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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Heather Macbeth
 -/
 import Analysis.InnerProductSpace.Projection
-import Analysis.NormedSpace.LpSpace
+import Analysis.NormedSpace.lpSpace
 import Analysis.InnerProductSpace.PiL2
 
 #align_import analysis.inner_product_space.l2_space from "leanprover-community/mathlib"@"af471b9e3ce868f296626d33189b4ce730fa4c00"
@@ -85,7 +85,7 @@ Hilbert space, Hilbert sum, l2, Hilbert basis, unitary equivalence, isometric is
 -/
 
 
-open IsROrC Submodule Filter
+open RCLike Submodule Filter
 
 open scoped BigOperators NNReal ENNReal Classical ComplexConjugate Topology
 
@@ -93,7 +93,7 @@ noncomputable section
 
 variable {ι : Type _}
 
-variable {𝕜 : Type _} [IsROrC 𝕜] {E : Type _}
+variable {𝕜 : Type _} [RCLike 𝕜] {E : Type _}
 
 variable [NormedAddCommGroup E] [InnerProductSpace 𝕜 E] [cplt : CompleteSpace E]
 

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

@@ -526,7 +526,7 @@ protected theorem hasSum_repr_symm (b : HilbertBasis ι 𝕜 E) (f : ℓ²(ι, 
   apply b.repr.injective
   letI : NormedSpace 𝕜 ↥(lp (fun i : ι => 𝕜) 2) := by infer_instance
   have : lp.single 2 i (f i * 1) = f i • lp.single 2 i 1 := lp.single_smul 2 i (1 : 𝕜) (f i)
-  rw [mul_one] at this 
+  rw [mul_one] at this
   rw [LinearIsometryEquiv.map_smul, b.repr_self, ← this,
     LinearIsometryEquiv.coe_toContinuousLinearEquiv]
   exact (b.repr.apply_symm_apply (lp.single 2 i (f i))).symm

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

@@ -113,7 +113,7 @@ theorem summable_inner (f g : lp G 2) : Summable fun i => ⟪f i, g i⟫ :=
   by
   -- Apply the Direct Comparison Test, comparing with ∑' i, ‖f i‖ * ‖g i‖ (summable by Hölder)
   refine' Summable.of_norm_bounded (fun i => ‖f i‖ * ‖g i‖) (lp.summable_mul _ f g) _
-  · rw [Real.isConjugateExponent_iff] <;> norm_num
+  · rw [Real.isConjExponent_iff] <;> norm_num
   intro i
   -- Then apply Cauchy-Schwarz pointwise
   exact norm_inner_le_norm _ _

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

@@ -223,12 +223,20 @@ protected def linearIsometry : lp G 2 →ₗᵢ[𝕜] E
   map_smul' c f := by
     simpa only [LinearIsometry.map_smul, Pi.smul_apply, lp.coeFn_smul] using
       tsum_const_smul c (hV.summable_of_lp f)
-  norm_map' f := by classical
+  norm_map' f := by
+    classical
+    -- needed for lattice instance on `finset ι`, for `filter.at_top_ne_bot`
+    have H : 0 < (2 : ℝ≥0∞).toReal := by norm_num
+    suffices ‖∑' i : ι, V i (f i)‖ ^ (2 : ℝ≥0∞).toReal = ‖f‖ ^ (2 : ℝ≥0∞).toReal by
+      exact Real.rpow_left_injOn H.ne' (norm_nonneg _) (norm_nonneg _) this
+    refine' tendsto_nhds_unique _ (lp.hasSum_norm H f)
+    convert (hV.summable_of_lp f).HasSum.norm.rpow_const (Or.inr H.le)
+    ext s
+    exact_mod_cast (hV.norm_sum f s).symm
 #align orthogonal_family.linear_isometry OrthogonalFamily.linearIsometry
 -/
 
 #print OrthogonalFamily.linearIsometry_apply /-
--- needed for lattice instance on `finset ι`, for `filter.at_top_ne_bot`
 protected theorem linearIsometry_apply (f : lp G 2) : hV.LinearIsometry f = ∑' i, V i (f i) :=
   rfl
 #align orthogonal_family.linear_isometry_apply OrthogonalFamily.linearIsometry_apply
@@ -534,7 +542,17 @@ protected theorem hasSum_repr (b : HilbertBasis ι 𝕜 E) (x : E) :
 #print HilbertBasis.dense_span /-
 @[simp]
 protected theorem dense_span (b : HilbertBasis ι 𝕜 E) :
-    (span 𝕜 (Set.range b)).topologicalClosure = ⊤ := by classical
+    (span 𝕜 (Set.range b)).topologicalClosure = ⊤ := by
+  classical
+  rw [eq_top_iff]
+  rintro x -
+  refine' mem_closure_of_tendsto (b.has_sum_repr x) (eventually_of_forall _)
+  intro s
+  simp only [SetLike.mem_coe]
+  refine' sum_mem _
+  rintro i -
+  refine' smul_mem _ _ _
+  exact subset_span ⟨i, rfl⟩
 #align hilbert_basis.dense_span HilbertBasis.dense_span
 -/
 

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

@@ -223,20 +223,12 @@ protected def linearIsometry : lp G 2 →ₗᵢ[𝕜] E
   map_smul' c f := by
     simpa only [LinearIsometry.map_smul, Pi.smul_apply, lp.coeFn_smul] using
       tsum_const_smul c (hV.summable_of_lp f)
-  norm_map' f := by
-    classical
-    -- needed for lattice instance on `finset ι`, for `filter.at_top_ne_bot`
-    have H : 0 < (2 : ℝ≥0∞).toReal := by norm_num
-    suffices ‖∑' i : ι, V i (f i)‖ ^ (2 : ℝ≥0∞).toReal = ‖f‖ ^ (2 : ℝ≥0∞).toReal by
-      exact Real.rpow_left_injOn H.ne' (norm_nonneg _) (norm_nonneg _) this
-    refine' tendsto_nhds_unique _ (lp.hasSum_norm H f)
-    convert (hV.summable_of_lp f).HasSum.norm.rpow_const (Or.inr H.le)
-    ext s
-    exact_mod_cast (hV.norm_sum f s).symm
+  norm_map' f := by classical
 #align orthogonal_family.linear_isometry OrthogonalFamily.linearIsometry
 -/
 
 #print OrthogonalFamily.linearIsometry_apply /-
+-- needed for lattice instance on `finset ι`, for `filter.at_top_ne_bot`
 protected theorem linearIsometry_apply (f : lp G 2) : hV.LinearIsometry f = ∑' i, V i (f i) :=
   rfl
 #align orthogonal_family.linear_isometry_apply OrthogonalFamily.linearIsometry_apply
@@ -542,17 +534,7 @@ protected theorem hasSum_repr (b : HilbertBasis ι 𝕜 E) (x : E) :
 #print HilbertBasis.dense_span /-
 @[simp]
 protected theorem dense_span (b : HilbertBasis ι 𝕜 E) :
-    (span 𝕜 (Set.range b)).topologicalClosure = ⊤ := by
-  classical
-  rw [eq_top_iff]
-  rintro x -
-  refine' mem_closure_of_tendsto (b.has_sum_repr x) (eventually_of_forall _)
-  intro s
-  simp only [SetLike.mem_coe]
-  refine' sum_mem _
-  rintro i -
-  refine' smul_mem _ _ _
-  exact subset_span ⟨i, rfl⟩
+    (span 𝕜 (Set.range b)).topologicalClosure = ⊤ := by classical
 #align hilbert_basis.dense_span HilbertBasis.dense_span
 -/
 

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

@@ -112,7 +112,7 @@ namespace lp
 theorem summable_inner (f g : lp G 2) : Summable fun i => ⟪f i, g i⟫ :=
   by
   -- Apply the Direct Comparison Test, comparing with ∑' i, ‖f i‖ * ‖g i‖ (summable by Hölder)
-  refine' summable_of_norm_bounded (fun i => ‖f i‖ * ‖g i‖) (lp.summable_mul _ f g) _
+  refine' Summable.of_norm_bounded (fun i => ‖f i‖ * ‖g i‖) (lp.summable_mul _ f g) _
   · rw [Real.isConjugateExponent_iff] <;> norm_num
   intro i
   -- Then apply Cauchy-Schwarz pointwise

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

@@ -3,9 +3,9 @@ Copyright (c) 2022 Heather Macbeth. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Heather Macbeth
 -/
-import Mathbin.Analysis.InnerProductSpace.Projection
-import Mathbin.Analysis.NormedSpace.LpSpace
-import Mathbin.Analysis.InnerProductSpace.PiL2
+import Analysis.InnerProductSpace.Projection
+import Analysis.NormedSpace.LpSpace
+import Analysis.InnerProductSpace.PiL2
 
 #align_import analysis.inner_product_space.l2_space from "leanprover-community/mathlib"@"af471b9e3ce868f296626d33189b4ce730fa4c00"
 

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

@@ -2,16 +2,13 @@
 Copyright (c) 2022 Heather Macbeth. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Heather Macbeth
-
-! This file was ported from Lean 3 source module analysis.inner_product_space.l2_space
-! leanprover-community/mathlib commit af471b9e3ce868f296626d33189b4ce730fa4c00
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Analysis.InnerProductSpace.Projection
 import Mathbin.Analysis.NormedSpace.LpSpace
 import Mathbin.Analysis.InnerProductSpace.PiL2
 
+#align_import analysis.inner_product_space.l2_space from "leanprover-community/mathlib"@"af471b9e3ce868f296626d33189b4ce730fa4c00"
+
 /-!
 # Hilbert sum of a family of inner product spaces
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/4e24c4bfcff371c71f7ba22050308aa17815626c

@@ -276,7 +276,7 @@ protected theorem linearIsometry_apply_dfinsupp_sum_single (W₀ : Π₀ i : ι,
     hV.linear_isometry (∑ i in W₀.support, lp.single 2 i (W₀ i)) =
       ∑ i in W₀.support, hV.linear_isometry (lp.single 2 i (W₀ i)) :=
     hV.linear_isometry.to_linear_map.map_sum
-  simp (config := { contextual := true }) [Dfinsupp.sum, this]
+  simp (config := { contextual := true }) [DFinsupp.sum, this]
 #align orthogonal_family.linear_isometry_apply_dfinsupp_sum_single OrthogonalFamily.linearIsometry_apply_dfinsupp_sum_single
 -/
 
@@ -415,7 +415,7 @@ protected theorem IsHilbertSum.linearIsometryEquiv_apply_dfinsupp_sum_single
   rw [← hV.linear_isometry_equiv_symm_apply_dfinsupp_sum_single]
   rw [LinearIsometryEquiv.apply_symm_apply]
   ext i
-  simp (config := { contextual := true }) [Dfinsupp.sum, lp.single_apply]
+  simp (config := { contextual := true }) [DFinsupp.sum, lp.single_apply]
 #align is_hilbert_sum.linear_isometry_equiv_apply_dfinsupp_sum_single IsHilbertSum.linearIsometryEquiv_apply_dfinsupp_sum_single
 -/
 

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

@@ -102,10 +102,8 @@ variable [NormedAddCommGroup E] [InnerProductSpace 𝕜 E] [cplt : CompleteSpace
 
 variable {G : ι → Type _} [∀ i, NormedAddCommGroup (G i)] [∀ i, InnerProductSpace 𝕜 (G i)]
 
--- mathport name: «expr⟪ , ⟫»
 local notation "⟪" x ", " y "⟫" => @inner 𝕜 _ _ x y
 
--- mathport name: «exprℓ²( , )»
 notation "ℓ²(" ι ", " 𝕜 ")" => lp (fun i : ι => 𝕜) 2
 
 /-! ### Inner product space structure on `lp G 2` -/
@@ -113,6 +111,7 @@ notation "ℓ²(" ι ", " 𝕜 ")" => lp (fun i : ι => 𝕜) 2
 
 namespace lp
 
+#print lp.summable_inner /-
 theorem summable_inner (f g : lp G 2) : Summable fun i => ⟪f i, g i⟫ :=
   by
   -- Apply the Direct Comparison Test, comparing with ∑' i, ‖f i‖ * ‖g i‖ (summable by Hölder)
@@ -122,6 +121,7 @@ theorem summable_inner (f g : lp G 2) : Summable fun i => ⟪f i, g i⟫ :=
   -- Then apply Cauchy-Schwarz pointwise
   exact norm_inner_le_norm _ _
 #align lp.summable_inner lp.summable_inner
+-/
 
 instance : InnerProductSpace 𝕜 (lp G 2) :=
   { lp.normedSpace with
@@ -164,14 +164,19 @@ instance : InnerProductSpace 𝕜 (lp G 2) :=
       · simp only [coe_fn_smul, Pi.smul_apply]
       · congr }
 
+#print lp.inner_eq_tsum /-
 theorem inner_eq_tsum (f g : lp G 2) : ⟪f, g⟫ = ∑' i, ⟪f i, g i⟫ :=
   rfl
 #align lp.inner_eq_tsum lp.inner_eq_tsum
+-/
 
+#print lp.hasSum_inner /-
 theorem hasSum_inner (f g : lp G 2) : HasSum (fun i => ⟪f i, g i⟫) ⟪f, g⟫ :=
   (summable_inner f g).HasSum
 #align lp.has_sum_inner lp.hasSum_inner
+-/
 
+#print lp.inner_single_left /-
 theorem inner_single_left (i : ι) (a : G i) (f : lp G 2) : ⟪lp.single 2 i a, f⟫ = ⟪a, f i⟫ :=
   by
   refine' (has_sum_inner (lp.single 2 i a) f).unique _
@@ -182,10 +187,13 @@ theorem inner_single_left (i : ι) (a : G i) (f : lp G 2) : ⟪lp.single 2 i a,
   · subst h
   · simp
 #align lp.inner_single_left lp.inner_single_left
+-/
 
+#print lp.inner_single_right /-
 theorem inner_single_right (i : ι) (a : G i) (f : lp G 2) : ⟪f, lp.single 2 i a⟫ = ⟪f i, a⟫ := by
   simpa [inner_conj_symm] using congr_arg conj (@inner_single_left _ 𝕜 _ _ _ _ i a f)
 #align lp.inner_single_right lp.inner_single_right
+-/
 
 end lp
 
@@ -196,8 +204,7 @@ namespace OrthogonalFamily
 
 variable {V : ∀ i, G i →ₗᵢ[𝕜] E} (hV : OrthogonalFamily 𝕜 G V)
 
-include cplt hV
-
+#print OrthogonalFamily.summable_of_lp /-
 protected theorem summable_of_lp (f : lp G 2) : Summable fun i => V i (f i) :=
   by
   rw [hV.summable_iff_norm_sq_summable]
@@ -205,7 +212,9 @@ protected theorem summable_of_lp (f : lp G 2) : Summable fun i => V i (f i) :=
   · norm_cast
   · norm_num
 #align orthogonal_family.summable_of_lp OrthogonalFamily.summable_of_lp
+-/
 
