analysis.inner_product_space.dual | Mathlib porting status

Changes since the initial port

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

Changes in mathlib3

46b633fd

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

0b7c740e

bump to nightly-2024-04-06-08

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

e34029c9

Diff

@@ -48,11 +48,11 @@ universe u v
 
 namespace InnerProductSpace
 
-open IsROrC ContinuousLinearMap
+open RCLike ContinuousLinearMap
 
 variable (𝕜 : Type _)
 
-variable (E : Type _) [IsROrC 𝕜] [NormedAddCommGroup E] [InnerProductSpace 𝕜 E]
+variable (E : Type _) [RCLike 𝕜] [NormedAddCommGroup E] [InnerProductSpace 𝕜 E]
 
 local notation "⟪" x ", " y "⟫" => @inner 𝕜 E _ x y

0b7c740e

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -126,13 +126,13 @@ def toDual : E ≃ₗᵢ⋆[𝕜] NormedSpace.Dual 𝕜 E :=
       by_cases htriv : Y = ⊤
       · have hℓ : ℓ = 0 := by
           have h' := linear_map.ker_eq_top.mp htriv
-          rw [← coe_zero] at h' 
+          rw [← coe_zero] at h'
           apply coe_injective
           exact h'
         exact ⟨0, by simp [hℓ]⟩
-      · rw [← Submodule.orthogonal_eq_bot_iff] at htriv 
-        change Yᗮ ≠ ⊥ at htriv 
-        rw [Submodule.ne_bot_iff] at htriv 
+      · rw [← Submodule.orthogonal_eq_bot_iff] at htriv
+        change Yᗮ ≠ ⊥ at htriv
+        rw [Submodule.ne_bot_iff] at htriv
         obtain ⟨z : E, hz : z ∈ Yᗮ, z_ne_0 : z ≠ 0⟩ := htriv
         refine' ⟨(ℓ z† / ⟪z, z⟫) • z, _⟩
         ext x

0b7c740e

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,9 +3,9 @@ Copyright (c) 2020 Frédéric Dupuis. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Frédéric Dupuis
 -/
-import Mathbin.Analysis.InnerProductSpace.Projection
-import Mathbin.Analysis.NormedSpace.Dual
-import Mathbin.Analysis.NormedSpace.Star.Basic
+import Analysis.InnerProductSpace.Projection
+import Analysis.NormedSpace.Dual
+import Analysis.NormedSpace.Star.Basic
 
 #align_import analysis.inner_product_space.dual from "leanprover-community/mathlib"@"0b7c740e25651db0ba63648fbae9f9d6f941e31b"

0b7c740e

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,16 +2,13 @@
 Copyright (c) 2020 Frédéric Dupuis. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Frédéric Dupuis
-
-! This file was ported from Lean 3 source module analysis.inner_product_space.dual
-! leanprover-community/mathlib commit 0b7c740e25651db0ba63648fbae9f9d6f941e31b
-! 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.Dual
 import Mathbin.Analysis.NormedSpace.Star.Basic
 
+#align_import analysis.inner_product_space.dual from "leanprover-community/mathlib"@"0b7c740e25651db0ba63648fbae9f9d6f941e31b"
+
 /-!
 # The Fréchet-Riesz representation theorem

0b7c740e

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -57,10 +57,8 @@ variable (𝕜 : Type _)
 
 variable (E : Type _) [IsROrC 𝕜] [NormedAddCommGroup E] [InnerProductSpace 𝕜 E]
 
--- mathport name: «expr⟪ , ⟫»
 local notation "⟪" x ", " y "⟫" => @inner 𝕜 E _ x y
 
--- mathport name: «expr †»
 local postfix:90 "†" => starRingEnd _
 
 #print InnerProductSpace.toDualMap /-
@@ -77,17 +75,22 @@ def toDualMap : E →ₗᵢ⋆[𝕜] NormedSpace.Dual 𝕜 E :=
 
 variable {E}
 
+#print InnerProductSpace.toDualMap_apply /-
 @[simp]
 theorem toDualMap_apply {x y : E} : toDualMap 𝕜 E x y = ⟪x, y⟫ :=
   rfl
 #align inner_product_space.to_dual_map_apply InnerProductSpace.toDualMap_apply
+-/
 
