRing A] [StarRing A]
+    [NormedAlgebra 𝕜 A] [StarModule 𝕜 A] (S : StarSubalgebra 𝕜 A) : NormedAlgebra 𝕜 S :=
+  @NormedAlgebra.induced _ 𝕜 S A _ (SubringClass.toRing S) S.Algebra _ _ _ S.Subtype
+#align star_subalgebra.to_normed_algebra StarSubalgebra.toNormedAlgebra
+
+instance to_cstarRing {R A} [CommRing R] [StarRing R] [NormedRing A] [StarRing A] [CstarRing A]
+    [Algebra R A] [StarModule R A] (S : StarSubalgebra R A) : CstarRing S
+    where norm_star_mul_self x := @CstarRing.norm_star_mul_self A _ _ _ x
+#align star_subalgebra.to_cstar_ring StarSubalgebra.to_cstarRing
+
+end StarSubalgebra
+

f2ce6086

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

aa666983

chore: avoid id.def (adaptation for nightly-2024-03-27) (#11829)

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

b8a0f589

Diff

@@ -86,7 +86,7 @@ class CstarRing (E : Type*) [NonUnitalNormedRing E] [StarRing E] : Prop where
   norm_star_mul_self : ∀ {x : E}, ‖x⋆ * x‖ = ‖x‖ * ‖x‖
 #align cstar_ring CstarRing
 
-instance : CstarRing ℝ where norm_star_mul_self {x} := by simp only [star, id.def, norm_mul]
+instance : CstarRing ℝ where norm_star_mul_self {x} := by simp only [star, id, norm_mul]
 
 namespace CstarRing

aa666983

chore: superfluous parentheses part 2 (#12131)

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

d48d30ac

Diff

@@ -248,7 +248,7 @@ theorem norm_mul_coe_unitary (A : E) (U : unitary E) : ‖A * U‖ = ‖A‖ :=
   calc
     _ = ‖((U : E)⋆ * A⋆)⋆‖ := by simp only [star_star, star_mul]
     _ = ‖(U : E)⋆ * A⋆‖ := by rw [norm_star]
-    _ = ‖A⋆‖ := (norm_mem_unitary_mul (star A) (unitary.star_mem U.prop))
+    _ = ‖A⋆‖ := norm_mem_unitary_mul (star A) (unitary.star_mem U.prop)
     _ = ‖A‖ := norm_star _
 #align cstar_ring.norm_mul_coe_unitary CstarRing.norm_mul_coe_unitary

aa666983

chore: avoid Ne.def (adaptation for nightly-2024-03-27) (#11801)

1b40c7bc

Diff

@@ -138,7 +138,7 @@ theorem star_mul_self_eq_zero_iff (x : E) : x⋆ * x = 0 ↔ x = 0 := by
 #align cstar_ring.star_mul_self_eq_zero_iff CstarRing.star_mul_self_eq_zero_iff
 
 theorem star_mul_self_ne_zero_iff (x : E) : x⋆ * x ≠ 0 ↔ x ≠ 0 := by
-  simp only [Ne.def, star_mul_self_eq_zero_iff]
+  simp only [Ne, star_mul_self_eq_zero_iff]
 #align cstar_ring.star_mul_self_ne_zero_iff CstarRing.star_mul_self_ne_zero_iff
 
 @[simp]
@@ -147,7 +147,7 @@ theorem mul_star_self_eq_zero_iff (x : E) : x * x⋆ = 0 ↔ x = 0 := by
 #align cstar_ring.mul_star_self_eq_zero_iff CstarRing.mul_star_self_eq_zero_iff
 
 theorem mul_star_self_ne_zero_iff (x : E) : x * x⋆ ≠ 0 ↔ x ≠ 0 := by
-  simp only [Ne.def, mul_star_self_eq_zero_iff]
+  simp only [Ne, mul_star_self_eq_zero_iff]
 #align cstar_ring.mul_star_self_ne_zero_iff CstarRing.mul_star_self_ne_zero_iff
 
 end NonUnital

aa666983

change the order of operation in zsmulRec and nsmulRec (#11451)

We change the following field in the definition of an additive commutative monoid:

 nsmul_succ : ∀ (n : ℕ) (x : G),
-  AddMonoid.nsmul (n + 1) x = x + AddMonoid.nsmul n x
+  AddMonoid.nsmul (n + 1) x = AddMonoid.nsmul n x + x

where the latter is more natural

We adjust the definitions of ^ in monoids, groups, etc. Originally there was a warning comment about why this natural order was preferred

use x * npowRec n x and not npowRec n x * x in the definition to make sure that definitional unfolding of npowRec is blocked, to avoid deep recursion issues.

but it seems to no longer apply.