+#print OrthogonalFamily.linearIsometry /-
 /-- A mutually orthogonal family of subspaces of `E` induce a linear isometry from `lp 2` of the
 subspaces into `E`. -/
 protected def linearIsometry : lp G 2 →ₗᵢ[𝕜] E
@@ -228,16 +237,22 @@ protected def linearIsometry : lp G 2 →ₗᵢ[𝕜] E
     ext s
     exact_mod_cast (hV.norm_sum f s).symm
 #align orthogonal_family.linear_isometry OrthogonalFamily.linearIsometry
+-/
 
+#print OrthogonalFamily.linearIsometry_apply /-
 protected theorem linearIsometry_apply (f : lp G 2) : hV.LinearIsometry f = ∑' i, V i (f i) :=
   rfl
 #align orthogonal_family.linear_isometry_apply OrthogonalFamily.linearIsometry_apply
+-/
 
+#print OrthogonalFamily.hasSum_linearIsometry /-
 protected theorem hasSum_linearIsometry (f : lp G 2) :
     HasSum (fun i => V i (f i)) (hV.LinearIsometry f) :=
   (hV.summable_of_lp f).HasSum
 #align orthogonal_family.has_sum_linear_isometry OrthogonalFamily.hasSum_linearIsometry
+-/
 
+#print OrthogonalFamily.linearIsometry_apply_single /-
 @[simp]
 protected theorem linearIsometry_apply_single {i : ι} (x : G i) :
     hV.LinearIsometry (lp.single 2 i x) = V i x :=
@@ -250,7 +265,9 @@ protected theorem linearIsometry_apply_single {i : ι} (x : G i) :
   · subst h
   · simp
 #align orthogonal_family.linear_isometry_apply_single OrthogonalFamily.linearIsometry_apply_single
+-/
 
+#print OrthogonalFamily.linearIsometry_apply_dfinsupp_sum_single /-
 @[simp]
 protected theorem linearIsometry_apply_dfinsupp_sum_single (W₀ : Π₀ i : ι, G i) :
     hV.LinearIsometry (W₀.Sum (lp.single 2)) = W₀.Sum fun i => V i :=
@@ -261,6 +278,7 @@ protected theorem linearIsometry_apply_dfinsupp_sum_single (W₀ : Π₀ i : ι,
     hV.linear_isometry.to_linear_map.map_sum
   simp (config := { contextual := true }) [Dfinsupp.sum, this]
 #align orthogonal_family.linear_isometry_apply_dfinsupp_sum_single OrthogonalFamily.linearIsometry_apply_dfinsupp_sum_single
+-/
 
 #print OrthogonalFamily.range_linearIsometry /-
 /-- The canonical linear isometry from the `lp 2` of a mutually orthogonal family of subspaces of
@@ -292,8 +310,6 @@ section IsHilbertSum
 
 variable (𝕜 G) (V : ∀ i, G i →ₗᵢ[𝕜] E) (F : ι → Submodule 𝕜 E)
 
-include cplt
-
 #print IsHilbertSum /-
 /-- Given a family of Hilbert spaces `G : ι → Type*`, a Hilbert sum of `G` consists of a Hilbert
 space `E` and an orthogonal family `V : Π i, G i →ₗᵢ[𝕜] E` such that the induced isometry
@@ -310,6 +326,7 @@ structure IsHilbertSum : Prop where ofSurjective ::
 
 variable {𝕜 G V}
 
+#print IsHilbertSum.mk /-
 /-- If `V : Π i, G i →ₗᵢ[𝕜] E` is an orthogonal family such that the supremum of the ranges of
 `V i` is dense, then `(E, V)` is a Hilbert sum of `G`. -/
 theorem IsHilbertSum.mk [∀ i, CompleteSpace <| G i] (hVortho : OrthogonalFamily 𝕜 G V)
@@ -321,7 +338,9 @@ theorem IsHilbertSum.mk [∀ i, CompleteSpace <| G i] (hVortho : OrthogonalFamil
         linear_map.range_eq_top.mp
           (eq_top_iff.mpr <| hVtotal.trans_eq hVortho.range_linear_isometry.symm) }
 #align is_hilbert_sum.mk IsHilbertSum.mk
+-/
 
+#print IsHilbertSum.mkInternal /-
 /-- This is `orthogonal_family.is_hilbert_sum` in the case of actual inclusions from subspaces. -/
 theorem IsHilbertSum.mkInternal [∀ i, CompleteSpace <| F i]
     (hFortho : OrthogonalFamily 𝕜 (fun i => F i) fun i => (F i).subtypeₗᵢ)
@@ -329,7 +348,9 @@ theorem IsHilbertSum.mkInternal [∀ i, CompleteSpace <| F i]
     IsHilbertSum 𝕜 (fun i => F i) fun i => (F i).subtypeₗᵢ :=
   IsHilbertSum.mk hFortho (by simpa [subtypeₗᵢ_to_linear_map, range_subtype] using hFtotal)
 #align is_hilbert_sum.mk_internal IsHilbertSum.mkInternal
+-/
 
+#print IsHilbertSum.linearIsometryEquiv /-
 /-- *A* Hilbert sum `(E, V)` of `G` is canonically isomorphic to *the* Hilbert sum of `G`,
 i.e `lp G 2`.
 
@@ -338,14 +359,18 @@ noncomputable def IsHilbertSum.linearIsometryEquiv (hV : IsHilbertSum 𝕜 G V)
   LinearIsometryEquiv.symm <|
     LinearIsometryEquiv.ofSurjective hV.OrthogonalFamily.LinearIsometry hV.surjective_isometry
 #align is_hilbert_sum.linear_isometry_equiv IsHilbertSum.linearIsometryEquiv
+-/
 
+#print IsHilbertSum.linearIsometryEquiv_symm_apply /-
 /-- In the canonical isometric isomorphism between a Hilbert sum `E` of `G` and `lp G 2`,
 a vector `w : lp G 2` is the image of the infinite sum of the associated elements in `E`. -/
 protected theorem IsHilbertSum.linearIsometryEquiv_symm_apply (hV : IsHilbertSum 𝕜 G V)
     (w : lp G 2) : hV.LinearIsometryEquiv.symm w = ∑' i, V i (w i) := by
   simp [IsHilbertSum.linearIsometryEquiv, OrthogonalFamily.linearIsometry_apply]
 #align is_hilbert_sum.linear_isometry_equiv_symm_apply IsHilbertSum.linearIsometryEquiv_symm_apply
+-/
 
+#print IsHilbertSum.hasSum_linearIsometryEquiv_symm /-
 /-- In the canonical isometric isomorphism between a Hilbert sum `E` of `G` and `lp G 2`,
 a vector `w : lp G 2` is the image of the infinite sum of the associated elements in `E`, and this
 sum indeed converges. -/
@@ -353,7 +378,9 @@ protected theorem IsHilbertSum.hasSum_linearIsometryEquiv_symm (hV : IsHilbertSu
     (w : lp G 2) : HasSum (fun i => V i (w i)) (hV.LinearIsometryEquiv.symm w) := by
   simp [IsHilbertSum.linearIsometryEquiv, OrthogonalFamily.hasSum_linearIsometry]
 #align is_hilbert_sum.has_sum_linear_isometry_equiv_symm IsHilbertSum.hasSum_linearIsometryEquiv_symm
+-/
 
+#print IsHilbertSum.linearIsometryEquiv_symm_apply_single /-
 /-- In the canonical isometric isomorphism between a Hilbert sum `E` of `G : ι → Type*` and
 `lp G 2`, an "elementary basis vector" in `lp G 2` supported at `i : ι` is the image of the
 associated element in `E`. -/
@@ -362,7 +389,9 @@ protected theorem IsHilbertSum.linearIsometryEquiv_symm_apply_single (hV : IsHil
     {i : ι} (x : G i) : hV.LinearIsometryEquiv.symm (lp.single 2 i x) = V i x := by
   simp [IsHilbertSum.linearIsometryEquiv, OrthogonalFamily.linearIsometry_apply_single]
 #align is_hilbert_sum.linear_isometry_equiv_symm_apply_single IsHilbertSum.linearIsometryEquiv_symm_apply_single
+-/
 
+#print IsHilbertSum.linearIsometryEquiv_symm_apply_dfinsupp_sum_single /-
 /-- In the canonical isometric isomorphism between a Hilbert sum `E` of `G : ι → Type*` and
 `lp G 2`, a finitely-supported vector in `lp G 2` is the image of the associated finite sum of
 elements of `E`. -/
@@ -372,7 +401,9 @@ protected theorem IsHilbertSum.linearIsometryEquiv_symm_apply_dfinsupp_sum_singl
     hV.LinearIsometryEquiv.symm (W₀.Sum (lp.single 2)) = W₀.Sum fun i => V i := by
   simp [IsHilbertSum.linearIsometryEquiv, OrthogonalFamily.linearIsometry_apply_dfinsupp_sum_single]
 #align is_hilbert_sum.linear_isometry_equiv_symm_apply_dfinsupp_sum_single IsHilbertSum.linearIsometryEquiv_symm_apply_dfinsupp_sum_single
+-/
 
+#print IsHilbertSum.linearIsometryEquiv_apply_dfinsupp_sum_single /-
 /-- In the canonical isometric isomorphism between a Hilbert sum `E` of `G : ι → Type*` and
 `lp G 2`, a finitely-supported vector in `lp G 2` is the image of the associated finite sum of
 elements of `E`. -/
@@ -386,7 +417,9 @@ protected theorem IsHilbertSum.linearIsometryEquiv_apply_dfinsupp_sum_single
   ext i
   simp (config := { contextual := true }) [Dfinsupp.sum, lp.single_apply]
 #align is_hilbert_sum.linear_isometry_equiv_apply_dfinsupp_sum_single IsHilbertSum.linearIsometryEquiv_apply_dfinsupp_sum_single
+-/
 
+#print Orthonormal.isHilbertSum /-
 /-- Given a total orthonormal family `v : ι → E`, `E` is a Hilbert sum of `λ i : ι, 𝕜` relative to
 the family of linear isometries `λ i, λ k, k • v i`. -/
 theorem Orthonormal.isHilbertSum {v : ι → E} (hv : Orthonormal 𝕜 v)
@@ -397,7 +430,9 @@ theorem Orthonormal.isHilbertSum {v : ι → E} (hv : Orthonormal 𝕜 v)
       convert hsp
       simp [← LinearMap.span_singleton_eq_range, ← Submodule.span_iUnion])
 #align orthonormal.is_hilbert_sum Orthonormal.isHilbertSum
+-/
 
+#print Submodule.isHilbertSumOrthogonal /-
 theorem Submodule.isHilbertSumOrthogonal (K : Submodule 𝕜 E) [hK : CompleteSpace K] :
     IsHilbertSum 𝕜 (fun b => ↥(cond b K Kᗮ)) fun b => (cond b K Kᗮ).subtypeₗᵢ :=
   by
@@ -413,6 +448,7 @@ theorem Submodule.isHilbertSumOrthogonal (K : Submodule 𝕜 E) [hK : CompleteSp
   refine' Codisjoint.top_le _
   exact submodule.is_compl_orthogonal_of_complete_space.codisjoint
 #align submodule.is_hilbert_sum_orthogonal Submodule.isHilbertSumOrthogonal
+-/
 
 end IsHilbertSum
 
@@ -442,25 +478,32 @@ instance {ι : Type _} : Inhabited (HilbertBasis ι 𝕜 ℓ²(ι, 𝕜)) :=
 instance : CoeFun (HilbertBasis ι 𝕜 E) fun _ => ι → E
     where coe b i := b.repr.symm (lp.single 2 i (1 : 𝕜))
 
+#print HilbertBasis.repr_symm_single /-
 @[simp]
 protected theorem repr_symm_single (b : HilbertBasis ι 𝕜 E) (i : ι) :
     b.repr.symm (lp.single 2 i (1 : 𝕜)) = b i :=
   rfl
 #align hilbert_basis.repr_symm_single HilbertBasis.repr_symm_single
+-/
 
+#print HilbertBasis.repr_self /-
 @[simp]
 protected theorem repr_self (b : HilbertBasis ι 𝕜 E) (i : ι) :
     b.repr (b i) = lp.single 2 i (1 : 𝕜) := by
   rw [← b.repr_symm_single, LinearIsometryEquiv.apply_symm_apply]
 #align hilbert_basis.repr_self HilbertBasis.repr_self
+-/
 
+#print HilbertBasis.repr_apply_apply /-
 protected theorem repr_apply_apply (b : HilbertBasis ι 𝕜 E) (v : E) (i : ι) :
     b.repr v i = ⟪b i, v⟫ :=
   by
   rw [← b.repr.inner_map_map (b i) v, b.repr_self, lp.inner_single_left]
   simp
 #align hilbert_basis.repr_apply_apply HilbertBasis.repr_apply_apply
+-/
 
+#print HilbertBasis.orthonormal /-
 @[simp]
 protected theorem orthonormal (b : HilbertBasis ι 𝕜 E) : Orthonormal 𝕜 b :=
   by
@@ -470,7 +513,9 @@ protected theorem orthonormal (b : HilbertBasis ι 𝕜 E) : Orthonormal 𝕜 b
     lp.single_apply]
   simp
 #align hilbert_basis.orthonormal HilbertBasis.orthonormal
+-/
 
+#print HilbertBasis.hasSum_repr_symm /-
 protected theorem hasSum_repr_symm (b : HilbertBasis ι 𝕜 E) (f : ℓ²(ι, 𝕜)) :
     HasSum (fun i => f i • b i) (b.repr.symm f) :=
   by
@@ -489,11 +534,15 @@ protected theorem hasSum_repr_symm (b : HilbertBasis ι 𝕜 E) (f : ℓ²(ι, 
     LinearIsometryEquiv.coe_toContinuousLinearEquiv]
   exact (b.repr.apply_symm_apply (lp.single 2 i (f i))).symm
 #align hilbert_basis.has_sum_repr_symm HilbertBasis.hasSum_repr_symm
+-/
 
+#print HilbertBasis.hasSum_repr /-
 protected theorem hasSum_repr (b : HilbertBasis ι 𝕜 E) (x : E) :
     HasSum (fun i => b.repr x i • b i) x := by simpa using b.has_sum_repr_symm (b.repr x)
 #align hilbert_basis.has_sum_repr HilbertBasis.hasSum_repr
+-/
 
+#print HilbertBasis.dense_span /-
 @[simp]
 protected theorem dense_span (b : HilbertBasis ι 𝕜 E) :
     (span 𝕜 (Set.range b)).topologicalClosure = ⊤ := by
@@ -508,7 +557,9 @@ protected theorem dense_span (b : HilbertBasis ι 𝕜 E) :
   refine' smul_mem _ _ _
   exact subset_span ⟨i, rfl⟩
 #align hilbert_basis.dense_span HilbertBasis.dense_span
+-/
 
+#print HilbertBasis.hasSum_inner_mul_inner /-
 protected theorem hasSum_inner_mul_inner (b : HilbertBasis ι 𝕜 E) (x y : E) :
     HasSum (fun i => ⟪x, b i⟫ * ⟪b i, y⟫) ⟪x, y⟫ :=
   by
@@ -516,16 +567,21 @@ protected theorem hasSum_inner_mul_inner (b : HilbertBasis ι 𝕜 E) (x y : E)
   ext i
   rw [innerSL_apply, b.repr_apply_apply, inner_smul_right, mul_comm]
 #align hilbert_basis.has_sum_inner_mul_inner HilbertBasis.hasSum_inner_mul_inner
+-/
 
