analysis.normed_space.star.continuous_functional_calculus ⟷ Mathlib.Analysis.NormedSpace.Star.ContinuousFunctionalCalculus

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

@@ -189,8 +189,8 @@ theorem elementalStarAlgebra.isUnit_of_isUnit_of_isStarNormal (h : IsUnit a) :
         _ = spectralRadius ℂ (algebraMap ℂ A ‖star a * a‖ - star a * a) :=
           by
           refine' (IsSelfAdjoint.spectralRadius_eq_nnnorm _).symm
-          rw [IsSelfAdjoint, star_sub, star_mul, star_star, ← algebraMap_star_comm, IsROrC.star_def,
-            IsROrC.conj_ofReal]
+          rw [IsSelfAdjoint, star_sub, star_mul, star_star, ← algebraMap_star_comm, RCLike.star_def,
+            RCLike.conj_ofReal]
         _ < ‖star a * a‖₊ := spectrum.spectralRadius_lt_of_forall_lt _ h₂)
 #align elemental_star_algebra.is_unit_of_is_unit_of_is_star_normal elementalStarAlgebra.isUnit_of_isUnit_of_isStarNormal
 -/

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

@@ -162,20 +162,20 @@ theorem elementalStarAlgebra.isUnit_of_isUnit_of_isStarNormal (h : IsUnit a) :
   have h₂ : ∀ z ∈ spectrum ℂ (algebraMap ℂ A ‖star a * a‖ - star a * a), ‖z‖₊ < ‖star a * a‖₊ :=
     by
     intro z hz
-    rw [← spectrum.singleton_sub_eq, Set.singleton_sub] at hz 
+    rw [← spectrum.singleton_sub_eq, Set.singleton_sub] at hz
     have h₃ : z ∈ Set.Icc (0 : ℂ) ‖star a * a‖ :=
       by
       replace hz := Set.image_subset _ (spectrum_star_mul_self_of_isStarNormal a) hz
-      rwa [Set.image_const_sub_Icc, sub_self, sub_zero] at hz 
+      rwa [Set.image_const_sub_Icc, sub_self, sub_zero] at hz
     refine' lt_of_le_of_ne (Complex.real_le_real.1 <| Complex.eq_coe_norm_of_nonneg h₃.1 ▸ h₃.2) _
     · intro hz'
       replace hz' := congr_arg (fun x : ℝ≥0 => ((x : ℝ) : ℂ)) hz'
-      simp only [coe_nnnorm] at hz' 
-      rw [← Complex.eq_coe_norm_of_nonneg h₃.1] at hz' 
+      simp only [coe_nnnorm] at hz'
+      rw [← Complex.eq_coe_norm_of_nonneg h₃.1] at hz'
       obtain ⟨w, hw₁, hw₂⟩ := hz
       refine' (spectrum.zero_not_mem_iff ℂ).mpr h _
-      rw [hz', sub_eq_self] at hw₂ 
-      rwa [hw₂] at hw₁ 
+      rw [hz', sub_eq_self] at hw₂
+      rwa [hw₂] at hw₁
   /- The norm of `‖star a * a‖ • 1 - star a * a` in the subalgebra and in `A` coincide. In `A`,
     because this element is selfadjoint, by `is_self_adjoint.spectral_radius_eq_nnnorm`, its norm is
     the supremum of the norms of the elements of the spectrum, which is strictly less than
@@ -284,7 +284,7 @@ theorem elementalStarAlgebra.bijective_characterSpaceToSpectrum :
   rintro ⟨z, hz⟩
   have hz' :=
     (StarSubalgebra.spectrum_eq (elementalStarAlgebra.isClosed ℂ a) ⟨a, self_mem ℂ a⟩).symm.subst hz
-  rw [character_space.mem_spectrum_iff_exists] at hz' 
+  rw [character_space.mem_spectrum_iff_exists] at hz'
   obtain ⟨φ, rfl⟩ := hz'
   exact ⟨φ, rfl⟩
 #align elemental_star_algebra.bijective_character_space_to_spectrum elementalStarAlgebra.bijective_characterSpaceToSpectrum

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

@@ -3,8 +3,8 @@ Copyright (c) 2022 Jireh Loreaux. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jireh Loreaux
 -/
-import Mathbin.Analysis.NormedSpace.Star.GelfandDuality
-import Mathbin.Topology.Algebra.StarSubalgebra
+import Analysis.NormedSpace.Star.GelfandDuality
+import Topology.Algebra.StarSubalgebra
 
 #align_import analysis.normed_space.star.continuous_functional_calculus from "leanprover-community/mathlib"@"44e2ae8cffc713925494e4975ee31ec1d06929b3"
 

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

@@ -2,15 +2,12 @@
 Copyright (c) 2022 Jireh Loreaux. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jireh Loreaux
-
-! This file was ported from Lean 3 source module analysis.normed_space.star.continuous_functional_calculus
-! leanprover-community/mathlib commit 44e2ae8cffc713925494e4975ee31ec1d06929b3
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Analysis.NormedSpace.Star.GelfandDuality
 import Mathbin.Topology.Algebra.StarSubalgebra
 
+#align_import analysis.normed_space.star.continuous_functional_calculus from "leanprover-community/mathlib"@"44e2ae8cffc713925494e4975ee31ec1d06929b3"
+
 /-! # Continuous functional calculus
 
 > THIS FILE IS SYNCHRONIZED WITH MATHLIB4.

mathlib commit https://github.com/leanprover-community/mathlib/commit/8efcf8022aac8e01df8d302dcebdbc25d6a886c8