+#print InnerProductSpace.innerSL_norm /-
 theorem innerSL_norm [Nontrivial E] : ‖(innerSL 𝕜 : E →L⋆[𝕜] E →L[𝕜] 𝕜)‖ = 1 :=
   show ‖(toDualMap 𝕜 E).toContinuousLinearMap‖ = 1 from LinearIsometry.norm_toContinuousLinearMap _
 #align inner_product_space.innerSL_norm InnerProductSpace.innerSL_norm
+-/
 
 variable {𝕜}
 
+#print InnerProductSpace.ext_inner_left_basis /-
 theorem ext_inner_left_basis {ι : Type _} {x y : E} (b : Basis ι 𝕜 E)
     (h : ∀ i : ι, ⟪b i, x⟫ = ⟪b i, y⟫) : x = y :=
   by
@@ -99,7 +102,9 @@ theorem ext_inner_left_basis {ι : Type _} {x y : E} (b : Basis ι 𝕜 E)
   nth_rw_rhs 1 [← inner_conj_symm]
   exact congr_arg conj (h i)
 #align inner_product_space.ext_inner_left_basis InnerProductSpace.ext_inner_left_basis
+-/
 
+#print InnerProductSpace.ext_inner_right_basis /-
 theorem ext_inner_right_basis {ι : Type _} {x y : E} (b : Basis ι 𝕜 E)
     (h : ∀ i : ι, ⟪x, b i⟫ = ⟪y, b i⟫) : x = y :=
   by
@@ -108,6 +113,7 @@ theorem ext_inner_right_basis {ι : Type _} {x y : E} (b : Basis ι 𝕜 E)
   nth_rw_rhs 1 [← inner_conj_symm]
   exact congr_arg conj (h i)
 #align inner_product_space.ext_inner_right_basis InnerProductSpace.ext_inner_right_basis
+-/
 
 variable (𝕜) (E) [CompleteSpace E]
 
@@ -157,17 +163,21 @@ def toDual : E ≃ₗᵢ⋆[𝕜] NormedSpace.Dual 𝕜 E :=
 
 variable {𝕜} {E}
 
+#print InnerProductSpace.toDual_apply /-
 @[simp]
 theorem toDual_apply {x y : E} : toDual 𝕜 E x y = ⟪x, y⟫ :=
   rfl
 #align inner_product_space.to_dual_apply InnerProductSpace.toDual_apply
+-/
 
+#print InnerProductSpace.toDual_symm_apply /-
 @[simp]
 theorem toDual_symm_apply {x : E} {y : NormedSpace.Dual 𝕜 E} : ⟪(toDual 𝕜 E).symm y, x⟫ = y x :=
   by
   rw [← to_dual_apply]
   simp only [LinearIsometryEquiv.apply_symm_apply]
 #align inner_product_space.to_dual_symm_apply InnerProductSpace.toDual_symm_apply
+-/
 
 variable {E 𝕜}
 
@@ -181,16 +191,18 @@ def continuousLinearMapOfBilin (B : E →L⋆[𝕜] E →L[𝕜] 𝕜) : E →L[
 #align inner_product_space.continuous_linear_map_of_bilin InnerProductSpace.continuousLinearMapOfBilin
 -/
 
--- mathport name: «expr ♯»
 local postfix:1024 "♯" => continuousLinearMapOfBilin
 
 variable (B : E →L⋆[𝕜] E →L[𝕜] 𝕜)
 
+#print InnerProductSpace.continuousLinearMapOfBilin_apply /-
 @[simp]
 theorem continuousLinearMapOfBilin_apply (v w : E) : ⟪B♯ v, w⟫ = B v w := by
   simp [continuous_linear_map_of_bilin]
 #align inner_product_space.continuous_linear_map_of_bilin_apply InnerProductSpace.continuousLinearMapOfBilin_apply
+-/
 