+#print HilbertBasis.summable_inner_mul_inner /-
 protected theorem summable_inner_mul_inner (b : HilbertBasis ι 𝕜 E) (x y : E) :
     Summable fun i => ⟪x, b i⟫ * ⟪b i, y⟫ :=
   (b.hasSum_inner_mul_inner x y).Summable
 #align hilbert_basis.summable_inner_mul_inner HilbertBasis.summable_inner_mul_inner
+-/
 
+#print HilbertBasis.tsum_inner_mul_inner /-
 protected theorem tsum_inner_mul_inner (b : HilbertBasis ι 𝕜 E) (x y : E) :
     ∑' i, ⟪x, b i⟫ * ⟪b i, y⟫ = ⟪x, y⟫ :=
   (b.hasSum_inner_mul_inner x y).tsum_eq
 #align hilbert_basis.tsum_inner_mul_inner HilbertBasis.tsum_inner_mul_inner
+-/
 
 #print HilbertBasis.toOrthonormalBasis /-
 -- Note : this should be `b.repr` composed with an identification of `lp (λ i : ι, 𝕜) p` with
@@ -541,19 +597,24 @@ protected def toOrthonormalBasis [Fintype ι] (b : HilbertBasis ι 𝕜 E) : Ort
 #align hilbert_basis.to_orthonormal_basis HilbertBasis.toOrthonormalBasis
 -/
 
+#print HilbertBasis.coe_toOrthonormalBasis /-
 @[simp]
 theorem coe_toOrthonormalBasis [Fintype ι] (b : HilbertBasis ι 𝕜 E) :
     (b.toOrthonormalBasis : ι → E) = b :=
   OrthonormalBasis.coe_mk _ _
 #align hilbert_basis.coe_to_orthonormal_basis HilbertBasis.coe_toOrthonormalBasis
+-/
 
+#print HilbertBasis.hasSum_orthogonalProjection /-
 protected theorem hasSum_orthogonalProjection {U : Submodule 𝕜 E} [CompleteSpace U]
     (b : HilbertBasis ι 𝕜 U) (x : E) :
     HasSum (fun i => ⟪(b i : E), x⟫ • b i) (orthogonalProjection U x) := by
   simpa only [b.repr_apply_apply, inner_orthogonalProjection_eq_of_mem_left] using
     b.has_sum_repr (orthogonalProjection U x)
 #align hilbert_basis.has_sum_orthogonal_projection HilbertBasis.hasSum_orthogonalProjection
+-/
 
+#print HilbertBasis.finite_spans_dense /-
 theorem finite_spans_dense (b : HilbertBasis ι 𝕜 E) :
     (⨆ J : Finset ι, span 𝕜 (J.image b : Set E)).topologicalClosure = ⊤ :=
   eq_top_iff.mpr <|
@@ -567,42 +628,49 @@ theorem finite_spans_dense (b : HilbertBasis ι 𝕜 E) :
                 Set.mem_iUnion_of_mem {i} <|
                   finset.mem_coe.mpr <| Finset.mem_image_of_mem _ <| Finset.mem_singleton_self i))
 #align hilbert_basis.finite_spans_dense HilbertBasis.finite_spans_dense
+-/
 
 variable {v : ι → E} (hv : Orthonormal 𝕜 v)
 
-include hv cplt
-
+#print HilbertBasis.mk /-
 /-- An orthonormal family of vectors whose span is dense in the whole module is a Hilbert basis. -/
 protected def mk (hsp : ⊤ ≤ (span 𝕜 (Set.range v)).topologicalClosure) : HilbertBasis ι 𝕜 E :=
   HilbertBasis.ofRepr <| (hv.IsHilbertSum hsp).LinearIsometryEquiv
 #align hilbert_basis.mk HilbertBasis.mk
+-/
 
+#print Orthonormal.linearIsometryEquiv_symm_apply_single_one /-
 theorem Orthonormal.linearIsometryEquiv_symm_apply_single_one (h i) :
     (hv.IsHilbertSum h).LinearIsometryEquiv.symm (lp.single 2 i 1) = v i := by
   rw [IsHilbertSum.linearIsometryEquiv_symm_apply_single, LinearIsometry.toSpanSingleton_apply,
     one_smul]
 #align orthonormal.linear_isometry_equiv_symm_apply_single_one Orthonormal.linearIsometryEquiv_symm_apply_single_one
+-/
 
+#print HilbertBasis.coe_mk /-
 @[simp]
 protected theorem coe_mk (hsp : ⊤ ≤ (span 𝕜 (Set.range v)).topologicalClosure) :
     ⇑(HilbertBasis.mk hv hsp) = v := by
   apply funext <| Orthonormal.linearIsometryEquiv_symm_apply_single_one hv hsp
 #align hilbert_basis.coe_mk HilbertBasis.coe_mk
+-/
 
+#print HilbertBasis.mkOfOrthogonalEqBot /-
 /-- An orthonormal family of vectors whose span has trivial orthogonal complement is a Hilbert
 basis. -/
 protected def mkOfOrthogonalEqBot (hsp : (span 𝕜 (Set.range v))ᗮ = ⊥) : HilbertBasis ι 𝕜 E :=
   HilbertBasis.mk hv
     (by rw [← orthogonal_orthogonal_eq_closure, ← eq_top_iff, orthogonal_eq_top_iff, hsp])
 #align hilbert_basis.mk_of_orthogonal_eq_bot HilbertBasis.mkOfOrthogonalEqBot
+-/
 
+#print HilbertBasis.coe_mkOfOrthogonalEqBot /-
 @[simp]
 protected theorem coe_mkOfOrthogonalEqBot (hsp : (span 𝕜 (Set.range v))ᗮ = ⊥) :
     ⇑(HilbertBasis.mkOfOrthogonalEqBot hv hsp) = v :=
   HilbertBasis.coe_mk hv _
 #align hilbert_basis.coe_of_orthogonal_eq_bot_mk HilbertBasis.coe_mkOfOrthogonalEqBot
-
-omit hv
+-/
 
 #print OrthonormalBasis.toHilbertBasis /-
 -- Note : this should be `b.repr` composed with an identification of `lp (λ i : ι, 𝕜) p` with
@@ -616,12 +684,15 @@ protected def OrthonormalBasis.toHilbertBasis [Fintype ι] (b : OrthonormalBasis
 #align orthonormal_basis.to_hilbert_basis OrthonormalBasis.toHilbertBasis
 -/
 
+#print OrthonormalBasis.coe_toHilbertBasis /-
 @[simp]
 theorem OrthonormalBasis.coe_toHilbertBasis [Fintype ι] (b : OrthonormalBasis ι 𝕜 E) :
     (b.toHilbertBasis : ι → E) = b :=
   HilbertBasis.coe_mk _ _
 #align orthonormal_basis.coe_to_hilbert_basis OrthonormalBasis.coe_toHilbertBasis
+-/
 
+#print Orthonormal.exists_hilbertBasis_extension /-
 /-- A Hilbert space admits a Hilbert basis extending a given orthonormal subset. -/
 theorem Orthonormal.exists_hilbertBasis_extension {s : Set E} (hs : Orthonormal 𝕜 (coe : s → E)) :
     ∃ (w : Set E) (b : HilbertBasis w 𝕜 E), s ⊆ w ∧ ⇑b = (coe : w → E) :=
@@ -631,14 +702,17 @@ theorem Orthonormal.exists_hilbertBasis_extension {s : Set E} (hs : Orthonormal
       (by simpa [maximal_orthonormal_iff_orthogonalComplement_eq_bot hw_ortho] using hw_max),
     hws, HilbertBasis.coe_mkOfOrthogonalEqBot _ _⟩
 #align orthonormal.exists_hilbert_basis_extension Orthonormal.exists_hilbertBasis_extension
+-/
 
 variable (𝕜 E)
 
+#print exists_hilbertBasis /-
 /-- A Hilbert space admits a Hilbert basis. -/
 theorem exists_hilbertBasis : ∃ (w : Set E) (b : HilbertBasis w 𝕜 E), ⇑b = (coe : w → E) :=
   let ⟨w, hw, hw', hw''⟩ := (orthonormal_empty 𝕜 E).exists_hilbertBasis_extension
   ⟨w, hw, hw''⟩
 #align exists_hilbert_basis exists_hilbertBasis
+-/
 
 end HilbertBasis
 

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

@@ -147,9 +147,9 @@ instance : InnerProductSpace 𝕜 (lp G 2) :=
       by
       calc
         _ = ∑' i, ⟪(f₁ + f₂) i, g i⟫ := _
-        _ = ∑' i, ⟪f₁ i, g i⟫ + ⟪f₂ i, g i⟫ := by
+        _ = ∑' i, (⟪f₁ i, g i⟫ + ⟪f₂ i, g i⟫) := by
           simp only [inner_add_left, Pi.add_apply, coe_fn_add]
-        _ = (∑' i, ⟪f₁ i, g i⟫) + ∑' i, ⟪f₂ i, g i⟫ := (tsum_add _ _)
+        _ = ∑' i, ⟪f₁ i, g i⟫ + ∑' i, ⟪f₂ i, g i⟫ := (tsum_add _ _)
         _ = _ := by congr
       · congr
       · exact summable_inner f₁ g
@@ -523,7 +523,7 @@ protected theorem summable_inner_mul_inner (b : HilbertBasis ι 𝕜 E) (x y : E
 #align hilbert_basis.summable_inner_mul_inner HilbertBasis.summable_inner_mul_inner
 
 protected theorem tsum_inner_mul_inner (b : HilbertBasis ι 𝕜 E) (x y : E) :
-    (∑' i, ⟪x, b i⟫ * ⟪b i, y⟫) = ⟪x, y⟫ :=
+    ∑' i, ⟪x, b i⟫ * ⟪b i, y⟫ = ⟪x, y⟫ :=
   (b.hasSum_inner_mul_inner x y).tsum_eq
 #align hilbert_basis.tsum_inner_mul_inner HilbertBasis.tsum_inner_mul_inner
 

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

@@ -135,7 +135,6 @@ instance : InnerProductSpace 𝕜 (lp G 2) :=
         _ = ∑' i, re ⟪f i, f i⟫ := by simp only [@norm_sq_eq_inner 𝕜]
         _ = re (∑' i, ⟪f i, f i⟫) := (is_R_or_C.re_clm.map_tsum _).symm
         _ = _ := by congr
-        
       · norm_num
       · exact summable_inner f f
     conj_symm := fun f g => by
@@ -144,7 +143,6 @@ instance : InnerProductSpace 𝕜 (lp G 2) :=
         _ = ∑' i, conj ⟪g i, f i⟫ := is_R_or_C.conj_cle.map_tsum
         _ = ∑' i, ⟪f i, g i⟫ := by simp only [inner_conj_symm]
         _ = _ := by congr
-        
     add_left := fun f₁ f₂ g =>
       by
       calc
@@ -153,7 +151,6 @@ instance : InnerProductSpace 𝕜 (lp G 2) :=
           simp only [inner_add_left, Pi.add_apply, coe_fn_add]
         _ = (∑' i, ⟪f₁ i, g i⟫) + ∑' i, ⟪f₂ i, g i⟫ := (tsum_add _ _)
         _ = _ := by congr
-        
       · congr
       · exact summable_inner f₁ g
       · exact summable_inner f₂ g
@@ -164,7 +161,6 @@ instance : InnerProductSpace 𝕜 (lp G 2) :=
         _ = ∑' i, conj c * ⟪f i, g i⟫ := by simp only [inner_smul_left]
         _ = conj c * ∑' i, ⟪f i, g i⟫ := tsum_mul_left
         _ = _ := _
-        
       · simp only [coe_fn_smul, Pi.smul_apply]
       · congr }
 

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Heather Macbeth
 
 ! This file was ported from Lean 3 source module analysis.inner_product_space.l2_space
-! leanprover-community/mathlib commit 46b633fd842bef9469441c0209906f6dddd2b4f5
+! leanprover-community/mathlib commit af471b9e3ce868f296626d33189b4ce730fa4c00
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -15,6 +15,9 @@ import Mathbin.Analysis.InnerProductSpace.PiL2
 /-!
 # Hilbert sum of a family of inner product spaces
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 Given a family `(G : ι → Type*) [Π i, inner_product_space 𝕜 (G i)]` of inner product spaces, this
 file equips `lp G 2` with an inner product space structure, where `lp G 2` consists of those
 dependent functions `f : Π i, G i` for which `∑' i, ‖f i‖ ^ 2`, the sum of the norms-squared, is
@@ -202,7 +205,7 @@ include cplt hV
 protected theorem summable_of_lp (f : lp G 2) : Summable fun i => V i (f i) :=
   by
   rw [hV.summable_iff_norm_sq_summable]
-  convert(lp.memℓp f).Summable _
+  convert (lp.memℓp f).Summable _
   · norm_cast
   · norm_num
 #align orthogonal_family.summable_of_lp OrthogonalFamily.summable_of_lp
@@ -220,14 +223,14 @@ protected def linearIsometry : lp G 2 →ₗᵢ[𝕜] E
       tsum_const_smul c (hV.summable_of_lp f)
   norm_map' f := by
     classical
-      -- needed for lattice instance on `finset ι`, for `filter.at_top_ne_bot`
-      have H : 0 < (2 : ℝ≥0∞).toReal := by norm_num
-      suffices ‖∑' i : ι, V i (f i)‖ ^ (2 : ℝ≥0∞).toReal = ‖f‖ ^ (2 : ℝ≥0∞).toReal by
-        exact Real.rpow_left_injOn H.ne' (norm_nonneg _) (norm_nonneg _) this
-      refine' tendsto_nhds_unique _ (lp.hasSum_norm H f)
-      convert(hV.summable_of_lp f).HasSum.norm.rpow_const (Or.inr H.le)
-      ext s
-      exact_mod_cast (hV.norm_sum f s).symm
+    -- needed for lattice instance on `finset ι`, for `filter.at_top_ne_bot`
+    have H : 0 < (2 : ℝ≥0∞).toReal := by norm_num
+    suffices ‖∑' i : ι, V i (f i)‖ ^ (2 : ℝ≥0∞).toReal = ‖f‖ ^ (2 : ℝ≥0∞).toReal by
+      exact Real.rpow_left_injOn H.ne' (norm_nonneg _) (norm_nonneg _) this
+    refine' tendsto_nhds_unique _ (lp.hasSum_norm H f)
+    convert (hV.summable_of_lp f).HasSum.norm.rpow_const (Or.inr H.le)
+    ext s
+    exact_mod_cast (hV.norm_sum f s).symm
 #align orthogonal_family.linear_isometry OrthogonalFamily.linearIsometry
 
 protected theorem linearIsometry_apply (f : lp G 2) : hV.LinearIsometry f = ∑' i, V i (f i) :=
@@ -499,21 +502,21 @@ protected theorem hasSum_repr (b : HilbertBasis ι 𝕜 E) (x : E) :
 protected theorem dense_span (b : HilbertBasis ι 𝕜 E) :
     (span 𝕜 (Set.range b)).topologicalClosure = ⊤ := by
   classical
-    rw [eq_top_iff]
-    rintro x -
-    refine' mem_closure_of_tendsto (b.has_sum_repr x) (eventually_of_forall _)
-    intro s
-    simp only [SetLike.mem_coe]
-    refine' sum_mem _
-    rintro i -
-    refine' smul_mem _ _ _
-    exact subset_span ⟨i, rfl⟩
+  rw [eq_top_iff]
+  rintro x -
+  refine' mem_closure_of_tendsto (b.has_sum_repr x) (eventually_of_forall _)
+  intro s
+  simp only [SetLike.mem_coe]
+  refine' sum_mem _
+  rintro i -
+  refine' smul_mem _ _ _
+  exact subset_span ⟨i, rfl⟩
 #align hilbert_basis.dense_span HilbertBasis.dense_span
 
 protected theorem hasSum_inner_mul_inner (b : HilbertBasis ι 𝕜 E) (x y : E) :
     HasSum (fun i => ⟪x, b i⟫ * ⟪b i, y⟫) ⟪x, y⟫ :=
   by
-  convert(b.has_sum_repr y).mapL (innerSL _ x)
+  convert (b.has_sum_repr y).mapL (innerSL _ x)
   ext i
   rw [innerSL_apply, b.repr_apply_apply, inner_smul_right, mul_comm]
 #align hilbert_basis.has_sum_inner_mul_inner HilbertBasis.hasSum_inner_mul_inner

mathlib commit https://github.com/leanprover-community/mathlib/commit/34ebaffc1d1e8e783fc05438ec2e70af87275ac9