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jireh Loreaux
 
 ! This file was ported from Lean 3 source module analysis.normed_space.star.continuous_functional_calculus
-! leanprover-community/mathlib commit 31c24aa72e7b3e5ed97a8412470e904f82b81004
+! leanprover-community/mathlib commit 44e2ae8cffc713925494e4975ee31ec1d06929b3
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -13,6 +13,9 @@ import Mathbin.Topology.Algebra.StarSubalgebra
 
 /-! # Continuous functional calculus
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 In this file we construct the `continuous_functional_calculus` for a normal element `a` of a
 (unital) C⋆-algebra over `ℂ`. This is a star algebra equivalence
 `C(spectrum ℂ a, ℂ) ≃⋆ₐ[ℂ] elemental_star_algebra ℂ a` which sends the (restriction of) the

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

@@ -88,6 +88,7 @@ noncomputable instance elementalStarAlgebra.Complex.normedAlgebra (a : A) :
 
 variable [CompleteSpace A] (a : A) [IsStarNormal a] (S : StarSubalgebra ℂ A)
 
+#print spectrum_star_mul_self_of_isStarNormal /-
 /-- This lemma is used in the proof of `star_subalgebra.is_unit_of_is_unit_of_is_star_normal`,
 which in turn is the key to spectral permanence `star_subalgebra.spectrum_eq`, which is itself
 necessary for the continuous functional calculus. Using the continuous functional calculus, this
@@ -110,9 +111,11 @@ theorem spectrum_star_mul_self_of_isStarNormal :
       ⟨Complex.zero_le_real.2 (norm_nonneg _),
         Complex.real_le_real.2 (AlgHom.norm_apply_le_self φ (star a' * a'))⟩
 #align spectrum_star_mul_self_of_is_star_normal spectrum_star_mul_self_of_isStarNormal
+-/
 
 variable {a}
 
+#print elementalStarAlgebra.isUnit_of_isUnit_of_isStarNormal /-
 /-- This is the key lemma on the way to establishing spectral permanence for C⋆-algebras, which is
 established in `star_subalgebra.spectrum_eq`. This lemma is superseded by
 `star_subalgebra.coe_is_unit`, which does not require an `is_star_normal` hypothesis and holds for
@@ -190,7 +193,9 @@ theorem elementalStarAlgebra.isUnit_of_isUnit_of_isStarNormal (h : IsUnit a) :
             IsROrC.conj_ofReal]
         _ < ‖star a * a‖₊ := spectrum.spectralRadius_lt_of_forall_lt _ h₂)
 #align elemental_star_algebra.is_unit_of_is_unit_of_is_star_normal elementalStarAlgebra.isUnit_of_isUnit_of_isStarNormal
+-/
 
+#print StarSubalgebra.isUnit_coe_inv_mem /-
 /-- For `x : A` which is invertible in `A`, the inverse lies in any unital C⋆-subalgebra `S`
 containing `x`. -/
 theorem StarSubalgebra.isUnit_coe_inv_mem {S : StarSubalgebra ℂ A} (hS : IsClosed (S : Set A))
@@ -207,7 +212,9 @@ theorem StarSubalgebra.isUnit_coe_inv_mem {S : StarSubalgebra ℂ A} (hS : IsClo
   convert (↑hx'.unit⁻¹ : elementalStarAlgebra ℂ (star x * x)).Prop using 1
   exact left_inv_eq_right_inv hx.unit.inv_mul (congr_arg coe hx'.unit.mul_inv)
 #align star_subalgebra.is_unit_coe_inv_mem StarSubalgebra.isUnit_coe_inv_mem
+-/
 
+#print StarSubalgebra.coe_isUnit /-
 /-- For a unital C⋆-subalgebra `S` of `A` and `x : S`, if `↑x : A` is invertible in `A`, then
 `x` is invertible in `S`. -/
 theorem StarSubalgebra.coe_isUnit {S : StarSubalgebra ℂ A} (hS : IsClosed (S : Set A)) {x : S} :
@@ -218,21 +225,27 @@ theorem StarSubalgebra.coe_isUnit {S : StarSubalgebra ℂ A} (hS : IsClosed (S :
       fun hx => hx.map S.subtype⟩
   exacts [Subtype.coe_injective hx.mul_coe_inv, Subtype.coe_injective hx.coe_inv_mul]
 #align star_subalgebra.coe_is_unit StarSubalgebra.coe_isUnit
+-/
 
+#print StarSubalgebra.mem_spectrum_iff /-
 theorem StarSubalgebra.mem_spectrum_iff {S : StarSubalgebra ℂ A} (hS : IsClosed (S : Set A)) {x : S}
     {z : ℂ} : z ∈ spectrum ℂ x ↔ z ∈ spectrum ℂ (x : A) :=
   not_iff_not.2 (StarSubalgebra.coe_isUnit hS).symm
 #align star_subalgebra.mem_spectrum_iff StarSubalgebra.mem_spectrum_iff
+-/
 
+#print StarSubalgebra.spectrum_eq /-
 /-- **Spectral permanence.** The spectrum of an element is invariant of the (closed)
 `star_subalgebra` in which it is contained. -/
 theorem StarSubalgebra.spectrum_eq {S : StarSubalgebra ℂ A} (hS : IsClosed (S : Set A)) (x : S) :
     spectrum ℂ x = spectrum ℂ (x : A) :=
   Set.ext fun z => StarSubalgebra.mem_spectrum_iff hS
 #align star_subalgebra.spectrum_eq StarSubalgebra.spectrum_eq
+-/
 
 variable (a)
 