Remarks on the PR :

pow_succ and pow_succ' have switched their meanings.
Most of the time, the proofs were adjusted by priming/unpriming one lemma, or exchanging left and right; a few proofs were more complicated to adjust.
In particular, [Mathlib/NumberTheory/RamificationInertia.lean] used Ideal.IsPrime.mul_mem_pow which is defined in [Mathlib/RingTheory/DedekindDomain/Ideal.lean]. Changing the order of operation forced me to add the symmetric lemma Ideal.IsPrime.mem_pow_mul.
the docstring for Cauchy condensation test in [Mathlib/Analysis/PSeries.lean] was mathematically incorrect, I added the mention that the function is antitone.

9a3feeae

Diff

@@ -264,7 +264,7 @@ theorem IsSelfAdjoint.nnnorm_pow_two_pow [NormedRing E] [StarRing E] [CstarRing
     (hx : IsSelfAdjoint x) (n : ℕ) : ‖x ^ 2 ^ n‖₊ = ‖x‖₊ ^ 2 ^ n := by
   induction' n with k hk
   · simp only [pow_zero, pow_one, Nat.zero_eq]
-  · rw [pow_succ, pow_mul', sq]
+  · rw [pow_succ', pow_mul', sq]
     nth_rw 1 [← selfAdjoint.mem_iff.mp hx]
     rw [← star_pow, CstarRing.nnnorm_star_mul_self, ← sq, hk, pow_mul']
 #align is_self_adjoint.nnnorm_pow_two_pow IsSelfAdjoint.nnnorm_pow_two_pow

aa666983

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

@@ -155,11 +155,8 @@ end NonUnital
 section ProdPi
 
 variable {ι R₁ R₂ : Type*} {R : ι → Type*}
-
 variable [NonUnitalNormedRing R₁] [StarRing R₁] [CstarRing R₁]
-
 variable [NonUnitalNormedRing R₂] [StarRing R₂] [CstarRing R₂]
-
 variable [∀ i, NonUnitalNormedRing (R i)] [∀ i, StarRing (R i)]
 
 /-- This instance exists to short circuit type class resolution because of problems with
@@ -280,11 +277,8 @@ theorem selfAdjoint.nnnorm_pow_two_pow [NormedRing E] [StarRing E] [CstarRing E]
 section starₗᵢ
 
 variable [CommSemiring 𝕜] [StarRing 𝕜]
-
 variable [SeminormedAddCommGroup E] [StarAddMonoid E] [NormedStarGroup E]
-
 variable [Module 𝕜 E] [StarModule 𝕜 E]
-
 variable (𝕜)
 
 /-- `star` bundled as a linear isometric equivalence -/

aa666983

chore: classify simp cannot prove porting notes (#10960)

Classifies by adding issue number #10959 porting notes claiming anything semantically equivalent to:

"simp cannot prove this"
"simp used to be able to close this goal"
"simp can't handle this"
"simp used to work here"

c70ed957

Diff

@@ -202,7 +202,7 @@ section Unital
 
 variable [NormedRing E] [StarRing E] [CstarRing E]
 
-@[simp, nolint simpNF] -- Porting note: simp cannot prove this
+@[simp, nolint simpNF] -- Porting note (#10959): simp cannot prove this
 theorem norm_one [Nontrivial E] : ‖(1 : E)‖ = 1 := by
   have : 0 < ‖(1 : E)‖ := norm_pos_iff.mpr one_ne_zero
   rw [← mul_left_inj' this.ne', ← norm_star_mul_self, mul_one, star_one, one_mul]

aa666983

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

@@ -317,7 +317,7 @@ namespace StarSubalgebra
 
 instance toNormedAlgebra {𝕜 A : Type*} [NormedField 𝕜] [StarRing 𝕜] [SeminormedRing A] [StarRing A]
     [NormedAlgebra 𝕜 A] [StarModule 𝕜 A] (S : StarSubalgebra 𝕜 A) : NormedAlgebra 𝕜 S :=
-  @NormedAlgebra.induced _ 𝕜 S A _ (SubringClass.toRing S) S.algebra _ _ _ S.subtype
+  NormedAlgebra.induced 𝕜 S A S.subtype
 #align star_subalgebra.to_normed_algebra StarSubalgebra.toNormedAlgebra
 