@@ -263,6 +263,7 @@ protected theorem linearIsometry_apply_dfinsupp_sum_single (W₀ : Π₀ i : ι,
   simp (config := { contextual := true }) [Dfinsupp.sum, this]
 #align orthogonal_family.linear_isometry_apply_dfinsupp_sum_single OrthogonalFamily.linearIsometry_apply_dfinsupp_sum_single
 
+#print OrthogonalFamily.range_linearIsometry /-
 /-- The canonical linear isometry from the `lp 2` of a mutually orthogonal family of subspaces of
 `E` into E, has range the closure of the span of the subspaces. -/
 protected theorem range_linearIsometry [∀ i, CompleteSpace (G i)] :
@@ -284,6 +285,7 @@ protected theorem range_linearIsometry [∀ i, CompleteSpace (G i)] :
       exact hV.linear_isometry_apply_single x
     exact hV.linear_isometry.isometry.uniform_inducing.is_complete_range.is_closed
 #align orthogonal_family.range_linear_isometry OrthogonalFamily.range_linearIsometry
+-/
 
 end OrthogonalFamily
 
@@ -293,6 +295,7 @@ variable (𝕜 G) (V : ∀ i, G i →ₗᵢ[𝕜] E) (F : ι → Submodule 𝕜
 
 include cplt
 
+#print IsHilbertSum /-
 /-- Given a family of Hilbert spaces `G : ι → Type*`, a Hilbert sum of `G` consists of a Hilbert
 space `E` and an orthogonal family `V : Π i, G i →ₗᵢ[𝕜] E` such that the induced isometry
 `Φ : lp G 2 → E` is surjective.
@@ -304,6 +307,7 @@ structure IsHilbertSum : Prop where ofSurjective ::
   OrthogonalFamily : OrthogonalFamily 𝕜 G V
   surjective_isometry : Function.Surjective OrthogonalFamily.LinearIsometry
 #align is_hilbert_sum IsHilbertSum
+-/
 
 variable {𝕜 G V}
 
@@ -420,18 +424,20 @@ section
 
 variable (ι) (𝕜) (E)
 
+#print HilbertBasis /-
 /-- A Hilbert basis on `ι` for an inner product space `E` is an identification of `E` with the `lp`
 space `ℓ²(ι, 𝕜)`. -/
 structure HilbertBasis where ofRepr ::
   repr : E ≃ₗᵢ[𝕜] ℓ²(ι, 𝕜)
 #align hilbert_basis HilbertBasis
+-/
 
 end
 
 namespace HilbertBasis
 
 instance {ι : Type _} : Inhabited (HilbertBasis ι 𝕜 ℓ²(ι, 𝕜)) :=
-  ⟨of_repr (LinearIsometryEquiv.refl 𝕜 _)⟩
+  ⟨ofRepr (LinearIsometryEquiv.refl 𝕜 _)⟩
 
 /-- `b i` is the `i`th basis vector. -/
 instance : CoeFun (HilbertBasis ι 𝕜 E) fun _ => ι → E
@@ -522,6 +528,7 @@ protected theorem tsum_inner_mul_inner (b : HilbertBasis ι 𝕜 E) (x y : E) :
   (b.hasSum_inner_mul_inner x y).tsum_eq
 #align hilbert_basis.tsum_inner_mul_inner HilbertBasis.tsum_inner_mul_inner
 
+#print HilbertBasis.toOrthonormalBasis /-
 -- Note : this should be `b.repr` composed with an identification of `lp (λ i : ι, 𝕜) p` with
 -- `pi_Lp p (λ i : ι, 𝕜)` (in this case with `p = 2`), but we don't have this yet (July 2022).
 /-- A finite Hilbert basis is an orthonormal basis. -/
@@ -533,6 +540,7 @@ protected def toOrthonormalBasis [Fintype ι] (b : HilbertBasis ι 𝕜 E) : Ort
       simpa only [Finset.coe_image, Finset.coe_univ, Set.image_univ, HilbertBasis.dense_span] using
         this.submodule_topological_closure_eq.symm)
 #align hilbert_basis.to_orthonormal_basis HilbertBasis.toOrthonormalBasis
+-/
 
 @[simp]
 theorem coe_toOrthonormalBasis [Fintype ι] (b : HilbertBasis ι 𝕜 E) :
@@ -567,7 +575,7 @@ include hv cplt
 
 /-- An orthonormal family of vectors whose span is dense in the whole module is a Hilbert basis. -/
 protected def mk (hsp : ⊤ ≤ (span 𝕜 (Set.range v)).topologicalClosure) : HilbertBasis ι 𝕜 E :=
-  HilbertBasis.of_repr <| (hv.IsHilbertSum hsp).LinearIsometryEquiv
+  HilbertBasis.ofRepr <| (hv.IsHilbertSum hsp).LinearIsometryEquiv
 #align hilbert_basis.mk HilbertBasis.mk
 
 theorem Orthonormal.linearIsometryEquiv_symm_apply_single_one (h i) :
@@ -590,13 +598,14 @@ protected def mkOfOrthogonalEqBot (hsp : (span 𝕜 (Set.range v))ᗮ = ⊥) : H
 #align hilbert_basis.mk_of_orthogonal_eq_bot HilbertBasis.mkOfOrthogonalEqBot
 
 @[simp]
-protected theorem coe_of_orthogonal_eq_bot_mk (hsp : (span 𝕜 (Set.range v))ᗮ = ⊥) :
+protected theorem coe_mkOfOrthogonalEqBot (hsp : (span 𝕜 (Set.range v))ᗮ = ⊥) :
     ⇑(HilbertBasis.mkOfOrthogonalEqBot hv hsp) = v :=
   HilbertBasis.coe_mk hv _
-#align hilbert_basis.coe_of_orthogonal_eq_bot_mk HilbertBasis.coe_of_orthogonal_eq_bot_mk
+#align hilbert_basis.coe_of_orthogonal_eq_bot_mk HilbertBasis.coe_mkOfOrthogonalEqBot
 
 omit hv
 
+#print OrthonormalBasis.toHilbertBasis /-
 -- Note : this should be `b.repr` composed with an identification of `lp (λ i : ι, 𝕜) p` with
 -- `pi_Lp p (λ i : ι, 𝕜)` (in this case with `p = 2`), but we don't have this yet (July 2022).
 /-- An orthonormal basis is an Hilbert basis. -/
@@ -606,6 +615,7 @@ protected def OrthonormalBasis.toHilbertBasis [Fintype ι] (b : OrthonormalBasis
     simpa only [← OrthonormalBasis.coe_toBasis, b.to_basis.span_eq, eq_top_iff] using
       @subset_closure E _ _
 #align orthonormal_basis.to_hilbert_basis OrthonormalBasis.toHilbertBasis
+-/
 
 @[simp]
 theorem OrthonormalBasis.coe_toHilbertBasis [Fintype ι] (b : OrthonormalBasis ι 𝕜 E) :
@@ -620,7 +630,7 @@ theorem Orthonormal.exists_hilbertBasis_extension {s : Set E} (hs : Orthonormal
   ⟨w,
     HilbertBasis.mkOfOrthogonalEqBot hw_ortho
       (by simpa [maximal_orthonormal_iff_orthogonalComplement_eq_bot hw_ortho] using hw_max),
-    hws, HilbertBasis.coe_of_orthogonal_eq_bot_mk _ _⟩
+    hws, HilbertBasis.coe_mkOfOrthogonalEqBot _ _⟩
 #align orthonormal.exists_hilbert_basis_extension Orthonormal.exists_hilbertBasis_extension
 
 variable (𝕜 E)

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

@@ -400,7 +400,10 @@ theorem Submodule.isHilbertSumOrthogonal (K : Submodule 𝕜 E) [hK : CompleteSp
   by
   have : ∀ b, CompleteSpace ↥(cond b K Kᗮ) := by
     intro b
-    cases b <;> first |exact orthogonal.complete_space K|assumption
+    cases b <;>
+      first
+      | exact orthogonal.complete_space K
+      | assumption
   refine' IsHilbertSum.mkInternal _ K.orthogonal_family_self _
   refine' le_trans _ (Submodule.le_topologicalClosure _)
   rw [iSup_bool_eq, cond, cond]
@@ -476,7 +479,7 @@ protected theorem hasSum_repr_symm (b : HilbertBasis ι 𝕜 E) (f : ℓ²(ι, 
   apply b.repr.injective
   letI : NormedSpace 𝕜 ↥(lp (fun i : ι => 𝕜) 2) := by infer_instance
   have : lp.single 2 i (f i * 1) = f i • lp.single 2 i 1 := lp.single_smul 2 i (1 : 𝕜) (f i)
-  rw [mul_one] at this
+  rw [mul_one] at this 
   rw [LinearIsometryEquiv.map_smul, b.repr_self, ← this,
     LinearIsometryEquiv.coe_toContinuousLinearEquiv]
   exact (b.repr.apply_symm_apply (lp.single 2 i (f i))).symm
@@ -612,7 +615,7 @@ theorem OrthonormalBasis.coe_toHilbertBasis [Fintype ι] (b : OrthonormalBasis 
 
 /-- A Hilbert space admits a Hilbert basis extending a given orthonormal subset. -/
 theorem Orthonormal.exists_hilbertBasis_extension {s : Set E} (hs : Orthonormal 𝕜 (coe : s → E)) :
-    ∃ (w : Set E)(b : HilbertBasis w 𝕜 E), s ⊆ w ∧ ⇑b = (coe : w → E) :=
+    ∃ (w : Set E) (b : HilbertBasis w 𝕜 E), s ⊆ w ∧ ⇑b = (coe : w → E) :=
   let ⟨w, hws, hw_ortho, hw_max⟩ := exists_maximal_orthonormal hs
   ⟨w,
     HilbertBasis.mkOfOrthogonalEqBot hw_ortho
@@ -623,7 +626,7 @@ theorem Orthonormal.exists_hilbertBasis_extension {s : Set E} (hs : Orthonormal
 variable (𝕜 E)
 
 /-- A Hilbert space admits a Hilbert basis. -/
-theorem exists_hilbertBasis : ∃ (w : Set E)(b : HilbertBasis w 𝕜 E), ⇑b = (coe : w → E) :=
+theorem exists_hilbertBasis : ∃ (w : Set E) (b : HilbertBasis w 𝕜 E), ⇑b = (coe : w → E) :=
   let ⟨w, hw, hw', hw''⟩ := (orthonormal_empty 𝕜 E).exists_hilbertBasis_extension
   ⟨w, hw, hw''⟩
 #align exists_hilbert_basis exists_hilbertBasis

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

@@ -87,7 +87,7 @@ Hilbert space, Hilbert sum, l2, Hilbert basis, unitary equivalence, isometric is
 
 open IsROrC Submodule Filter
 
-open BigOperators NNReal ENNReal Classical ComplexConjugate Topology
+open scoped BigOperators NNReal ENNReal Classical ComplexConjugate Topology
 
 noncomputable section
 

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

@@ -616,7 +616,7 @@ theorem Orthonormal.exists_hilbertBasis_extension {s : Set E} (hs : Orthonormal
   let ⟨w, hws, hw_ortho, hw_max⟩ := exists_maximal_orthonormal hs
   ⟨w,
     HilbertBasis.mkOfOrthogonalEqBot hw_ortho
-      (by simpa [maximal_orthonormal_iff_orthogonal_complement_eq_bot hw_ortho] using hw_max),
+      (by simpa [maximal_orthonormal_iff_orthogonalComplement_eq_bot hw_ortho] using hw_max),
     hws, HilbertBasis.coe_of_orthogonal_eq_bot_mk _ _⟩
 #align orthonormal.exists_hilbert_basis_extension Orthonormal.exists_hilbertBasis_extension
 

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

@@ -624,7 +624,7 @@ variable (𝕜 E)
 
 /-- A Hilbert space admits a Hilbert basis. -/
 theorem exists_hilbertBasis : ∃ (w : Set E)(b : HilbertBasis w 𝕜 E), ⇑b = (coe : w → E) :=
-  let ⟨w, hw, hw', hw''⟩ := (orthonormalEmpty 𝕜 E).exists_hilbertBasis_extension
+  let ⟨w, hw, hw', hw''⟩ := (orthonormal_empty 𝕜 E).exists_hilbertBasis_extension
   ⟨w, hw, hw''⟩
 #align exists_hilbert_basis exists_hilbertBasis
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/e3fb84046afd187b710170887195d50bada934ee