+#print elementalStarAlgebra.characterSpaceToSpectrum /-
 /-- The natural map from `character_space ℂ (elemental_star_algebra ℂ x)` to `spectrum ℂ x` given
 by evaluating `φ` at `x`. This is essentially just evaluation of the `gelfand_transform` of `x`,
 but because we want something in `spectrum ℂ x`, as opposed to
@@ -247,13 +260,17 @@ noncomputable def elementalStarAlgebra.characterSpaceToSpectrum (x : A)
         ⟨x, self_mem ℂ x⟩] using
       AlgHom.apply_mem_spectrum φ ⟨x, self_mem ℂ x⟩
 #align elemental_star_algebra.character_space_to_spectrum elementalStarAlgebra.characterSpaceToSpectrum
+-/
 
+#print elementalStarAlgebra.continuous_characterSpaceToSpectrum /-
 theorem elementalStarAlgebra.continuous_characterSpaceToSpectrum (x : A) :
     Continuous (elementalStarAlgebra.characterSpaceToSpectrum x) :=
   continuous_induced_rng.2
     (map_continuous <| gelfandTransform ℂ (elementalStarAlgebra ℂ x) ⟨x, self_mem ℂ x⟩)
 #align elemental_star_algebra.continuous_character_space_to_spectrum elementalStarAlgebra.continuous_characterSpaceToSpectrum
+-/
 
+#print elementalStarAlgebra.bijective_characterSpaceToSpectrum /-
 theorem elementalStarAlgebra.bijective_characterSpaceToSpectrum :
     Function.Bijective (elementalStarAlgebra.characterSpaceToSpectrum a) :=
   by
@@ -271,7 +288,9 @@ theorem elementalStarAlgebra.bijective_characterSpaceToSpectrum :
   obtain ⟨φ, rfl⟩ := hz'
   exact ⟨φ, rfl⟩
 #align elemental_star_algebra.bijective_character_space_to_spectrum elementalStarAlgebra.bijective_characterSpaceToSpectrum
+-/
 
+#print elementalStarAlgebra.characterSpaceHomeo /-
 /-- The homeomorphism between the character space of the unital C⋆-subalgebra generated by a
 single normal element `a : A` and `spectrum ℂ a`. -/
 noncomputable def elementalStarAlgebra.characterSpaceHomeo :
@@ -281,7 +300,9 @@ noncomputable def elementalStarAlgebra.characterSpaceHomeo :
       (elementalStarAlgebra.bijective_characterSpaceToSpectrum a))
     (elementalStarAlgebra.continuous_characterSpaceToSpectrum a)
 #align elemental_star_algebra.character_space_homeo elementalStarAlgebra.characterSpaceHomeo
+-/
 
+#print continuousFunctionalCalculus /-
 /-- **Continuous functional calculus.** Given a normal element `a : A` of a unital C⋆-algebra,
 the continuous functional calculus is a `star_alg_equiv` from the complex-valued continuous
 functions on the spectrum of `a` to the unital C⋆-subalgebra generated by `a`. Moreover, this
@@ -292,10 +313,13 @@ noncomputable def continuousFunctionalCalculus :
   ((elementalStarAlgebra.characterSpaceHomeo a).compStarAlgEquiv' ℂ ℂ).trans
     (gelfandStarTransform (elementalStarAlgebra ℂ a)).symm
 #align continuous_functional_calculus continuousFunctionalCalculus
+-/
 
+#print continuousFunctionalCalculus_map_id /-
 theorem continuousFunctionalCalculus_map_id :
     continuousFunctionalCalculus a ((ContinuousMap.id ℂ).restrict (spectrum ℂ a)) =
       ⟨a, self_mem ℂ a⟩ :=
   StarAlgEquiv.symm_apply_apply _ _
 #align continuous_functional_calculus_map_id continuousFunctionalCalculus_map_id
+-/
 

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

@@ -188,8 +188,7 @@ theorem elementalStarAlgebra.isUnit_of_isUnit_of_isStarNormal (h : IsUnit a) :
           refine' (IsSelfAdjoint.spectralRadius_eq_nnnorm _).symm
           rw [IsSelfAdjoint, star_sub, star_mul, star_star, ← algebraMap_star_comm, IsROrC.star_def,
             IsROrC.conj_ofReal]
-        _ < ‖star a * a‖₊ := spectrum.spectralRadius_lt_of_forall_lt _ h₂
-        )
+        _ < ‖star a * a‖₊ := spectrum.spectralRadius_lt_of_forall_lt _ h₂)
 #align elemental_star_algebra.is_unit_of_is_unit_of_is_star_normal elementalStarAlgebra.isUnit_of_isUnit_of_isStarNormal
 
 /-- For `x : A` which is invertible in `A`, the inverse lies in any unital C⋆-subalgebra `S`

mathlib commit https://github.com/leanprover-community/mathlib/commit/31c24aa72e7b3e5ed97a8412470e904f82b81004

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jireh Loreaux
 
 ! This file was ported from Lean 3 source module analysis.normed_space.star.continuous_functional_calculus
-! leanprover-community/mathlib commit f9dd3204df14a0749cd456fac1e6849dfe7d2b88
+! leanprover-community/mathlib commit 31c24aa72e7b3e5ed97a8412470e904f82b81004
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -105,7 +105,7 @@ theorem spectrum_star_mul_self_of_isStarNormal :
     rw [← spectrum.gelfandTransform_eq (star a' * a'), ContinuousMap.spectrum_eq_range]
     rintro - ⟨φ, rfl⟩
     rw [gelfand_transform_apply_apply ℂ _ (star a' * a') φ, map_mul φ, map_star φ]
-    rw [Complex.eq_coe_norm_of_nonneg star_mul_self_nonneg, ← map_star, ← map_mul]
+    rw [Complex.eq_coe_norm_of_nonneg (star_mul_self_nonneg _), ← map_star, ← map_mul]
     exact
       ⟨Complex.zero_le_real.2 (norm_nonneg _),
         Complex.real_le_real.2 (AlgHom.norm_apply_le_self φ (star a' * a'))⟩