 instance to_cstarRing {R A} [CommRing R] [StarRing R] [NormedRing A] [StarRing A] [CstarRing A]

aa666983

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

@@ -7,8 +7,8 @@ import Mathlib.Analysis.Normed.Group.Hom
 import Mathlib.Analysis.NormedSpace.Basic
 import Mathlib.Analysis.NormedSpace.LinearIsometry
 import Mathlib.Algebra.Star.SelfAdjoint
+import Mathlib.Algebra.Star.Subalgebra
 import Mathlib.Algebra.Star.Unitary
-import Mathlib.Topology.Algebra.StarSubalgebra
 import Mathlib.Topology.Algebra.Module.Star
 
 #align_import analysis.normed_space.star.basic from "leanprover-community/mathlib"@"aa6669832974f87406a3d9d70fc5707a60546207"

aa666983

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

@@ -39,7 +39,7 @@ open Topology
 local postfix:max "⋆" => star
 
 /-- A normed star group is a normed group with a compatible `star` which is isometric. -/
-class NormedStarGroup (E : Type _) [SeminormedAddCommGroup E] [StarAddMonoid E] : Prop where
+class NormedStarGroup (E : Type*) [SeminormedAddCommGroup E] [StarAddMonoid E] : Prop where
   norm_star : ∀ x : E, ‖x⋆‖ = ‖x‖
 #align normed_star_group NormedStarGroup
 
@@ -47,7 +47,7 @@ export NormedStarGroup (norm_star)
 
 attribute [simp] norm_star
 
-variable {𝕜 E α : Type _}
+variable {𝕜 E α : Type*}
 
 section NormedStarGroup
 
@@ -82,7 +82,7 @@ instance RingHomIsometric.starRingEnd [NormedCommRing E] [StarRing E] [NormedSta
 
 /-- A C*-ring is a normed star ring that satisfies the stronger condition `‖x⋆ * x‖ = ‖x‖^2`
 for every `x`. -/
-class CstarRing (E : Type _) [NonUnitalNormedRing E] [StarRing E] : Prop where
+class CstarRing (E : Type*) [NonUnitalNormedRing E] [StarRing E] : Prop where
   norm_star_mul_self : ∀ {x : E}, ‖x⋆ * x‖ = ‖x‖ * ‖x‖
 #align cstar_ring CstarRing
 
@@ -154,7 +154,7 @@ end NonUnital
 
 section ProdPi
 
-variable {ι R₁ R₂ : Type _} {R : ι → Type _}
+variable {ι R₁ R₂ : Type*} {R : ι → Type*}
 
 variable [NonUnitalNormedRing R₁] [StarRing R₁] [CstarRing R₁]
 
@@ -315,7 +315,7 @@ end starₗᵢ
 
 namespace StarSubalgebra
 
-instance toNormedAlgebra {𝕜 A : Type _} [NormedField 𝕜] [StarRing 𝕜] [SeminormedRing A] [StarRing A]
+instance toNormedAlgebra {𝕜 A : Type*} [NormedField 𝕜] [StarRing 𝕜] [SeminormedRing A] [StarRing A]
     [NormedAlgebra 𝕜 A] [StarModule 𝕜 A] (S : StarSubalgebra 𝕜 A) : NormedAlgebra 𝕜 S :=
   @NormedAlgebra.induced _ 𝕜 S A _ (SubringClass.toRing S) S.algebra _ _ _ S.subtype
 #align star_subalgebra.to_normed_algebra StarSubalgebra.toNormedAlgebra

aa666983

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

@@ -2,11 +2,6 @@
 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 analysis.normed_space.star.basic
-! leanprover-community/mathlib commit aa6669832974f87406a3d9d70fc5707a60546207
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Analysis.Normed.Group.Hom
 import Mathlib.Analysis.NormedSpace.Basic
@@ -16,6 +11,8 @@ import Mathlib.Algebra.Star.Unitary
 import Mathlib.Topology.Algebra.StarSubalgebra
 import Mathlib.Topology.Algebra.Module.Star
 
+#align_import analysis.normed_space.star.basic from "leanprover-community/mathlib"@"aa6669832974f87406a3d9d70fc5707a60546207"
+
 /-!
 # Normed star rings and algebras

aa666983

fix: change instance priorities in algebra hierarchy (#5941)

WIP: experiments with changing instance priorities. See https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/std4.20.2F.20Lean4.20bump/near/374996945 .