+#print InnerProductSpace.unique_continuousLinearMapOfBilin /-
 theorem unique_continuousLinearMapOfBilin {v f : E} (is_lax_milgram : ∀ w, ⟪f, w⟫ = B v w) :
     f = B♯ v := by
   refine' ext_inner_right 𝕜 _
@@ -198,6 +210,7 @@ theorem unique_continuousLinearMapOfBilin {v f : E} (is_lax_milgram : ∀ w, ⟪
   rw [continuous_linear_map_of_bilin_apply]
   exact is_lax_milgram w
 #align inner_product_space.unique_continuous_linear_map_of_bilin InnerProductSpace.unique_continuousLinearMapOfBilin
+-/
 
 end InnerProductSpace

0b7c740e

bump to nightly-2023-06-09-07

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

16afdc39

Diff

@@ -144,7 +144,6 @@ def toDual : E ≃ₗᵢ⋆[𝕜] NormedSpace.Dual 𝕜 E :=
               0 = ⟪z, ℓ z • x - ℓ x • z⟫ := by rw [(Y.mem_orthogonal' z).mp hz]; exact h₁
               _ = ⟪z, ℓ z • x⟫ - ⟪z, ℓ x • z⟫ := by rw [inner_sub_right]
               _ = ℓ z * ⟪z, x⟫ - ℓ x * ⟪z, z⟫ := by simp [inner_smul_right]
-              
           sub_eq_zero.mp (Eq.symm h₃)
         have h₄ :=
           calc
@@ -152,7 +151,6 @@ def toDual : E ≃ₗᵢ⋆[𝕜] NormedSpace.Dual 𝕜 E :=
             _ = ℓ z * ⟪z, x⟫ / ⟪z, z⟫ := by rw [← div_mul_eq_mul_div]
             _ = ℓ x * ⟪z, z⟫ / ⟪z, z⟫ := by rw [h₂]
             _ = ℓ x := by field_simp [inner_self_ne_zero.2 z_ne_0]
-            
         exact h₄)
 #align inner_product_space.to_dual InnerProductSpace.toDual
 -/

0b7c740e

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -123,13 +123,13 @@ def toDual : E ≃ₗᵢ⋆[𝕜] NormedSpace.Dual 𝕜 E :=
       by_cases htriv : Y = ⊤
       · have hℓ : ℓ = 0 := by
           have h' := linear_map.ker_eq_top.mp htriv
-          rw [← coe_zero] at h'
+          rw [← coe_zero] at h' 
           apply coe_injective
           exact h'
         exact ⟨0, by simp [hℓ]⟩
-      · rw [← Submodule.orthogonal_eq_bot_iff] at htriv
-        change Yᗮ ≠ ⊥ at htriv
-        rw [Submodule.ne_bot_iff] at htriv
+      · rw [← Submodule.orthogonal_eq_bot_iff] at htriv 
+        change Yᗮ ≠ ⊥ at htriv 
+        rw [Submodule.ne_bot_iff] at htriv 
         obtain ⟨z : E, hz : z ∈ Yᗮ, z_ne_0 : z ≠ 0⟩ := htriv
         refine' ⟨(ℓ z† / ⟪z, z⟫) • z, _⟩
         ext x

0b7c740e

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -45,7 +45,7 @@ dual, Fréchet-Riesz
 
 noncomputable section
 
-open Classical ComplexConjugate
+open scoped Classical ComplexConjugate
 
 universe u v

0b7c740e

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -77,26 +77,17 @@ def toDualMap : E →ₗᵢ⋆[𝕜] NormedSpace.Dual 𝕜 E :=
 
 variable {E}
 
-/- warning: inner_product_space.to_dual_map_apply -> InnerProductSpace.toDualMap_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align inner_product_space.to_dual_map_apply InnerProductSpace.toDualMap_applyₓ'. -/
 @[simp]
 theorem toDualMap_apply {x y : E} : toDualMap 𝕜 E x y = ⟪x, y⟫ :=
   rfl
 #align inner_product_space.to_dual_map_apply InnerProductSpace.toDualMap_apply
 