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

@@ -205,7 +205,7 @@ theorem StarSubalgebra.isUnit_coe_inv_mem {S : StarSubalgebra ℂ A} (hS : IsClo
   refine' le_of_is_closed_of_mem ℂ hS (mul_mem (star_mem hxS) hxS) _
   haveI := (IsSelfAdjoint.star_mul_self x).IsStarNormal
   have hx' := elementalStarAlgebra.isUnit_of_isUnit_of_isStarNormal hx
-  convert(↑hx'.unit⁻¹ : elementalStarAlgebra ℂ (star x * x)).Prop using 1
+  convert (↑hx'.unit⁻¹ : elementalStarAlgebra ℂ (star x * x)).Prop using 1
   exact left_inv_eq_right_inv hx.unit.inv_mul (congr_arg coe hx'.unit.mul_inv)
 #align star_subalgebra.is_unit_coe_inv_mem StarSubalgebra.isUnit_coe_inv_mem
 

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

@@ -159,20 +159,20 @@ theorem elementalStarAlgebra.isUnit_of_isUnit_of_isStarNormal (h : IsUnit a) :
   have h₂ : ∀ z ∈ spectrum ℂ (algebraMap ℂ A ‖star a * a‖ - star a * a), ‖z‖₊ < ‖star a * a‖₊ :=
     by
     intro z hz
-    rw [← spectrum.singleton_sub_eq, Set.singleton_sub] at hz
+    rw [← spectrum.singleton_sub_eq, Set.singleton_sub] at hz 
     have h₃ : z ∈ Set.Icc (0 : ℂ) ‖star a * a‖ :=
       by
       replace hz := Set.image_subset _ (spectrum_star_mul_self_of_isStarNormal a) hz
-      rwa [Set.image_const_sub_Icc, sub_self, sub_zero] at hz
+      rwa [Set.image_const_sub_Icc, sub_self, sub_zero] at hz 
     refine' lt_of_le_of_ne (Complex.real_le_real.1 <| Complex.eq_coe_norm_of_nonneg h₃.1 ▸ h₃.2) _
     · intro hz'
       replace hz' := congr_arg (fun x : ℝ≥0 => ((x : ℝ) : ℂ)) hz'
-      simp only [coe_nnnorm] at hz'
-      rw [← Complex.eq_coe_norm_of_nonneg h₃.1] at hz'
+      simp only [coe_nnnorm] at hz' 
+      rw [← Complex.eq_coe_norm_of_nonneg h₃.1] at hz' 
       obtain ⟨w, hw₁, hw₂⟩ := hz
       refine' (spectrum.zero_not_mem_iff ℂ).mpr h _
-      rw [hz', sub_eq_self] at hw₂
-      rwa [hw₂] at hw₁
+      rw [hz', sub_eq_self] at hw₂ 
+      rwa [hw₂] at hw₁ 
   /- The norm of `‖star a * a‖ • 1 - star a * a` in the subalgebra and in `A` coincide. In `A`,
     because this element is selfadjoint, by `is_self_adjoint.spectral_radius_eq_nnnorm`, its norm is
     the supremum of the norms of the elements of the spectrum, which is strictly less than
@@ -217,7 +217,7 @@ theorem StarSubalgebra.coe_isUnit {S : StarSubalgebra ℂ A} (hS : IsClosed (S :
   refine'
     ⟨fun hx => ⟨⟨x, ⟨(↑hx.Unit⁻¹ : A), StarSubalgebra.isUnit_coe_inv_mem hS hx x.prop⟩, _, _⟩, rfl⟩,
       fun hx => hx.map S.subtype⟩
-  exacts[Subtype.coe_injective hx.mul_coe_inv, Subtype.coe_injective hx.coe_inv_mul]
+  exacts [Subtype.coe_injective hx.mul_coe_inv, Subtype.coe_injective hx.coe_inv_mul]
 #align star_subalgebra.coe_is_unit StarSubalgebra.coe_isUnit
 
 theorem StarSubalgebra.mem_spectrum_iff {S : StarSubalgebra ℂ A} (hS : IsClosed (S : Set A)) {x : S}
@@ -268,7 +268,7 @@ theorem elementalStarAlgebra.bijective_characterSpaceToSpectrum :
   rintro ⟨z, hz⟩
   have hz' :=
     (StarSubalgebra.spectrum_eq (elementalStarAlgebra.isClosed ℂ a) ⟨a, self_mem ℂ a⟩).symm.subst hz
-  rw [character_space.mem_spectrum_iff_exists] at hz'
+  rw [character_space.mem_spectrum_iff_exists] at hz' 
   obtain ⟨φ, rfl⟩ := hz'
   exact ⟨φ, rfl⟩
 #align elemental_star_algebra.bijective_character_space_to_spectrum elementalStarAlgebra.bijective_characterSpaceToSpectrum

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

@@ -149,9 +149,9 @@ theorem elementalStarAlgebra.isUnit_of_isUnit_of_isStarNormal (h : IsUnit a) :
   set u : Units (elementalStarAlgebra ℂ a) :=
     Units.map (algebraMap ℂ (elementalStarAlgebra ℂ a)).toMonoidHom (Units.mk0 _ h₁)
   refine' ⟨u.unit_of_nearby _ _, rfl⟩
-  simp only [Complex.abs_ofReal, map_inv₀, Units.coe_map, Units.val_inv_eq_inv_val, [anonymous],
-    RingHom.toMonoidHom_eq_coe, Units.val_mk0, Units.coe_map_inv, norm_algebraMap', inv_inv,
-    Complex.norm_eq_abs, abs_norm, Subtype.val_eq_coe, coe_coe]
+  simp only [Complex.abs_ofReal, map_inv₀, Units.coe_map, Units.val_inv_eq_inv_val,
+    RingHom.coe_monoidHom, RingHom.toMonoidHom_eq_coe, Units.val_mk0, Units.coe_map_inv,
+    norm_algebraMap', inv_inv, Complex.norm_eq_abs, abs_norm, Subtype.val_eq_coe, coe_coe]
   /- Since `a` is invertible, by `spectrum_star_mul_self_of_is_star_normal`, the spectrum (in `A`)
     of `star a * a` is contained in the half-open interval `(0, ‖star a * a‖]`. Therefore, by basic
     spectral mapping properties, the spectrum of `‖star a * a‖ • 1 - star a * a` is contained in