@@ -278,7 +278,7 @@ protected theorem range_linearIsometry [∀ i, CompleteSpace (G i)] :
     refine' mem_supr_of_mem i _
     exact LinearMap.mem_range_self _ (f i)
   · apply topological_closure_minimal
-    · refine' supᵢ_le _
+    · refine' iSup_le _
       rintro i x ⟨x, rfl⟩
       use lp.single 2 i x
       exact hV.linear_isometry_apply_single x
@@ -392,7 +392,7 @@ theorem Orthonormal.isHilbertSum {v : ι → E} (hv : Orthonormal 𝕜 v)
   IsHilbertSum.mk hv.OrthogonalFamily
     (by
       convert hsp
-      simp [← LinearMap.span_singleton_eq_range, ← Submodule.span_unionᵢ])
+      simp [← LinearMap.span_singleton_eq_range, ← Submodule.span_iUnion])
 #align orthonormal.is_hilbert_sum Orthonormal.isHilbertSum
 
 theorem Submodule.isHilbertSumOrthogonal (K : Submodule 𝕜 E) [hK : CompleteSpace K] :
@@ -403,7 +403,7 @@ theorem Submodule.isHilbertSumOrthogonal (K : Submodule 𝕜 E) [hK : CompleteSp
     cases b <;> first |exact orthogonal.complete_space K|assumption
   refine' IsHilbertSum.mkInternal _ K.orthogonal_family_self _
   refine' le_trans _ (Submodule.le_topologicalClosure _)
-  rw [supᵢ_bool_eq, cond, cond]
+  rw [iSup_bool_eq, cond, cond]
   refine' Codisjoint.top_le _
   exact submodule.is_compl_orthogonal_of_complete_space.codisjoint
 #align submodule.is_hilbert_sum_orthogonal Submodule.isHilbertSumOrthogonal
@@ -549,12 +549,12 @@ theorem finite_spans_dense (b : HilbertBasis ι 𝕜 E) :
   eq_top_iff.mpr <|
     b.dense_span.ge.trans
       (by
-        simp_rw [← Submodule.span_unionᵢ]
+        simp_rw [← Submodule.span_iUnion]
         exact
           topological_closure_mono
             (span_mono <|
               set.range_subset_iff.mpr fun i =>
-                Set.mem_unionᵢ_of_mem {i} <|
+                Set.mem_iUnion_of_mem {i} <|
                   finset.mem_coe.mpr <| Finset.mem_image_of_mem _ <| Finset.mem_singleton_self i))
 #align hilbert_basis.finite_spans_dense HilbertBasis.finite_spans_dense
 

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

@@ -624,7 +624,7 @@ variable (𝕜 E)
 
 /-- A Hilbert space admits a Hilbert basis. -/
 theorem exists_hilbertBasis : ∃ (w : Set E)(b : HilbertBasis w 𝕜 E), ⇑b = (coe : w → E) :=
-  let ⟨w, hw, hw', hw''⟩ := (orthonormal_empty 𝕜 E).exists_hilbertBasis_extension
+  let ⟨w, hw, hw', hw''⟩ := (orthonormalEmpty 𝕜 E).exists_hilbertBasis_extension
   ⟨w, hw, hw''⟩
 #align exists_hilbert_basis exists_hilbertBasis
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/55d771df074d0dd020139ee1cd4b95521422df9f

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Heather Macbeth
 
 ! This file was ported from Lean 3 source module analysis.inner_product_space.l2_space
-! leanprover-community/mathlib commit c78cad350eb321c81e1eacf68d14e3d3ba1e17f7
+! leanprover-community/mathlib commit 46b633fd842bef9469441c0209906f6dddd2b4f5
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -93,9 +93,11 @@ noncomputable section
 
 variable {ι : Type _}
 
-variable {𝕜 : Type _} [IsROrC 𝕜] {E : Type _} [InnerProductSpace 𝕜 E] [cplt : CompleteSpace E]
+variable {𝕜 : Type _} [IsROrC 𝕜] {E : Type _}
 
-variable {G : ι → Type _} [∀ i, InnerProductSpace 𝕜 (G i)]
+variable [NormedAddCommGroup E] [InnerProductSpace 𝕜 E] [cplt : CompleteSpace E]
+
+variable {G : ι → Type _} [∀ i, NormedAddCommGroup (G i)] [∀ i, InnerProductSpace 𝕜 (G i)]
 
 -- mathport name: «expr⟪ , ⟫»
 local notation "⟪" x ", " y "⟫" => @inner 𝕜 _ _ x y
@@ -127,7 +129,7 @@ instance : InnerProductSpace 𝕜 (lp G 2) :=
         ‖f‖ ^ 2 = ‖f‖ ^ (2 : ℝ≥0∞).toReal := by norm_cast
         _ = ∑' i, ‖f i‖ ^ (2 : ℝ≥0∞).toReal := (lp.norm_rpow_eq_tsum _ f)
         _ = ∑' i, ‖f i‖ ^ 2 := by norm_cast
-        _ = ∑' i, re ⟪f i, f i⟫ := by simp only [norm_sq_eq_inner]
+        _ = ∑' i, re ⟪f i, f i⟫ := by simp only [@norm_sq_eq_inner 𝕜]
         _ = re (∑' i, ⟪f i, f i⟫) := (is_R_or_C.re_clm.map_tsum _).symm
         _ = _ := by congr
         
@@ -183,7 +185,7 @@ theorem inner_single_left (i : ι) (a : G i) (f : lp G 2) : ⟪lp.single 2 i a,
 #align lp.inner_single_left lp.inner_single_left
 
 theorem inner_single_right (i : ι) (a : G i) (f : lp G 2) : ⟪f, lp.single 2 i a⟫ = ⟪f i, a⟫ := by
-  simpa [inner_conj_symm] using congr_arg conj (inner_single_left i a f)
+  simpa [inner_conj_symm] using congr_arg conj (@inner_single_left _ 𝕜 _ _ _ _ i a f)
 #align lp.inner_single_right lp.inner_single_right
 
 end lp
@@ -472,6 +474,7 @@ protected theorem hasSum_repr_symm (b : HilbertBasis ι 𝕜 E) (f : ℓ²(ι, 
     exact (↑b.repr.symm.to_continuous_linear_equiv : ℓ²(ι, 𝕜) →L[𝕜] E).HasSum this
   ext i
   apply b.repr.injective
+  letI : NormedSpace 𝕜 ↥(lp (fun i : ι => 𝕜) 2) := by infer_instance
   have : lp.single 2 i (f i * 1) = f i • lp.single 2 i 1 := lp.single_smul 2 i (1 : 𝕜) (f i)
   rw [mul_one] at this
   rw [LinearIsometryEquiv.map_smul, b.repr_self, ← this,

mathlib commit https://github.com/leanprover-community/mathlib/commit/57e09a1296bfb4330ddf6624f1028ba186117d82

@@ -417,7 +417,7 @@ variable (ι) (𝕜) (E)
 
 /-- A Hilbert basis on `ι` for an inner product space `E` is an identification of `E` with the `lp`
 space `ℓ²(ι, 𝕜)`. -/
-structure HilbertBasis where of_repr ::
+structure HilbertBasis where ofRepr ::
   repr : E ≃ₗᵢ[𝕜] ℓ²(ι, 𝕜)
 #align hilbert_basis HilbertBasis
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/7ec294687917cbc5c73620b4414ae9b5dd9ae1b4

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Heather Macbeth
 
 ! This file was ported from Lean 3 source module analysis.inner_product_space.l2_space
-! leanprover-community/mathlib commit 4681620dafca6a7d710f437bd10fb69428ec2209
+! leanprover-community/mathlib commit c78cad350eb321c81e1eacf68d14e3d3ba1e17f7
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -501,7 +501,7 @@ protected theorem dense_span (b : HilbertBasis ι 𝕜 E) :
 protected theorem hasSum_inner_mul_inner (b : HilbertBasis ι 𝕜 E) (x y : E) :
     HasSum (fun i => ⟪x, b i⟫ * ⟪b i, y⟫) ⟪x, y⟫ :=
   by
-  convert(b.has_sum_repr y).mapL (innerSL x)
+  convert(b.has_sum_repr y).mapL (innerSL _ x)
   ext i
   rw [innerSL_apply, b.repr_apply_apply, inner_smul_right, mul_comm]
 #align hilbert_basis.has_sum_inner_mul_inner HilbertBasis.hasSum_inner_mul_inner

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

@@ -200,7 +200,7 @@ include cplt hV
 protected theorem summable_of_lp (f : lp G 2) : Summable fun i => V i (f i) :=
   by
   rw [hV.summable_iff_norm_sq_summable]
-  convert (lp.memℓp f).Summable _
+  convert(lp.memℓp f).Summable _
   · norm_cast
   · norm_num
 #align orthogonal_family.summable_of_lp OrthogonalFamily.summable_of_lp
@@ -223,7 +223,7 @@ protected def linearIsometry : lp G 2 →ₗᵢ[𝕜] E
       suffices ‖∑' i : ι, V i (f i)‖ ^ (2 : ℝ≥0∞).toReal = ‖f‖ ^ (2 : ℝ≥0∞).toReal by
         exact Real.rpow_left_injOn H.ne' (norm_nonneg _) (norm_nonneg _) this
       refine' tendsto_nhds_unique _ (lp.hasSum_norm H f)
-      convert (hV.summable_of_lp f).HasSum.norm.rpow_const (Or.inr H.le)
+      convert(hV.summable_of_lp f).HasSum.norm.rpow_const (Or.inr H.le)
       ext s
       exact_mod_cast (hV.norm_sum f s).symm
 #align orthogonal_family.linear_isometry OrthogonalFamily.linearIsometry
@@ -501,7 +501,7 @@ protected theorem dense_span (b : HilbertBasis ι 𝕜 E) :
 protected theorem hasSum_inner_mul_inner (b : HilbertBasis ι 𝕜 E) (x y : E) :
     HasSum (fun i => ⟪x, b i⟫ * ⟪b i, y⟫) ⟪x, y⟫ :=
   by
-  convert (b.has_sum_repr y).mapL (innerSL x)
+  convert(b.has_sum_repr y).mapL (innerSL x)
   ext i
   rw [innerSL_apply, b.repr_apply_apply, inner_smul_right, mul_comm]
 #align hilbert_basis.has_sum_inner_mul_inner HilbertBasis.hasSum_inner_mul_inner

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Heather Macbeth
 
 ! This file was ported from Lean 3 source module analysis.inner_product_space.l2_space
-! leanprover-community/mathlib commit 3fc0b254310908f70a1a75f01147d52e53e9f8a2
+! leanprover-community/mathlib commit 4681620dafca6a7d710f437bd10fb69428ec2209
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -21,7 +21,7 @@ dependent functions `f : Π i, G i` for which `∑' i, ‖f i‖ ^ 2`, the sum o
 summable.  This construction is sometimes called the *Hilbert sum* of the family `G`.  By choosing
 `G` to be `ι → 𝕜`, the Hilbert space `ℓ²(ι, 𝕜)` may be seen as a special case of this construction.
 
-We also define a *predicate* `is_hilbert_sum 𝕜 E V`, where `V : Π i, G i →ₗᵢ[𝕜] E`, expressing that
+We also define a *predicate* `is_hilbert_sum 𝕜 G V`, where `V : Π i, G i →ₗᵢ[𝕜] E`, expressing that
 `V` is an `orthogonal_family` and that the associated map `lp G 2 →ₗᵢ[𝕜] E` is surjective.
 
 ## Main definitions
@@ -33,7 +33,7 @@ We also define a *predicate* `is_hilbert_sum 𝕜 E V`, where `V : Π i, G i →
 
 * `is_hilbert_sum`: Given a Hilbert space `E`, a family `G` of inner product
   spaces and a family `V : Π i, G i →ₗᵢ[𝕜] E` of isometric embeddings of the `G i` into `E`,
-  `is_hilbert_sum 𝕜 E V` means that `V` is an `orthogonal_family` and that the above
+  `is_hilbert_sum 𝕜 G V` means that `V` is an `orthogonal_family` and that the above
   linear isometry is surjective.
 
 * `is_hilbert_sum.linear_isometry_equiv`: If a Hilbert space `E` is a Hilbert sum of the
@@ -193,7 +193,7 @@ end lp
 
 namespace OrthogonalFamily
 
-variable {V : ∀ i, G i →ₗᵢ[𝕜] E} (hV : OrthogonalFamily 𝕜 V)
+variable {V : ∀ i, G i →ₗᵢ[𝕜] E} (hV : OrthogonalFamily 𝕜 G V)
 
 include cplt hV
 
@@ -287,7 +287,7 @@ end OrthogonalFamily
 
 section IsHilbertSum
 
-variable (𝕜 E) (V : ∀ i, G i →ₗᵢ[𝕜] E) (F : ι → Submodule 𝕜 E)
+variable (𝕜 G) (V : ∀ i, G i →ₗᵢ[𝕜] E) (F : ι → Submodule 𝕜 E)
 
 include cplt
 
@@ -299,16 +299,16 @@ Keeping in mind that `lp G 2` is "the" external Hilbert sum of `G : ι → Type*
 to `direct_sum.is_internal`, except that we don't express it in terms of actual submodules. -/
 @[protect_proj]
 structure IsHilbertSum : Prop where ofSurjective ::
-  OrthogonalFamily : OrthogonalFamily 𝕜 V
+  OrthogonalFamily : OrthogonalFamily 𝕜 G V
   surjective_isometry : Function.Surjective OrthogonalFamily.LinearIsometry
 #align is_hilbert_sum IsHilbertSum
 
-variable {𝕜 E V}
+variable {𝕜 G V}
 
 /-- If `V : Π i, G i →ₗᵢ[𝕜] E` is an orthogonal family such that the supremum of the ranges of
 `V i` is dense, then `(E, V)` is a Hilbert sum of `G`. -/
-theorem IsHilbertSum.mk [∀ i, CompleteSpace <| G i] (hVortho : OrthogonalFamily 𝕜 V)
-    (hVtotal : ⊤ ≤ (⨆ i, (V i).toLinearMap.range).topologicalClosure) : IsHilbertSum 𝕜 E V :=
+theorem IsHilbertSum.mk [∀ i, CompleteSpace <| G i] (hVortho : OrthogonalFamily 𝕜 G V)
+    (hVtotal : ⊤ ≤ (⨆ i, (V i).toLinearMap.range).topologicalClosure) : IsHilbertSum 𝕜 G V :=
   { OrthogonalFamily := hVortho
     surjective_isometry := by
       rw [← LinearIsometry.coe_toLinearMap]
@@ -319,9 +319,9 @@ theorem IsHilbertSum.mk [∀ i, CompleteSpace <| G i] (hVortho : OrthogonalFamil
 
 /-- This is `orthogonal_family.is_hilbert_sum` in the case of actual inclusions from subspaces. -/
 theorem IsHilbertSum.mkInternal [∀ i, CompleteSpace <| F i]
-    (hFortho : @OrthogonalFamily 𝕜 E _ _ _ (fun i => F i) _ fun i => (F i).subtypeₗᵢ)
+    (hFortho : OrthogonalFamily 𝕜 (fun i => F i) fun i => (F i).subtypeₗᵢ)
     (hFtotal : ⊤ ≤ (⨆ i, F i).topologicalClosure) :
-    @IsHilbertSum _ 𝕜 _ E _ _ (fun i => F i) _ fun i => (F i).subtypeₗᵢ :=
+    IsHilbertSum 𝕜 (fun i => F i) fun i => (F i).subtypeₗᵢ :=
   IsHilbertSum.mk hFortho (by simpa [subtypeₗᵢ_to_linear_map, range_subtype] using hFtotal)
 #align is_hilbert_sum.mk_internal IsHilbertSum.mkInternal
 
@@ -329,14 +329,14 @@ theorem IsHilbertSum.mkInternal [∀ i, CompleteSpace <| F i]
 i.e `lp G 2`.
 