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

039dff72

Diff

@@ -106,7 +106,7 @@ instance (priority := 100) to_normedStarGroup : NormedStarGroup E :=
     · simp only [htriv, star_zero]
     · have hnt : 0 < ‖x‖ := norm_pos_iff.mpr htriv
       have hnt_star : 0 < ‖x⋆‖ :=
-        norm_pos_iff.mpr ((AddEquiv.map_ne_zero_iff starAddEquiv).mpr htriv)
+        norm_pos_iff.mpr ((AddEquiv.map_ne_zero_iff starAddEquiv (M := E)).mpr htriv)
       have h₁ :=
         calc
           ‖x‖ * ‖x‖ = ‖x⋆ * x‖ := norm_star_mul_self.symm

aa666983

chore: fix typos (#4518)

I ran codespell Mathlib and got tired halfway through the suggestions.

92beef58

Diff

@@ -83,7 +83,7 @@ instance RingHomIsometric.starRingEnd [NormedCommRing E] [StarRing E] [NormedSta
   ⟨@norm_star _ _ _ _⟩
 #align ring_hom_isometric.star_ring_end RingHomIsometric.starRingEnd
 
-/-- A C*-ring is a normed star ring that satifies the stronger condition `‖x⋆ * x‖ = ‖x‖^2`
+/-- A C*-ring is a normed star ring that satisfies the stronger condition `‖x⋆ * x‖ = ‖x‖^2`
 for every `x`. -/
 class CstarRing (E : Type _) [NonUnitalNormedRing E] [StarRing E] : Prop where
   norm_star_mul_self : ∀ {x : E}, ‖x⋆ * x‖ = ‖x‖ * ‖x‖

aa666983

chore: forward port leanprover-community/mathlib#19037 (#4136)

c809799e

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 analysis.normed_space.star.basic
-! leanprover-community/mathlib commit e65771194f9e923a70dfb49b6ca7be6e400d8b6f
+! leanprover-community/mathlib commit aa6669832974f87406a3d9d70fc5707a60546207
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,7 @@ import Mathlib.Analysis.NormedSpace.LinearIsometry
 import Mathlib.Algebra.Star.SelfAdjoint
 import Mathlib.Algebra.Star.Unitary
 import Mathlib.Topology.Algebra.StarSubalgebra
+import Mathlib.Topology.Algebra.Module.Star
 
 /-!
 # Normed star rings and algebras
@@ -307,6 +308,12 @@ theorem starₗᵢ_apply {x : E} : starₗᵢ 𝕜 x = star x :=
   rfl
 #align starₗᵢ_apply starₗᵢ_apply
 
+@[simp]
+theorem starₗᵢ_toContinuousLinearEquiv :
+    (starₗᵢ 𝕜 : E ≃ₗᵢ⋆[𝕜] E).toContinuousLinearEquiv = (starL 𝕜 : E ≃L⋆[𝕜] E) :=
+  ContinuousLinearEquiv.ext rfl
+#align starₗᵢ_to_continuous_linear_equiv starₗᵢ_toContinuousLinearEquiv
+
 end starₗᵢ
 
 namespace StarSubalgebra

e6577119

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

@@ -77,7 +77,6 @@ instance (priority := 100) NormedStarGroup.to_continuousStar : ContinuousStar E
 
 end NormedStarGroup
 
-set_option synthInstance.etaExperiment true in -- Porting note: gets around lean4#2074
 instance RingHomIsometric.starRingEnd [NormedCommRing E] [StarRing E] [NormedStarGroup E] :
     RingHomIsometric (starRingEnd E) :=
   ⟨@norm_star _ _ _ _⟩
@@ -202,7 +201,6 @@ end ProdPi
 
 section Unital
 
-set_option synthInstance.etaExperiment true
 
 variable [NormedRing E] [StarRing E] [CstarRing E]
 
@@ -267,7 +265,6 @@ end Unital
 
 end CstarRing
 
-set_option synthInstance.etaExperiment true in
 theorem IsSelfAdjoint.nnnorm_pow_two_pow [NormedRing E] [StarRing E] [CstarRing E] {x : E}
     (hx : IsSelfAdjoint x) (n : ℕ) : ‖x ^ 2 ^ n‖₊ = ‖x‖₊ ^ 2 ^ n := by
   induction' n with k hk
@@ -277,7 +274,6 @@ theorem IsSelfAdjoint.nnnorm_pow_two_pow [NormedRing E] [StarRing E] [CstarRing
     rw [← star_pow, CstarRing.nnnorm_star_mul_self, ← sq, hk, pow_mul']
 #align is_self_adjoint.nnnorm_pow_two_pow IsSelfAdjoint.nnnorm_pow_two_pow
 