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

@@ -59,7 +59,7 @@ the continuous functional calculus (including one for real-valued functions with
 applies to self-adjoint elements of the algebra). -/
 
 
-open Pointwise ENNReal NNReal ComplexOrder
+open scoped Pointwise ENNReal NNReal ComplexOrder
 
 open WeakDual WeakDual.characterSpace elementalStarAlgebra
 

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

@@ -140,8 +140,7 @@ theorem elementalStarAlgebra.isUnit_of_isUnit_of_isStarNormal (h : IsUnit a) :
     if `star a * a` is invertible, then so is `a`. -/
   nontriviality A
   set a' : elementalStarAlgebra ℂ a := ⟨a, self_mem ℂ a⟩
-  suffices : IsUnit (star a' * a')
-  exact (IsUnit.mul_iff.1 this).2
+  suffices : IsUnit (star a' * a'); exact (IsUnit.mul_iff.1 this).2
   replace h := (show Commute (star a) a from star_comm_self' a).isUnit_mul_iff.2 ⟨h.star, h⟩
   /- Since `a` is invertible, `‖star a * a‖ ≠ 0`, so `‖star a * a‖ • 1` is invertible in
     `elemental_star_algebra ℂ a`, and so it suffices to show that the distance between this unit and
@@ -183,9 +182,7 @@ theorem elementalStarAlgebra.isUnit_of_isUnit_of_isStarNormal (h : IsUnit a) :
       (calc
         (‖star a' * a' - algebraMap ℂ _ ‖star a * a‖‖₊ : ℝ≥0∞) =
             ‖algebraMap ℂ A ‖star a * a‖ - star a * a‖₊ :=
-          by
-          rw [← nnnorm_neg, neg_sub]
-          rfl
+          by rw [← nnnorm_neg, neg_sub]; rfl
         _ = spectralRadius ℂ (algebraMap ℂ A ‖star a * a‖ - star a * a) :=
           by
           refine' (IsSelfAdjoint.spectralRadius_eq_nnnorm _).symm

mathlib commit https://github.com/leanprover-community/mathlib/commit/2f8347015b12b0864dfaf366ec4909eb70c78740

@@ -190,7 +190,7 @@ theorem elementalStarAlgebra.isUnit_of_isUnit_of_isStarNormal (h : IsUnit a) :
           by
           refine' (IsSelfAdjoint.spectralRadius_eq_nnnorm _).symm
           rw [IsSelfAdjoint, star_sub, star_mul, star_star, ← algebraMap_star_comm, IsROrC.star_def,
-            IsROrC.conj_of_real]
+            IsROrC.conj_ofReal]
         _ < ‖star a * a‖₊ := spectrum.spectralRadius_lt_of_forall_lt _ h₂
         )
 #align elemental_star_algebra.is_unit_of_is_unit_of_is_star_normal elementalStarAlgebra.isUnit_of_isUnit_of_isStarNormal

mathlib commit https://github.com/leanprover-community/mathlib/commit/92c69b77c5a7dc0f7eeddb552508633305157caa

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jireh Loreaux
 
 ! This file was ported from Lean 3 source module analysis.normed_space.star.continuous_functional_calculus
-! leanprover-community/mathlib commit e65771194f9e923a70dfb49b6ca7be6e400d8b6f
+! leanprover-community/mathlib commit f9dd3204df14a0749cd456fac1e6849dfe7d2b88
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -152,7 +152,7 @@ theorem elementalStarAlgebra.isUnit_of_isUnit_of_isStarNormal (h : IsUnit a) :
   refine' ⟨u.unit_of_nearby _ _, rfl⟩
   simp only [Complex.abs_ofReal, map_inv₀, Units.coe_map, Units.val_inv_eq_inv_val, [anonymous],
     RingHom.toMonoidHom_eq_coe, Units.val_mk0, Units.coe_map_inv, norm_algebraMap', inv_inv,
-    Complex.norm_eq_abs, abs_norm_eq_norm, Subtype.val_eq_coe, coe_coe]
+    Complex.norm_eq_abs, abs_norm, Subtype.val_eq_coe, coe_coe]
   /- Since `a` is invertible, by `spectrum_star_mul_self_of_is_star_normal`, the spectrum (in `A`)
     of `star a * a` is contained in the half-open interval `(0, ‖star a * a‖]`. Therefore, by basic
     spectral mapping properties, the spectrum of `‖star a * a‖ • 1 - star a * a` is contained in

mathlib commit https://github.com/leanprover-community/mathlib/commit/039ef89bef6e58b32b62898dd48e9d1a4312bb65