 Note that this goes in the opposite direction from `orthogonal_family.linear_isometry`. -/
-noncomputable def IsHilbertSum.linearIsometryEquiv (hV : IsHilbertSum 𝕜 E V) : E ≃ₗᵢ[𝕜] lp G 2 :=
+noncomputable def IsHilbertSum.linearIsometryEquiv (hV : IsHilbertSum 𝕜 G V) : E ≃ₗᵢ[𝕜] lp G 2 :=
   LinearIsometryEquiv.symm <|
     LinearIsometryEquiv.ofSurjective hV.OrthogonalFamily.LinearIsometry hV.surjective_isometry
 #align is_hilbert_sum.linear_isometry_equiv IsHilbertSum.linearIsometryEquiv
 
 /-- In the canonical isometric isomorphism between a Hilbert sum `E` of `G` and `lp G 2`,
 a vector `w : lp G 2` is the image of the infinite sum of the associated elements in `E`. -/
-protected theorem IsHilbertSum.linearIsometryEquiv_symm_apply (hV : IsHilbertSum 𝕜 E V)
+protected theorem IsHilbertSum.linearIsometryEquiv_symm_apply (hV : IsHilbertSum 𝕜 G V)
     (w : lp G 2) : hV.LinearIsometryEquiv.symm w = ∑' i, V i (w i) := by
   simp [IsHilbertSum.linearIsometryEquiv, OrthogonalFamily.linearIsometry_apply]
 #align is_hilbert_sum.linear_isometry_equiv_symm_apply IsHilbertSum.linearIsometryEquiv_symm_apply
@@ -344,7 +344,7 @@ protected theorem IsHilbertSum.linearIsometryEquiv_symm_apply (hV : IsHilbertSum
 /-- In the canonical isometric isomorphism between a Hilbert sum `E` of `G` and `lp G 2`,
 a vector `w : lp G 2` is the image of the infinite sum of the associated elements in `E`, and this
 sum indeed converges. -/
-protected theorem IsHilbertSum.hasSum_linearIsometryEquiv_symm (hV : IsHilbertSum 𝕜 E V)
+protected theorem IsHilbertSum.hasSum_linearIsometryEquiv_symm (hV : IsHilbertSum 𝕜 G V)
     (w : lp G 2) : HasSum (fun i => V i (w i)) (hV.LinearIsometryEquiv.symm w) := by
   simp [IsHilbertSum.linearIsometryEquiv, OrthogonalFamily.hasSum_linearIsometry]
 #align is_hilbert_sum.has_sum_linear_isometry_equiv_symm IsHilbertSum.hasSum_linearIsometryEquiv_symm
@@ -353,7 +353,7 @@ protected theorem IsHilbertSum.hasSum_linearIsometryEquiv_symm (hV : IsHilbertSu
 `lp G 2`, an "elementary basis vector" in `lp G 2` supported at `i : ι` is the image of the
 associated element in `E`. -/
 @[simp]
-protected theorem IsHilbertSum.linearIsometryEquiv_symm_apply_single (hV : IsHilbertSum 𝕜 E V)
+protected theorem IsHilbertSum.linearIsometryEquiv_symm_apply_single (hV : IsHilbertSum 𝕜 G V)
     {i : ι} (x : G i) : hV.LinearIsometryEquiv.symm (lp.single 2 i x) = V i x := by
   simp [IsHilbertSum.linearIsometryEquiv, OrthogonalFamily.linearIsometry_apply_single]
 #align is_hilbert_sum.linear_isometry_equiv_symm_apply_single IsHilbertSum.linearIsometryEquiv_symm_apply_single
@@ -363,7 +363,7 @@ protected theorem IsHilbertSum.linearIsometryEquiv_symm_apply_single (hV : IsHil
 elements of `E`. -/
 @[simp]
 protected theorem IsHilbertSum.linearIsometryEquiv_symm_apply_dfinsupp_sum_single
-    (hV : IsHilbertSum 𝕜 E V) (W₀ : Π₀ i : ι, G i) :
+    (hV : IsHilbertSum 𝕜 G V) (W₀ : Π₀ i : ι, G i) :
     hV.LinearIsometryEquiv.symm (W₀.Sum (lp.single 2)) = W₀.Sum fun i => V i := by
   simp [IsHilbertSum.linearIsometryEquiv, OrthogonalFamily.linearIsometry_apply_dfinsupp_sum_single]
 #align is_hilbert_sum.linear_isometry_equiv_symm_apply_dfinsupp_sum_single IsHilbertSum.linearIsometryEquiv_symm_apply_dfinsupp_sum_single
@@ -373,7 +373,7 @@ protected theorem IsHilbertSum.linearIsometryEquiv_symm_apply_dfinsupp_sum_singl
 elements of `E`. -/
 @[simp]
 protected theorem IsHilbertSum.linearIsometryEquiv_apply_dfinsupp_sum_single
-    (hV : IsHilbertSum 𝕜 E V) (W₀ : Π₀ i : ι, G i) :
+    (hV : IsHilbertSum 𝕜 G V) (W₀ : Π₀ i : ι, G i) :
     (hV.LinearIsometryEquiv (W₀.Sum fun i => V i) : ∀ i, G i) = W₀ :=
   by
   rw [← hV.linear_isometry_equiv_symm_apply_dfinsupp_sum_single]
@@ -386,8 +386,7 @@ protected theorem IsHilbertSum.linearIsometryEquiv_apply_dfinsupp_sum_single
 the family of linear isometries `λ i, λ k, k • v i`. -/
 theorem Orthonormal.isHilbertSum {v : ι → E} (hv : Orthonormal 𝕜 v)
     (hsp : ⊤ ≤ (span 𝕜 (Set.range v)).topologicalClosure) :
-    @IsHilbertSum _ 𝕜 _ _ _ _ (fun i : ι => 𝕜) _ fun i =>
-      LinearIsometry.toSpanSingleton 𝕜 E (hv.1 i) :=
+    IsHilbertSum 𝕜 (fun i : ι => 𝕜) fun i => LinearIsometry.toSpanSingleton 𝕜 E (hv.1 i) :=
   IsHilbertSum.mk hv.OrthogonalFamily
     (by
       convert hsp
@@ -395,11 +394,9 @@ theorem Orthonormal.isHilbertSum {v : ι → E} (hv : Orthonormal 𝕜 v)
 #align orthonormal.is_hilbert_sum Orthonormal.isHilbertSum
 
 theorem Submodule.isHilbertSumOrthogonal (K : Submodule 𝕜 E) [hK : CompleteSpace K] :
-    @IsHilbertSum _ 𝕜 _ E _ _ (fun b => ((cond b K Kᗮ : Submodule 𝕜 E) : Type _)) _ fun b =>
-      (cond b K Kᗮ).subtypeₗᵢ :=
+    IsHilbertSum 𝕜 (fun b => ↥(cond b K Kᗮ)) fun b => (cond b K Kᗮ).subtypeₗᵢ :=
   by
-  have : ∀ b, CompleteSpace ((cond b K Kᗮ : Submodule 𝕜 E) : Type _) :=
-    by
+  have : ∀ b, CompleteSpace ↥(cond b K Kᗮ) := by
     intro b
     cases b <;> first |exact orthogonal.complete_space K|assumption
   refine' IsHilbertSum.mkInternal _ K.orthogonal_family_self _

mathlib commit https://github.com/leanprover-community/mathlib/commit/1a313d8bba1bad05faba71a4a4e9742ab5bd9efd

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Heather Macbeth
 
 ! This file was ported from Lean 3 source module analysis.inner_product_space.l2_space
-! leanprover-community/mathlib commit 639b66d9330da2cd8dd02be1a51b6d10d058e5e4
+! leanprover-community/mathlib commit 3fc0b254310908f70a1a75f01147d52e53e9f8a2
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -133,11 +133,11 @@ instance : InnerProductSpace 𝕜 (lp G 2) :=
         
       · norm_num
       · exact summable_inner f f
-    conj_sym := fun f g => by
+    conj_symm := fun f g => by
       calc
         conj _ = conj (∑' i, ⟪g i, f i⟫) := by congr
         _ = ∑' i, conj ⟪g i, f i⟫ := is_R_or_C.conj_cle.map_tsum
-        _ = ∑' i, ⟪f i, g i⟫ := by simp only [inner_conj_sym]
+        _ = ∑' i, ⟪f i, g i⟫ := by simp only [inner_conj_symm]
         _ = _ := by congr
         
     add_left := fun f₁ f₂ g =>
@@ -183,7 +183,7 @@ theorem inner_single_left (i : ι) (a : G i) (f : lp G 2) : ⟪lp.single 2 i a,
 #align lp.inner_single_left lp.inner_single_left
 
 theorem inner_single_right (i : ι) (a : G i) (f : lp G 2) : ⟪f, lp.single 2 i a⟫ = ⟪f i, a⟫ := by
-  simpa [inner_conj_sym] using congr_arg conj (inner_single_left i a f)
+  simpa [inner_conj_symm] using congr_arg conj (inner_single_left i a f)
 #align lp.inner_single_right lp.inner_single_right
 
 end lp

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

@@ -624,7 +624,7 @@ variable (𝕜 E)
 
 /-- A Hilbert space admits a Hilbert basis. -/
 theorem exists_hilbertBasis : ∃ (w : Set E)(b : HilbertBasis w 𝕜 E), ⇑b = (coe : w → E) :=
-  let ⟨w, hw, hw', hw''⟩ := (orthonormalEmpty 𝕜 E).exists_hilbertBasis_extension
+  let ⟨w, hw, hw', hw''⟩ := (orthonormal_empty 𝕜 E).exists_hilbertBasis_extension
   ⟨w, hw, hw''⟩
 #align exists_hilbert_basis exists_hilbertBasis
 

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

@@ -125,7 +125,7 @@ instance : InnerProductSpace 𝕜 (lp G 2) :=
       by
       calc
         ‖f‖ ^ 2 = ‖f‖ ^ (2 : ℝ≥0∞).toReal := by norm_cast
-        _ = ∑' i, ‖f i‖ ^ (2 : ℝ≥0∞).toReal := lp.norm_rpow_eq_tsum _ f
+        _ = ∑' i, ‖f i‖ ^ (2 : ℝ≥0∞).toReal := (lp.norm_rpow_eq_tsum _ f)
         _ = ∑' i, ‖f i‖ ^ 2 := by norm_cast
         _ = ∑' i, re ⟪f i, f i⟫ := by simp only [norm_sq_eq_inner]
         _ = re (∑' i, ⟪f i, f i⟫) := (is_R_or_C.re_clm.map_tsum _).symm
@@ -146,7 +146,7 @@ instance : InnerProductSpace 𝕜 (lp G 2) :=
         _ = ∑' i, ⟪(f₁ + f₂) i, g i⟫ := _
         _ = ∑' i, ⟪f₁ i, g i⟫ + ⟪f₂ i, g i⟫ := by
           simp only [inner_add_left, Pi.add_apply, coe_fn_add]
-        _ = (∑' i, ⟪f₁ i, g i⟫) + ∑' i, ⟪f₂ i, g i⟫ := tsum_add _ _
+        _ = (∑' i, ⟪f₁ i, g i⟫) + ∑' i, ⟪f₂ i, g i⟫ := (tsum_add _ _)
         _ = _ := by congr
         
       · congr

mathlib commit https://github.com/leanprover-community/mathlib/commit/eb0cb4511aaef0da2462207b67358a0e1fe1e2ee

@@ -87,7 +87,7 @@ Hilbert space, Hilbert sum, l2, Hilbert basis, unitary equivalence, isometric is
 
 open IsROrC Submodule Filter
 
-open BigOperators NNReal Ennreal Classical ComplexConjugate Topology
+open BigOperators NNReal ENNReal Classical ComplexConjugate Topology
 
 noncomputable section
 
@@ -471,7 +471,7 @@ protected theorem hasSum_repr_symm (b : HilbertBasis ι 𝕜 E) (f : ℓ²(ι, 
     (fun i : ι => f i • b i) = fun b_1 : ι =>
       b.repr.symm.to_continuous_linear_equiv ((fun i : ι => lp.single 2 i (f i)) b_1)
   · rw [H]
-    have : HasSum (fun i : ι => lp.single 2 i (f i)) f := lp.hasSum_single Ennreal.two_ne_top f
+    have : HasSum (fun i : ι => lp.single 2 i (f i)) f := lp.hasSum_single ENNReal.two_ne_top f
     exact (↑b.repr.symm.to_continuous_linear_equiv : ℓ²(ι, 𝕜) →L[𝕜] E).HasSum this
   ext i
   apply b.repr.injective

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

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

@@ -118,7 +118,7 @@ instance instInnerProductSpace : InnerProductSpace 𝕜 (lp G 2) :=
     norm_sq_eq_inner := fun f => by
       calc
         ‖f‖ ^ 2 = ‖f‖ ^ (2 : ℝ≥0∞).toReal := by norm_cast
-        _ = ∑' i, ‖f i‖ ^ (2 : ℝ≥0∞).toReal := (lp.norm_rpow_eq_tsum ?_ f)
+        _ = ∑' i, ‖f i‖ ^ (2 : ℝ≥0∞).toReal := lp.norm_rpow_eq_tsum ?_ f
         _ = ∑' i, ‖f i‖ ^ (2 : ℕ) := by norm_cast
         _ = ∑' i, re ⟪f i, f i⟫ := by
           congr
@@ -139,7 +139,7 @@ instance instInnerProductSpace : InnerProductSpace 𝕜 (lp G 2) :=
         _ = ∑' i, ⟪(f₁ + f₂) i, g i⟫ := ?_
         _ = ∑' i, (⟪f₁ i, g i⟫ + ⟪f₂ i, g i⟫) := by
           simp only [inner_add_left, Pi.add_apply, coeFn_add]
-        _ = (∑' i, ⟪f₁ i, g i⟫) + ∑' i, ⟪f₂ i, g i⟫ := (tsum_add ?_ ?_)
+        _ = (∑' i, ⟪f₁ i, g i⟫) + ∑' i, ⟪f₂ i, g i⟫ := tsum_add ?_ ?_
         _ = _ := by congr
       · congr
       · exact summable_inner f₁ g

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.