-set_option synthInstance.etaExperiment true in
 theorem selfAdjoint.nnnorm_pow_two_pow [NormedRing E] [StarRing E] [CstarRing E] (x : selfAdjoint E)
     (n : ℕ) : ‖x ^ 2 ^ n‖₊ = ‖x‖₊ ^ 2 ^ n :=
   x.prop.nnnorm_pow_two_pow _
@@ -315,13 +311,11 @@ end starₗᵢ
 
 namespace StarSubalgebra
 
-set_option synthInstance.etaExperiment true in -- Porting note: gets around lean4#2074
 instance toNormedAlgebra {𝕜 A : Type _} [NormedField 𝕜] [StarRing 𝕜] [SeminormedRing A] [StarRing A]
     [NormedAlgebra 𝕜 A] [StarModule 𝕜 A] (S : StarSubalgebra 𝕜 A) : NormedAlgebra 𝕜 S :=
   @NormedAlgebra.induced _ 𝕜 S A _ (SubringClass.toRing S) S.algebra _ _ _ S.subtype
 #align star_subalgebra.to_normed_algebra StarSubalgebra.toNormedAlgebra
 
-set_option synthInstance.etaExperiment true in -- Porting note: gets around lean4#2074
 instance to_cstarRing {R A} [CommRing R] [StarRing R] [NormedRing A] [StarRing A] [CstarRing A]
     [Algebra R A] [StarModule R A] (S : StarSubalgebra R A) : CstarRing S where
   norm_star_mul_self {x} := @CstarRing.norm_star_mul_self A _ _ _ x

e6577119

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

@@ -202,6 +202,8 @@ end ProdPi
 
 section Unital
 
+set_option synthInstance.etaExperiment true
+
 variable [NormedRing E] [StarRing E] [CstarRing E]
 
 @[simp, nolint simpNF] -- Porting note: simp cannot prove this
@@ -265,6 +267,7 @@ end Unital
 
 end CstarRing
 
+set_option synthInstance.etaExperiment true in
 theorem IsSelfAdjoint.nnnorm_pow_two_pow [NormedRing E] [StarRing E] [CstarRing E] {x : E}
     (hx : IsSelfAdjoint x) (n : ℕ) : ‖x ^ 2 ^ n‖₊ = ‖x‖₊ ^ 2 ^ n := by
   induction' n with k hk
@@ -274,6 +277,7 @@ theorem IsSelfAdjoint.nnnorm_pow_two_pow [NormedRing E] [StarRing E] [CstarRing
     rw [← star_pow, CstarRing.nnnorm_star_mul_self, ← sq, hk, pow_mul']
 #align is_self_adjoint.nnnorm_pow_two_pow IsSelfAdjoint.nnnorm_pow_two_pow
 
+set_option synthInstance.etaExperiment true in
 theorem selfAdjoint.nnnorm_pow_two_pow [NormedRing E] [StarRing E] [CstarRing E] (x : selfAdjoint E)
     (n : ℕ) : ‖x ^ 2 ^ n‖₊ = ‖x‖₊ ^ 2 ^ n :=
   x.prop.nnnorm_pow_two_pow _

e6577119

chore: tidy various files (#3718)

2215ff4f

Diff

@@ -194,9 +194,9 @@ instance _root_.Pi.cstarRing : CstarRing (∀ i, R i) where
           (fun x y h => by simpa only [sq] using mul_le_mul' h h) (by simp)).symm
 #align pi.cstar_ring Pi.cstarRing
 
-instance _root_.Pi.cstar_ring' : CstarRing (ι → R₁) :=
+instance _root_.Pi.cstarRing' : CstarRing (ι → R₁) :=
   Pi.cstarRing
-#align pi.cstar_ring' Pi.cstar_ring'
+#align pi.cstar_ring' Pi.cstarRing'
 
 end ProdPi

e6577119

feat: port Analysis.NormedSpace.Star.Basic (#3650)

a71a4a3c

`analysis.normed_space.star.basic` ⟷ `Mathlib.Analysis.NormedSpace.Star.Basic`

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 10 + 622

analysis.normed_space.star.basic ⟷ Mathlib.Analysis.NormedSpace.Star.Basic

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 10 + 622

`analysis.normed_space.star.basic` ⟷ `Mathlib.Analysis.NormedSpace.Star.Basic`

`simp` not firing sometimes