@@ -151,7 +151,7 @@ theorem elementalStarAlgebra.isUnit_of_isUnit_of_isStarNormal (h : IsUnit a) :
     Units.map (algebraMap ℂ (elementalStarAlgebra ℂ a)).toMonoidHom (Units.mk0 _ h₁)
   refine' ⟨u.unit_of_nearby _ _, rfl⟩
   simp only [Complex.abs_ofReal, map_inv₀, Units.coe_map, Units.val_inv_eq_inv_val, [anonymous],
-    RingHom.toMonoidHom_eq_coe, Units.val_mk0, Units.coe_map_inv, norm_algebra_map', inv_inv,
+    RingHom.toMonoidHom_eq_coe, Units.val_mk0, Units.coe_map_inv, norm_algebraMap', inv_inv,
     Complex.norm_eq_abs, abs_norm_eq_norm, Subtype.val_eq_coe, coe_coe]
   /- Since `a` is invertible, by `spectrum_star_mul_self_of_is_star_normal`, the spectrum (in `A`)
     of `star a * a` is contained in the half-open interval `(0, ‖star a * a‖]`. Therefore, by basic

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

@@ -107,8 +107,8 @@ theorem spectrum_star_mul_self_of_isStarNormal :
     rw [gelfand_transform_apply_apply ℂ _ (star a' * a') φ, map_mul φ, map_star φ]
     rw [Complex.eq_coe_norm_of_nonneg star_mul_self_nonneg, ← map_star, ← map_mul]
     exact
-      ⟨Complex.ComplexOrder.zero_le_real.2 (norm_nonneg _),
-        Complex.ComplexOrder.real_le_real.2 (AlgHom.norm_apply_le_self φ (star a' * a'))⟩
+      ⟨Complex.zero_le_real.2 (norm_nonneg _),
+        Complex.real_le_real.2 (AlgHom.norm_apply_le_self φ (star a' * a'))⟩
 #align spectrum_star_mul_self_of_is_star_normal spectrum_star_mul_self_of_isStarNormal
 
 variable {a}
@@ -165,9 +165,7 @@ theorem elementalStarAlgebra.isUnit_of_isUnit_of_isStarNormal (h : IsUnit a) :
       by
       replace hz := Set.image_subset _ (spectrum_star_mul_self_of_isStarNormal a) hz
       rwa [Set.image_const_sub_Icc, sub_self, sub_zero] at hz
-    refine'
-      lt_of_le_of_ne
-        (Complex.ComplexOrder.real_le_real.1 <| Complex.eq_coe_norm_of_nonneg h₃.1 ▸ h₃.2) _
+    refine' lt_of_le_of_ne (Complex.real_le_real.1 <| Complex.eq_coe_norm_of_nonneg h₃.1 ▸ h₃.2) _
     · intro hz'
       replace hz' := congr_arg (fun x : ℝ≥0 => ((x : ℝ) : ℂ)) hz'
       simp only [coe_nnnorm] at hz'

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

@@ -210,7 +210,7 @@ theorem StarSubalgebra.isUnit_coe_inv_mem {S : StarSubalgebra ℂ A} (hS : IsClo
   refine' le_of_is_closed_of_mem ℂ hS (mul_mem (star_mem hxS) hxS) _
   haveI := (IsSelfAdjoint.star_mul_self x).IsStarNormal
   have hx' := elementalStarAlgebra.isUnit_of_isUnit_of_isStarNormal hx
-  convert (↑hx'.unit⁻¹ : elementalStarAlgebra ℂ (star x * x)).Prop using 1
+  convert(↑hx'.unit⁻¹ : elementalStarAlgebra ℂ (star x * x)).Prop using 1
   exact left_inv_eq_right_inv hx.unit.inv_mul (congr_arg coe hx'.unit.mul_inv)
 #align star_subalgebra.is_unit_coe_inv_mem StarSubalgebra.isUnit_coe_inv_mem
 

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

@@ -107,8 +107,8 @@ theorem spectrum_star_mul_self_of_isStarNormal :
     rw [gelfand_transform_apply_apply ℂ _ (star a' * a') φ, map_mul φ, map_star φ]
     rw [Complex.eq_coe_norm_of_nonneg star_mul_self_nonneg, ← map_star, ← map_mul]
     exact
-      ⟨Complex.zero_le_real.2 (norm_nonneg _),
-        Complex.real_le_real.2 (AlgHom.norm_apply_le_self φ (star a' * a'))⟩
+      ⟨Complex.ComplexOrder.zero_le_real.2 (norm_nonneg _),
+        Complex.ComplexOrder.real_le_real.2 (AlgHom.norm_apply_le_self φ (star a' * a'))⟩
 #align spectrum_star_mul_self_of_is_star_normal spectrum_star_mul_self_of_isStarNormal
 
 variable {a}
@@ -150,7 +150,7 @@ theorem elementalStarAlgebra.isUnit_of_isUnit_of_isStarNormal (h : IsUnit a) :
   set u : Units (elementalStarAlgebra ℂ a) :=
     Units.map (algebraMap ℂ (elementalStarAlgebra ℂ a)).toMonoidHom (Units.mk0 _ h₁)
   refine' ⟨u.unit_of_nearby _ _, rfl⟩
-  simp only [Complex.abs_of_real, map_inv₀, Units.coe_map, Units.val_inv_eq_inv_val, [anonymous],
+  simp only [Complex.abs_ofReal, map_inv₀, Units.coe_map, Units.val_inv_eq_inv_val, [anonymous],
     RingHom.toMonoidHom_eq_coe, Units.val_mk0, Units.coe_map_inv, norm_algebra_map', inv_inv,
     Complex.norm_eq_abs, abs_norm_eq_norm, Subtype.val_eq_coe, coe_coe]
   /- Since `a` is invertible, by `spectrum_star_mul_self_of_is_star_normal`, the spectrum (in `A`)
@@ -165,7 +165,9 @@ theorem elementalStarAlgebra.isUnit_of_isUnit_of_isStarNormal (h : IsUnit a) :
       by
       replace hz := Set.image_subset _ (spectrum_star_mul_self_of_isStarNormal a) hz
       rwa [Set.image_const_sub_Icc, sub_self, sub_zero] at hz
-    refine' lt_of_le_of_ne (Complex.real_le_real.1 <| Complex.eq_coe_norm_of_nonneg h₃.1 ▸ h₃.2) _
+    refine'
+      lt_of_le_of_ne
+        (Complex.ComplexOrder.real_le_real.1 <| Complex.eq_coe_norm_of_nonneg h₃.1 ▸ h₃.2) _
     · intro hz'
       replace hz' := congr_arg (fun x : ℝ≥0 => ((x : ℝ) : ℂ)) hz'
       simp only [coe_nnnorm] at hz'

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

IsROrC contains data, which goes against the expectation that classes prefixed with Is are prop-valued. People have been complaining about this on and off, so this PR renames IsROrC to RCLike.