@@ -82,14 +82,13 @@ Hilbert space, Hilbert sum, l2, Hilbert basis, unitary equivalence, isometric is
 -/
 
 
-open IsROrC Submodule Filter
+open RCLike Submodule Filter
 
 open scoped BigOperators NNReal ENNReal Classical ComplexConjugate Topology
 
 noncomputable section
 
-variable {ι : Type*}
-variable {𝕜 : Type*} [IsROrC 𝕜] {E : Type*}
+variable {ι 𝕜 : Type*} [RCLike 𝕜] {E : Type*}
 variable [NormedAddCommGroup E] [InnerProductSpace 𝕜 E] [cplt : CompleteSpace E]
 variable {G : ι → Type*} [∀ i, NormedAddCommGroup (G i)] [∀ i, InnerProductSpace 𝕜 (G i)]
 
@@ -126,13 +125,13 @@ instance instInnerProductSpace : InnerProductSpace 𝕜 (lp G 2) :=
           funext i
           rw [norm_sq_eq_inner (𝕜 := 𝕜)]
           -- Porting note: `simp` couldn't do this anymore
-        _ = re (∑' i, ⟪f i, f i⟫) := (IsROrC.reCLM.map_tsum ?_).symm
+        _ = re (∑' i, ⟪f i, f i⟫) := (RCLike.reCLM.map_tsum ?_).symm
       · norm_num
       · exact summable_inner f f
     conj_symm := fun f g => by
       calc
         conj _ = conj (∑' i, ⟪g i, f i⟫) := by congr
-        _ = ∑' i, conj ⟪g i, f i⟫ := IsROrC.conjCLE.map_tsum
+        _ = ∑' i, conj ⟪g i, f i⟫ := RCLike.conjCLE.map_tsum
         _ = ∑' i, ⟪f i, g i⟫ := by simp only [inner_conj_symm]
         _ = _ := by congr
     add_left := fun f₁ f₂ g => by

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)

@@ -89,11 +89,8 @@ open scoped BigOperators NNReal ENNReal Classical ComplexConjugate Topology
 noncomputable section
 
 variable {ι : Type*}
-
 variable {𝕜 : Type*} [IsROrC 𝕜] {E : Type*}
-
 variable [NormedAddCommGroup E] [InnerProductSpace 𝕜 E] [cplt : CompleteSpace E]
-
 variable {G : ι → Type*} [∀ i, NormedAddCommGroup (G i)] [∀ i, InnerProductSpace 𝕜 (G i)]
 
 local notation "⟪" x ", " y "⟫" => @inner 𝕜 _ _ x y
@@ -271,7 +268,6 @@ end OrthogonalFamily
 section IsHilbertSum
 
 variable (𝕜 G)
-
 variable (V : ∀ i, G i →ₗᵢ[𝕜] E) (F : ι → Submodule 𝕜 E)
 
 /-- Given a family of Hilbert spaces `G : ι → Type*`, a Hilbert sum of `G` consists of a Hilbert

This is a very large PR, but it has been reviewed piecemeal already in PRs to the bump/v4.7.0 branch as we update to intermediate nightlies.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Kyle Miller <kmill31415@gmail.com> Co-authored-by: damiano <adomani@gmail.com>

@@ -346,11 +346,10 @@ protected theorem IsHilbertSum.linearIsometryEquiv_symm_apply_single (hV : IsHil
 /-- In the canonical isometric isomorphism between a Hilbert sum `E` of `G : ι → Type*` and
 `lp G 2`, a finitely-supported vector in `lp G 2` is the image of the associated finite sum of
 elements of `E`. -/
-@[simp]
 protected theorem IsHilbertSum.linearIsometryEquiv_symm_apply_dfinsupp_sum_single
     (hV : IsHilbertSum 𝕜 G V) (W₀ : Π₀ i : ι, G i) :
     hV.linearIsometryEquiv.symm (W₀.sum (lp.single 2)) = W₀.sum fun i => V i := by
-  simp [IsHilbertSum.linearIsometryEquiv, OrthogonalFamily.linearIsometry_apply_dfinsupp_sum_single]
+  simp only [map_dfinsupp_sum, IsHilbertSum.linearIsometryEquiv_symm_apply_single]
 #align is_hilbert_sum.linear_isometry_equiv_symm_apply_dfinsupp_sum_single IsHilbertSum.linearIsometryEquiv_symm_apply_dfinsupp_sum_single
 
 /-- In the canonical isometric isomorphism between a Hilbert sum `E` of `G : ι → Type*` and
@@ -359,7 +358,8 @@ elements of `E`. -/
 @[simp]
 protected theorem IsHilbertSum.linearIsometryEquiv_apply_dfinsupp_sum_single
     (hV : IsHilbertSum 𝕜 G V) (W₀ : Π₀ i : ι, G i) :
-    (hV.linearIsometryEquiv (W₀.sum fun i => V i) : ∀ i, G i) = W₀ := by
+    ((W₀.sum (γ := lp G 2) fun a b ↦ hV.linearIsometryEquiv (V a b)) : ∀ i, G i) = W₀ := by
+  rw [← map_dfinsupp_sum]
   rw [← hV.linearIsometryEquiv_symm_apply_dfinsupp_sum_single]
   rw [LinearIsometryEquiv.apply_symm_apply]
   ext i

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".

@@ -128,7 +128,7 @@ instance instInnerProductSpace : InnerProductSpace 𝕜 (lp G 2) :=
           congr
           funext i
           rw [norm_sq_eq_inner (𝕜 := 𝕜)]
-          -- porting note: `simp` couldn't do this anymore
+          -- Porting note: `simp` couldn't do this anymore
         _ = re (∑' i, ⟪f i, f i⟫) := (IsROrC.reCLM.map_tsum ?_).symm
       · norm_num
       · exact summable_inner f f
@@ -248,7 +248,7 @@ protected theorem linearIsometry_apply_dfinsupp_sum_single (W₀ : Π₀ i : ι,
 protected theorem range_linearIsometry [∀ i, CompleteSpace (G i)] :
     LinearMap.range hV.linearIsometry.toLinearMap =
       (⨆ i, LinearMap.range (V i).toLinearMap).topologicalClosure := by
-    -- porting note: dot notation broken
+    -- Porting note: dot notation broken
   refine' le_antisymm _ _
   · rintro x ⟨f, rfl⟩
     refine' mem_closure_of_tendsto (hV.hasSum_linearIsometry f) (eventually_of_forall _)

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>

@@ -444,8 +444,8 @@ protected theorem orthonormal (b : HilbertBasis ι 𝕜 E) : Orthonormal 𝕜 b
 protected theorem hasSum_repr_symm (b : HilbertBasis ι 𝕜 E) (f : ℓ²(ι, 𝕜)) :
     HasSum (fun i => f i • b i) (b.repr.symm f) := by
   suffices H : (fun i : ι => f i • b i) = fun b_1 : ι => b.repr.symm.toContinuousLinearEquiv <|
-    (fun i : ι => lp.single 2 i (f i) (E := (fun _ : ι => 𝕜))) b_1
-  · rw [H]
+      (fun i : ι => lp.single 2 i (f i) (E := (fun _ : ι => 𝕜))) b_1 by
+    rw [H]
     have : HasSum (fun i : ι => lp.single 2 i (f i)) f := lp.hasSum_single ENNReal.two_ne_top f
     exact (↑b.repr.symm.toContinuousLinearEquiv : ℓ²(ι, 𝕜) →L[𝕜] E).hasSum this
   ext i

It happens often that we have p q : ℝ≥0 that are conjugate. So far, we only had a predicate for real numbers to be conjugate, which made dealing with ℝ≥0 conjugates clumsy.

This PR

• introduces NNReal.IsConjExponent, NNReal.conjExponent
• renames Real.IsConjugateExponent, Real.conjugateExponent to Real.IsConjExponent, Real.conjExponent
• renames a few more lemmas to match up the Real and NNReal versions

From LeanAPAP

@@ -110,7 +110,7 @@ namespace lp
 theorem summable_inner (f g : lp G 2) : Summable fun i => ⟪f i, g i⟫ := by
   -- Apply the Direct Comparison Test, comparing with ∑' i, ‖f i‖ * ‖g i‖ (summable by Hölder)
   refine' .of_norm_bounded (fun i => ‖f i‖ * ‖g i‖) (lp.summable_mul _ f g) _
-  · rw [Real.isConjugateExponent_iff] <;> norm_num
+  · rw [Real.isConjExponent_iff]; norm_num
   intro i
   -- Then apply Cauchy-Schwarz pointwise
   exact norm_inner_le_norm (𝕜 := 𝕜) _ _

Rename

• Complex.equivRealProdClm → Complex.equivRealProdCLM;
  • TODO: should this one use CLE?
• Complex.reClm → Complex.reCLM;
• Complex.imClm → Complex.imCLM;
• Complex.conjLie → Complex.conjLIE;
• Complex.conjCle → Complex.conjCLE;
• Complex.ofRealLi → Complex.ofRealLI;
• Complex.ofRealClm → Complex.ofRealCLM;
• fderivInnerClm → fderivInnerCLM;
• LinearPMap.adjointDomainMkClm → LinearPMap.adjointDomainMkCLM;
• LinearPMap.adjointDomainMkClmExtend → LinearPMap.adjointDomainMkCLMExtend;
• IsROrC.reClm → IsROrC.reCLM;
• IsROrC.imClm → IsROrC.imCLM;
• IsROrC.conjLie → IsROrC.conjLIE;
• IsROrC.conjCle → IsROrC.conjCLE;
• IsROrC.ofRealLi → IsROrC.ofRealLI;
• IsROrC.ofRealClm → IsROrC.ofRealCLM;
• MeasureTheory.condexpL1Clm → MeasureTheory.condexpL1CLM;
• algebraMapClm → algebraMapCLM;
• WeakDual.CharacterSpace.toClm → WeakDual.CharacterSpace.toCLM;
• BoundedContinuousFunction.evalClm → BoundedContinuousFunction.evalCLM;
• ContinuousMap.evalClm → ContinuousMap.evalCLM;
• TrivSqZeroExt.fstClm → TrivSqZeroExt.fstClm;
• TrivSqZeroExt.sndClm → TrivSqZeroExt.sndCLM;
• TrivSqZeroExt.inlClm → TrivSqZeroExt.inlCLM;
• TrivSqZeroExt.inrClm → TrivSqZeroExt.inrCLM

and related theorems.

@@ -129,13 +129,13 @@ instance instInnerProductSpace : InnerProductSpace 𝕜 (lp G 2) :=
           funext i
           rw [norm_sq_eq_inner (𝕜 := 𝕜)]
           -- porting note: `simp` couldn't do this anymore
-        _ = re (∑' i, ⟪f i, f i⟫) := (IsROrC.reClm.map_tsum ?_).symm
+        _ = re (∑' i, ⟪f i, f i⟫) := (IsROrC.reCLM.map_tsum ?_).symm
       · norm_num
       · exact summable_inner f f
     conj_symm := fun f g => by
       calc
         conj _ = conj (∑' i, ⟪g i, f i⟫) := by congr
-        _ = ∑' i, conj ⟪g i, f i⟫ := IsROrC.conjCle.map_tsum
+        _ = ∑' i, conj ⟪g i, f i⟫ := IsROrC.conjCLE.map_tsum
         _ = ∑' i, ⟪f i, g i⟫ := by simp only [inner_conj_symm]
         _ = _ := by congr
     add_left := fun f₁ f₂ g => by

Remove some unnecessary arguments in simp calls, which will become problematic when the simp algorithm changes in leanprover/lean4#3124.

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

@@ -415,16 +415,15 @@ instance {ι : Type*} : Inhabited (HilbertBasis ι 𝕜 ℓ²(ι, 𝕜)) :=
 instance instCoeFun : CoeFun (HilbertBasis ι 𝕜 E) fun _ => ι → E where
   coe b i := b.repr.symm (lp.single 2 i (1 : 𝕜))
 
-@[simp]
+-- This is a bad `@[simp]` lemma: the RHS is a coercion containing the LHS.
 protected theorem repr_symm_single (b : HilbertBasis ι 𝕜 E) (i : ι) :
     b.repr.symm (lp.single 2 i (1 : 𝕜)) = b i :=
   rfl
 #align hilbert_basis.repr_symm_single HilbertBasis.repr_symm_single
 
--- porting note: removed `@[simp]` because `simp` can prove this
 protected theorem repr_self (b : HilbertBasis ι 𝕜 E) (i : ι) :
     b.repr (b i) = lp.single 2 i (1 : 𝕜) := by
-  simp
+  simp only [LinearIsometryEquiv.apply_symm_apply]
 #align hilbert_basis.repr_self HilbertBasis.repr_self
 
 protected theorem repr_apply_apply (b : HilbertBasis ι 𝕜 E) (v : E) (i : ι) :

A portion of results in Mathlib/LinearAlgebra/FiniteDimensional.lean were generalized to rings and moved to Mathlib/LinearAlgebra/FreeModule/Finite/Rank.lean. Most API lemmas for FiniteDimensional are kept but replaced with one lemma proofs. Definitions and niche lemmas are replaced by the generalized version completely.

Co-authored-by: erd1 <the.erd.one@gmail.com> Co-authored-by: Andrew Yang <the.erd.one@gmail.com>

@@ -584,7 +584,8 @@ theorem _root_.Orthonormal.exists_hilbertBasis_extension {s : Set E}
     ∃ (w : Set E) (b : HilbertBasis w 𝕜 E), s ⊆ w ∧ ⇑b = ((↑) : w → E) :=
   let ⟨w, hws, hw_ortho, hw_max⟩ := exists_maximal_orthonormal hs
   ⟨w, HilbertBasis.mkOfOrthogonalEqBot hw_ortho
-    (by simpa [maximal_orthonormal_iff_orthogonalComplement_eq_bot hw_ortho] using hw_max),
+    (by simpa only [Subtype.range_coe_subtype, Set.setOf_mem_eq,
+      maximal_orthonormal_iff_orthogonalComplement_eq_bot hw_ortho] using hw_max),
     hws, HilbertBasis.coe_mkOfOrthogonalEqBot _ _⟩
 #align orthonormal.exists_hilbert_basis_extension Orthonormal.exists_hilbertBasis_extension
 

We still have the exact_mod_cast tactic, used in a few places, which somehow (?) works a little bit harder to prevent the expected type influencing the elaboration of the term. I would like to get to the bottom of this, and it will be easier once the only usages of exact_mod_cast are the ones that don't work using the term elaborator by itself.

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

@@ -214,7 +214,7 @@ protected def linearIsometry : lp G 2 →ₗᵢ[𝕜] E where
       refine' tendsto_nhds_unique _ (lp.hasSum_norm H f)
       convert (hV.summable_of_lp f).hasSum.norm.rpow_const (Or.inr H.le) using 1
       ext s
-      exact_mod_cast (hV.norm_sum f s).symm
+      exact mod_cast (hV.norm_sum f s).symm
 #align orthogonal_family.linear_isometry OrthogonalFamily.linearIsometry
 
 protected theorem linearIsometry_apply (f : lp G 2) : hV.linearIsometry f = ∑' i, V i (f i) :=

PR contents

This is the supremum of

• #8284
• #8056
• #8023
• #8332
• #8226 (already approved)
• #7834 (already approved)

along with some minor fixes from failures on nightly-testing as Mathlib master is merged into it.

Note that some PRs for changes that are already compatible with the current toolchain and will be necessary have already been split out: #8380.

I am hopeful that in future we will be able to progressively merge adaptation PRs into a bump/v4.X.0 branch, so we never end up with a "big merge" like this. However one of these adaptation PRs (#8056) predates my new scheme for combined CI, and it wasn't possible to keep that PR viable in the meantime.