@@ -170,7 +170,7 @@ theorem elementalStarAlgebra.isUnit_of_isUnit_of_isStarNormal (h : IsUnit a) :
         refine' (IsSelfAdjoint.spectralRadius_eq_nnnorm _).symm
         rw [IsSelfAdjoint, star_sub, star_mul, star_star, ← algebraMap_star_comm]
         congr!
-        exact IsROrC.conj_ofReal _
+        exact RCLike.conj_ofReal _
       _ < ‖star a * a‖₊ := spectrum.spectralRadius_lt_of_forall_lt _ h₂)
 #align elemental_star_algebra.is_unit_of_is_unit_of_is_star_normal elementalStarAlgebra.isUnit_of_isUnit_of_isStarNormal
 

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)

@@ -61,7 +61,6 @@ open scoped Pointwise ENNReal NNReal ComplexOrder
 open WeakDual WeakDual.CharacterSpace elementalStarAlgebra
 
 variable {A : Type*} [NormedRing A] [NormedAlgebra ℂ A]
-
 variable [StarRing A] [CstarRing A] [StarModule ℂ A]
 
 instance {R A : Type*} [CommRing R] [StarRing R] [NormedRing A] [Algebra R A] [StarRing A]

Homogenises porting notes via capitalisation and addition of whitespace.

It makes the following changes:

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

@@ -70,7 +70,7 @@ instance {R A : Type*} [CommRing R] [StarRing R] [NormedRing A] [Algebra R A] [S
   { SubringClass.toNormedRing (elementalStarAlgebra R a) with
     mul_comm := mul_comm }
 
--- porting note: these hack instances no longer seem to be necessary
+-- Porting note: these hack instances no longer seem to be necessary
 #noalign elemental_star_algebra.complex.normed_algebra
 
 variable [CompleteSpace A] (a : A) [IsStarNormal a] (S : StarSubalgebra ℂ A)

From LeanAPAP

@@ -92,9 +92,7 @@ theorem spectrum_star_mul_self_of_isStarNormal :
     rintro - ⟨φ, rfl⟩
     rw [gelfandTransform_apply_apply ℂ _ (star a' * a') φ, map_mul φ, map_star φ]
     rw [Complex.eq_coe_norm_of_nonneg (star_mul_self_nonneg _), ← map_star, ← map_mul]
-    exact
-      ⟨Complex.zero_le_real.2 (norm_nonneg _),
-        Complex.real_le_real.2 (AlgHom.norm_apply_le_self φ (star a' * a'))⟩
+    exact ⟨by positivity, Complex.real_le_real.2 (AlgHom.norm_apply_le_self φ (star a' * a'))⟩
 #align spectrum_star_mul_self_of_is_star_normal spectrum_star_mul_self_of_isStarNormal
 
 variable {a}

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

@@ -135,7 +135,7 @@ theorem elementalStarAlgebra.isUnit_of_isUnit_of_isStarNormal (h : IsUnit a) :
   set u : Units (elementalStarAlgebra ℂ a) :=
     Units.map (algebraMap ℂ (elementalStarAlgebra ℂ a)).toMonoidHom (Units.mk0 _ h₁)
   refine' ⟨u.ofNearby _ _, rfl⟩
-  simp only [Units.coe_map, Units.val_inv_eq_inv_val, RingHom.toMonoidHom_eq_coe, Units.val_mk0,
+  simp only [u, Units.coe_map, Units.val_inv_eq_inv_val, RingHom.toMonoidHom_eq_coe, Units.val_mk0,
     Units.coe_map_inv, MonoidHom.coe_coe, norm_algebraMap', norm_inv, Complex.norm_eq_abs,
     Complex.abs_ofReal, abs_norm, inv_inv]
     --RingHom.coe_monoidHom,

No changes to tactic file, it's just boring fixes throughout the library.

This follows on from #6964.

Co-authored-by: sgouezel <sebastien.gouezel@univ-rennes1.fr> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

@@ -126,7 +126,7 @@ theorem elementalStarAlgebra.isUnit_of_isUnit_of_isStarNormal (h : IsUnit a) :
     if `star a * a` is invertible, then so is `a`. -/
   nontriviality A
   set a' : elementalStarAlgebra ℂ a := ⟨a, self_mem ℂ a⟩
-  suffices : IsUnit (star a' * a'); exact (IsUnit.mul_iff.1 this).2
+  suffices IsUnit (star a' * a') from (IsUnit.mul_iff.1 this).2
   replace h := (show Commute (star a) a from star_comm_self' a).isUnit_mul_iff.2 ⟨h.star, h⟩
   /- Since `a` is invertible, `‖star a * a‖ ≠ 0`, so `‖star a * a‖ • 1` is invertible in
     `elementalStarAlgebra ℂ a`, and so it suffices to show that the distance between this unit and
@@ -182,8 +182,8 @@ containing `x`. -/
 theorem StarSubalgebra.isUnit_coe_inv_mem {S : StarSubalgebra ℂ A} (hS : IsClosed (S : Set A))
     {x : A} (h : IsUnit x) (hxS : x ∈ S) : ↑h.unit⁻¹ ∈ S := by
   have hx := h.star.mul h
-  suffices this : (↑hx.unit⁻¹ : A) ∈ S
-  · rw [← one_mul (↑h.unit⁻¹ : A), ← hx.unit.inv_mul, mul_assoc, IsUnit.unit_spec, mul_assoc,
+  suffices this : (↑hx.unit⁻¹ : A) ∈ S by
+    rw [← one_mul (↑h.unit⁻¹ : A), ← hx.unit.inv_mul, mul_assoc, IsUnit.unit_spec, mul_assoc,
       h.mul_val_inv, mul_one]
     exact mul_mem this (star_mem hxS)
   refine' le_of_isClosed_of_mem ℂ hS (mul_mem (star_mem hxS) hxS) _

We clean up heart beat bumps after #6474.

@@ -253,8 +253,6 @@ theorem elementalStarAlgebra.bijective_characterSpaceToSpectrum :
     exact ⟨φ, rfl⟩
 #align elemental_star_algebra.bijective_character_space_to_spectrum elementalStarAlgebra.bijective_characterSpaceToSpectrum
 
--- porting note: it would be good to understand why and where Lean is having trouble here
-set_option synthInstance.maxHeartbeats 40000 in
 /-- The homeomorphism between the character space of the unital C⋆-subalgebra generated by a
 single normal element `a : A` and `spectrum ℂ a`. -/
 noncomputable def elementalStarAlgebra.characterSpaceHomeo :
@@ -265,8 +263,6 @@ noncomputable def elementalStarAlgebra.characterSpaceHomeo :
     (elementalStarAlgebra.continuous_characterSpaceToSpectrum a)
 #align elemental_star_algebra.character_space_homeo elementalStarAlgebra.characterSpaceHomeo
 
--- porting note: it would be good to understand why and where Lean is having trouble here
-set_option maxHeartbeats 350000 in
 /-- **Continuous functional calculus.** Given a normal element `a : A` of a unital C⋆-algebra,
 the continuous functional calculus is a `StarAlgEquiv` from the complex-valued continuous
 functions on the spectrum of `a` to the unital C⋆-subalgebra generated by `a`. Moreover, this

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

This has nice performance benefits.

@@ -60,11 +60,11 @@ open scoped Pointwise ENNReal NNReal ComplexOrder
 
 open WeakDual WeakDual.CharacterSpace elementalStarAlgebra
 
-variable {A : Type _} [NormedRing A] [NormedAlgebra ℂ A]
+variable {A : Type*} [NormedRing A] [NormedAlgebra ℂ A]
 
 variable [StarRing A] [CstarRing A] [StarModule ℂ A]
 
-instance {R A : Type _} [CommRing R] [StarRing R] [NormedRing A] [Algebra R A] [StarRing A]
+instance {R A : Type*} [CommRing R] [StarRing R] [NormedRing A] [Algebra R A] [StarRing A]
     [ContinuousStar A] [StarModule R A] (a : A) [IsStarNormal a] :
     NormedCommRing (elementalStarAlgebra R a) :=
   { SubringClass.toNormedRing (elementalStarAlgebra R a) with

• depends on: #5966

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

@@ -2,15 +2,12 @@
 Copyright (c) 2022 Jireh Loreaux. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jireh Loreaux
-
-! This file was ported from Lean 3 source module analysis.normed_space.star.continuous_functional_calculus
-! leanprover-community/mathlib commit 31c24aa72e7b3e5ed97a8412470e904f82b81004
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Analysis.NormedSpace.Star.GelfandDuality
 import Mathlib.Topology.Algebra.StarSubalgebra
 
+#align_import analysis.normed_space.star.continuous_functional_calculus from "leanprover-community/mathlib"@"31c24aa72e7b3e5ed97a8412470e904f82b81004"
+
 /-! # Continuous functional calculus
 
 In this file we construct the `continuousFunctionalCalculus` for a normal element `a` of a

Grepping for [^ .:{-] [^ :] and reviewing the results. Once I started I couldn't stop. :-)

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

@@ -23,7 +23,7 @@ Being a star algebra equivalence between C⋆-algebras, this map is continuous (
 and by the Stone-Weierstrass theorem it is the unique star algebra equivalence which extends the
 polynomial functional calculus (i.e., `Polynomial.aeval`).
 
-For any continuous function `f : spectrum ℂ a →  ℂ`, this makes it possible to define an element
+For any continuous function `f : spectrum ℂ a → ℂ`, this makes it possible to define an element
 `f a` (not valid notation) in the original algebra, which heuristically has the same eigenspaces as
 `a` and acts on eigenvector of `a` for an eigenvalue `λ` as multiplication by `f λ`. This
 description is perfectly accurate in finite dimension, but only heuristic in infinite dimension as

Modifying the definition of Field.toEuclideanDomain makes some declaration faster.

Co-authored-by: Sébastien Gouëzel

@@ -257,7 +257,7 @@ theorem elementalStarAlgebra.bijective_characterSpaceToSpectrum :
 #align elemental_star_algebra.bijective_character_space_to_spectrum elementalStarAlgebra.bijective_characterSpaceToSpectrum
 
 -- porting note: it would be good to understand why and where Lean is having trouble here
-set_option synthInstance.maxHeartbeats 43000 in
+set_option synthInstance.maxHeartbeats 40000 in
 /-- The homeomorphism between the character space of the unital C⋆-subalgebra generated by a
 single normal element `a : A` and `spectrum ℂ a`. -/
 noncomputable def elementalStarAlgebra.characterSpaceHomeo :