Lean PRs involved in this bump

In particular this includes adjustments for the Lean PRs

• leanprover/lean4#2778
• leanprover/lean4#2790
• leanprover/lean4#2783
• leanprover/lean4#2825
• leanprover/lean4#2722

leanprover/lean4#2778

We can get rid of all the

local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue [lean4#2220](https://github.com/leanprover/lean4/pull/2220)

macros across Mathlib (and in any projects that want to write natural number powers of reals).

leanprover/lean4#2722

Changes the default behaviour of simp to (config := {decide := false}). This makes simp (and consequentially norm_num) less powerful, but also more consistent, and less likely to blow up in long failures. This requires a variety of changes: changing some previously by simp or norm_num to decide or rfl, or adding (config := {decide := true}).

leanprover/lean4#2783

This changed the behaviour of simp so that simp [f] will only unfold "fully applied" occurrences of f. The old behaviour can be recovered with simp (config := { unfoldPartialApp := true }). We may in future add a syntax for this, e.g. simp [!f]; please provide feedback! In the meantime, we have made the following changes:

• switching to using explicit lemmas that have the intended level of application
• (config := { unfoldPartialApp := true }) in some places, to recover the old behaviour
• Using @[eqns] to manually adjust the equation lemmas for a particular definition, recovering the old behaviour just for that definition. See #8371, where we do this for Function.comp and Function.flip.

This change in Lean may require further changes down the line (e.g. adding the !f syntax, and/or upstreaming the special treatment for Function.comp and Function.flip, and/or removing this special treatment). Please keep an open and skeptical mind about these changes!

Co-authored-by: leanprover-community-mathlib4-bot <leanprover-community-mathlib4-bot@users.noreply.github.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Mauricio Collares <mauricio@collares.org>

@@ -88,8 +88,6 @@ open scoped BigOperators NNReal ENNReal Classical ComplexConjugate Topology
 
 noncomputable section
 
-local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue lean4#2220
-
 variable {ι : Type*}
 
 variable {𝕜 : Type*} [IsROrC 𝕜] {E : Type*}

Rename

• summable_of_norm_bounded -> Summable.of_norm_bounded;
• summable_of_norm_bounded_eventually -> Summable.of_norm_bounded_eventually;
• summable_of_nnnorm_bounded -> Summable.of_nnnorm_bounded;
• summable_of_summable_norm -> Summable.of_norm;
• summable_of_summable_nnnorm -> Summable.of_nnnorm;

New lemmas

• Summable.of_norm_bounded_eventually_nat
• Summable.norm

Misc changes

• Golf a few proofs.

@@ -111,7 +111,7 @@ namespace lp
 
 theorem summable_inner (f g : lp G 2) : Summable fun i => ⟪f i, g i⟫ := by
   -- Apply the Direct Comparison Test, comparing with ∑' i, ‖f i‖ * ‖g i‖ (summable by Hölder)
-  refine' summable_of_norm_bounded (fun i => ‖f i‖ * ‖g i‖) (lp.summable_mul _ f g) _
+  refine' .of_norm_bounded (fun i => ‖f i‖ * ‖g i‖) (lp.summable_mul _ f g) _
   · rw [Real.isConjugateExponent_iff] <;> norm_num
   intro i
   -- Then apply Cauchy-Schwarz pointwise

@@ -240,7 +240,6 @@ protected theorem linearIsometry_apply_single {i : ι} (x : G i) :
   · simp [h]
 #align orthogonal_family.linear_isometry_apply_single OrthogonalFamily.linearIsometry_apply_single
 
-@[simp]
 protected theorem linearIsometry_apply_dfinsupp_sum_single (W₀ : Π₀ i : ι, G i) :
     hV.linearIsometry (W₀.sum (lp.single 2)) = W₀.sum fun i => V i := by
   simp

@@ -243,11 +243,7 @@ protected theorem linearIsometry_apply_single {i : ι} (x : G i) :
 @[simp]
 protected theorem linearIsometry_apply_dfinsupp_sum_single (W₀ : Π₀ i : ι, G i) :
     hV.linearIsometry (W₀.sum (lp.single 2)) = W₀.sum fun i => V i := by
-  have :
-    hV.linearIsometry (∑ i in W₀.support, lp.single 2 i (W₀ i)) =
-      ∑ i in W₀.support, hV.linearIsometry (lp.single 2 i (W₀ i)) :=
-    hV.linearIsometry.toLinearMap.map_sum
-  simp (config := { contextual := true }) [DFinsupp.sum, this]
+  simp
 #align orthogonal_family.linear_isometry_apply_dfinsupp_sum_single OrthogonalFamily.linearIsometry_apply_dfinsupp_sum_single
 
 /-- The canonical linear isometry from the `lp 2` of a mutually orthogonal family of subspaces of

@@ -419,8 +419,8 @@ instance {ι : Type*} : Inhabited (HilbertBasis ι 𝕜 ℓ²(ι, 𝕜)) :=
   ⟨ofRepr (LinearIsometryEquiv.refl 𝕜 _)⟩
 
 /-- `b i` is the `i`th basis vector. -/
-instance instCoeFun : CoeFun (HilbertBasis ι 𝕜 E) fun _ => ι → E
-    where coe b i := b.repr.symm (lp.single 2 i (1 : 𝕜))
+instance instCoeFun : CoeFun (HilbertBasis ι 𝕜 E) fun _ => ι → E where
+  coe b i := b.repr.symm (lp.single 2 i (1 : 𝕜))
 
 @[simp]
 protected theorem repr_symm_single (b : HilbertBasis ι 𝕜 E) (i : ι) :

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

This has nice performance benefits.

@@ -90,13 +90,13 @@ noncomputable section
 
 local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue lean4#2220
 
-variable {ι : Type _}
+variable {ι : Type*}
 
-variable {𝕜 : Type _} [IsROrC 𝕜] {E : Type _}
+variable {𝕜 : Type*} [IsROrC 𝕜] {E : Type*}
 
 variable [NormedAddCommGroup E] [InnerProductSpace 𝕜 E] [cplt : CompleteSpace E]
 
-variable {G : ι → Type _} [∀ i, NormedAddCommGroup (G i)] [∀ i, InnerProductSpace 𝕜 (G i)]
+variable {G : ι → Type*} [∀ i, NormedAddCommGroup (G i)] [∀ i, InnerProductSpace 𝕜 (G i)]
 
 local notation "⟪" x ", " y "⟫" => @inner 𝕜 _ _ x y
 
@@ -281,11 +281,11 @@ variable (𝕜 G)
 
 variable (V : ∀ i, G i →ₗᵢ[𝕜] E) (F : ι → Submodule 𝕜 E)
 
-/-- Given a family of Hilbert spaces `G : ι → Type _`, a Hilbert sum of `G` consists of a Hilbert
+/-- Given a family of Hilbert spaces `G : ι → Type*`, a Hilbert sum of `G` consists of a Hilbert
 space `E` and an orthogonal family `V : Π i, G i →ₗᵢ[𝕜] E` such that the induced isometry
 `Φ : lp G 2 → E` is surjective.
 
-Keeping in mind that `lp G 2` is "the" external Hilbert sum of `G : ι → Type _`, this is analogous
+Keeping in mind that `lp G 2` is "the" external Hilbert sum of `G : ι → Type*`, this is analogous
 to `DirectSum.IsInternal`, except that we don't express it in terms of actual submodules. -/
 structure IsHilbertSum : Prop where
   ofSurjective ::
@@ -415,7 +415,7 @@ end
 
 namespace HilbertBasis
 
-instance {ι : Type _} : Inhabited (HilbertBasis ι 𝕜 ℓ²(ι, 𝕜)) :=
+instance {ι : Type*} : Inhabited (HilbertBasis ι 𝕜 ℓ²(ι, 𝕜)) :=
   ⟨ofRepr (LinearIsometryEquiv.refl 𝕜 _)⟩
 
 /-- `b i` is the `i`th basis vector. -/

@@ -88,8 +88,7 @@ open scoped BigOperators NNReal ENNReal Classical ComplexConjugate Topology
 
 noncomputable section
 
-local macro_rules | `($x ^ $y)   => `(HPow.hPow $x $y)
--- porting note: see lean4#2220
+local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue lean4#2220
 
 variable {ι : Type _}
 

• depends on: #5966

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

@@ -2,16 +2,13 @@
 Copyright (c) 2022 Heather Macbeth. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Heather Macbeth
-
-! This file was ported from Lean 3 source module analysis.inner_product_space.l2_space
-! leanprover-community/mathlib commit 46b633fd842bef9469441c0209906f6dddd2b4f5
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Analysis.InnerProductSpace.Projection
 import Mathlib.Analysis.NormedSpace.lpSpace
 import Mathlib.Analysis.InnerProductSpace.PiL2
 
+#align_import analysis.inner_product_space.l2_space from "leanprover-community/mathlib"@"46b633fd842bef9469441c0209906f6dddd2b4f5"
+
 /-!
 # Hilbert sum of a family of inner product spaces
 

See #4354

@@ -251,7 +251,7 @@ protected theorem linearIsometry_apply_dfinsupp_sum_single (W₀ : Π₀ i : ι,
     hV.linearIsometry (∑ i in W₀.support, lp.single 2 i (W₀ i)) =
       ∑ i in W₀.support, hV.linearIsometry (lp.single 2 i (W₀ i)) :=
     hV.linearIsometry.toLinearMap.map_sum
-  simp (config := { contextual := true }) [Dfinsupp.sum, this]
+  simp (config := { contextual := true }) [DFinsupp.sum, this]
 #align orthogonal_family.linear_isometry_apply_dfinsupp_sum_single OrthogonalFamily.linearIsometry_apply_dfinsupp_sum_single
 
 /-- The canonical linear isometry from the `lp 2` of a mutually orthogonal family of subspaces of
@@ -374,7 +374,7 @@ protected theorem IsHilbertSum.linearIsometryEquiv_apply_dfinsupp_sum_single
   rw [← hV.linearIsometryEquiv_symm_apply_dfinsupp_sum_single]
   rw [LinearIsometryEquiv.apply_symm_apply]
   ext i
-  simp (config := { contextual := true }) [Dfinsupp.sum, lp.single_apply]
+  simp (config := { contextual := true }) [DFinsupp.sum, lp.single_apply]
 #align is_hilbert_sum.linear_isometry_equiv_apply_dfinsupp_sum_single IsHilbertSum.linearIsometryEquiv_apply_dfinsupp_sum_single
 
 /-- Given a total orthonormal family `v : ι → E`, `E` is a Hilbert sum of `fun i : ι => 𝕜`

• Also remove most superfluous parentheses around big operators (∑, ∏ and variants).
• roughly the used regex: ([^a-zA-Zα-ωΑ-Ω'𝓝ℳ₀𝕂ₛ)]) \(([∑∏][^()∑∏]*,[^()∑∏:]*)\) ([⊂⊆=<≤]) replaced by $1 $2 $3

@@ -147,7 +147,7 @@ instance instInnerProductSpace : InnerProductSpace 𝕜 (lp G 2) :=
     add_left := fun f₁ f₂ g => by
       calc
         _ = ∑' i, ⟪(f₁ + f₂) i, g i⟫ := ?_
-        _ = ∑' i, ⟪f₁ i, g i⟫ + ⟪f₂ i, g i⟫ := by
+        _ = ∑' i, (⟪f₁ i, g i⟫ + ⟪f₂ i, g i⟫) := by
           simp only [inner_add_left, Pi.add_apply, coeFn_add]
         _ = (∑' i, ⟪f₁ i, g i⟫) + ∑' i, ⟪f₂ i, g i⟫ := (tsum_add ?_ ?_)
         _ = _ := by congr
@@ -503,7 +503,7 @@ protected theorem summable_inner_mul_inner (b : HilbertBasis ι 𝕜 E) (x y : E
 #align hilbert_basis.summable_inner_mul_inner HilbertBasis.summable_inner_mul_inner
 
 protected theorem tsum_inner_mul_inner (b : HilbertBasis ι 𝕜 E) (x y : E) :
-    (∑' i, ⟪x, b i⟫ * ⟪b i, y⟫) = ⟪x, y⟫ :=
+    ∑' i, ⟪x, b i⟫ * ⟪b i, y⟫ = ⟪x, y⟫ :=
   (b.hasSum_inner_mul_inner x y).tsum_eq
 #align hilbert_basis.tsum_inner_mul_inner HilbertBasis.tsum_inner_mul_inner
 

All of these are doc fixes

@@ -575,7 +575,7 @@ protected theorem coe_mkOfOrthogonalEqBot (hsp : (span 𝕜 (Set.range v))ᗮ =
 
 -- Note : this should be `b.repr` composed with an identification of `lp (fun i : ι => 𝕜) p` with
 -- `PiLp p (fun i : ι => 𝕜)` (in this case with `p = 2`), but we don't have this yet (July 2022).
-/-- An orthonormal basis is an Hilbert basis. -/
+/-- An orthonormal basis is a Hilbert basis. -/
 protected def _root_.OrthonormalBasis.toHilbertBasis [Fintype ι] (b : OrthonormalBasis ι 𝕜 E) :
     HilbertBasis ι 𝕜 E :=
   HilbertBasis.mk b.orthonormal <| by

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>

@@ -602,7 +602,7 @@ theorem _root_.Orthonormal.exists_hilbertBasis_extension {s : Set E}
 variable (𝕜 E)
 
 /-- A Hilbert space admits a Hilbert basis. -/
-theorem _root_.exists_hilbertBasis : ∃ (w : Set E)(b : HilbertBasis w 𝕜 E), ⇑b = ((↑) : w → E) :=
+theorem _root_.exists_hilbertBasis : ∃ (w : Set E) (b : HilbertBasis w 𝕜 E), ⇑b = ((↑) : w → E) :=
   let ⟨w, hw, _, hw''⟩ := (orthonormal_empty 𝕜 E).exists_hilbertBasis_extension
   ⟨w, hw, hw''⟩
 #align exists_hilbert_basis exists_hilbertBasis

These are all doc fixes

@@ -293,7 +293,7 @@ Keeping in mind that `lp G 2` is "the" external Hilbert sum of `G : ι → Type
 to `DirectSum.IsInternal`, except that we don't express it in terms of actual submodules. -/
 structure IsHilbertSum : Prop where
   ofSurjective ::
-  /-- The orthogonal family consituting the summands in the Hilbert sum. -/
+  /-- The orthogonal family constituting the summands in the Hilbert sum. -/
   protected OrthogonalFamily : OrthogonalFamily 𝕜 G V
   /-- The isometry `lp G 2 → E` induced by the orthogonal family is surjective. -/
   protected surjective_isometry : Function.Surjective OrthogonalFamily.linearIsometry
@@ -411,7 +411,7 @@ variable (ι) (𝕜) (E)
 /-- A Hilbert basis on `ι` for an inner product space `E` is an identification of `E` with the `lp`
 space `ℓ²(ι, 𝕜)`. -/
 structure HilbertBasis where ofRepr ::
-  /-- The linear isometric equivlence implementing identifiying the hilbert space with `ℓ²`. -/
+  /-- The linear isometric equivalence implementing identifying the Hilbert space with `ℓ²`. -/
   repr : E ≃ₗᵢ[𝕜] ℓ²(ι, 𝕜)
 #align hilbert_basis HilbertBasis
 

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