-/- warning: inner_product_space.innerSL_norm -> InnerProductSpace.innerSL_norm is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align inner_product_space.innerSL_norm InnerProductSpace.innerSL_normₓ'. -/
 theorem innerSL_norm [Nontrivial E] : ‖(innerSL 𝕜 : E →L⋆[𝕜] E →L[𝕜] 𝕜)‖ = 1 :=
   show ‖(toDualMap 𝕜 E).toContinuousLinearMap‖ = 1 from LinearIsometry.norm_toContinuousLinearMap _
 #align inner_product_space.innerSL_norm InnerProductSpace.innerSL_norm
 
 variable {𝕜}
 
-/- warning: inner_product_space.ext_inner_left_basis -> InnerProductSpace.ext_inner_left_basis is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align inner_product_space.ext_inner_left_basis InnerProductSpace.ext_inner_left_basisₓ'. -/
 theorem ext_inner_left_basis {ι : Type _} {x y : E} (b : Basis ι 𝕜 E)
     (h : ∀ i : ι, ⟪b i, x⟫ = ⟪b i, y⟫) : x = y :=
   by
@@ -109,9 +100,6 @@ theorem ext_inner_left_basis {ι : Type _} {x y : E} (b : Basis ι 𝕜 E)
   exact congr_arg conj (h i)
 #align inner_product_space.ext_inner_left_basis InnerProductSpace.ext_inner_left_basis
 
-/- warning: inner_product_space.ext_inner_right_basis -> InnerProductSpace.ext_inner_right_basis is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align inner_product_space.ext_inner_right_basis InnerProductSpace.ext_inner_right_basisₓ'. -/
 theorem ext_inner_right_basis {ι : Type _} {x y : E} (b : Basis ι 𝕜 E)
     (h : ∀ i : ι, ⟪x, b i⟫ = ⟪y, b i⟫) : x = y :=
   by
@@ -171,17 +159,11 @@ def toDual : E ≃ₗᵢ⋆[𝕜] NormedSpace.Dual 𝕜 E :=
 
 variable {𝕜} {E}
 
-/- warning: inner_product_space.to_dual_apply -> InnerProductSpace.toDual_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align inner_product_space.to_dual_apply InnerProductSpace.toDual_applyₓ'. -/
 @[simp]
 theorem toDual_apply {x y : E} : toDual 𝕜 E x y = ⟪x, y⟫ :=
   rfl
 #align inner_product_space.to_dual_apply InnerProductSpace.toDual_apply
 
-/- warning: inner_product_space.to_dual_symm_apply -> InnerProductSpace.toDual_symm_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align inner_product_space.to_dual_symm_apply InnerProductSpace.toDual_symm_applyₓ'. -/
 @[simp]
 theorem toDual_symm_apply {x : E} {y : NormedSpace.Dual 𝕜 E} : ⟪(toDual 𝕜 E).symm y, x⟫ = y x :=
   by
@@ -206,17 +188,11 @@ local postfix:1024 "♯" => continuousLinearMapOfBilin
 
 variable (B : E →L⋆[𝕜] E →L[𝕜] 𝕜)
 
-/- warning: inner_product_space.continuous_linear_map_of_bilin_apply -> InnerProductSpace.continuousLinearMapOfBilin_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align inner_product_space.continuous_linear_map_of_bilin_apply InnerProductSpace.continuousLinearMapOfBilin_applyₓ'. -/
 @[simp]
 theorem continuousLinearMapOfBilin_apply (v w : E) : ⟪B♯ v, w⟫ = B v w := by
   simp [continuous_linear_map_of_bilin]
 #align inner_product_space.continuous_linear_map_of_bilin_apply InnerProductSpace.continuousLinearMapOfBilin_apply
 
-/- warning: inner_product_space.unique_continuous_linear_map_of_bilin -> InnerProductSpace.unique_continuousLinearMapOfBilin is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align inner_product_space.unique_continuous_linear_map_of_bilin InnerProductSpace.unique_continuousLinearMapOfBilinₓ'. -/
 theorem unique_continuousLinearMapOfBilin {v f : E} (is_lax_milgram : ∀ w, ⟪f, w⟫ = B v w) :
     f = B♯ v := by
   refine' ext_inner_right 𝕜 _

0b7c740e

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -153,10 +153,7 @@ def toDual : E ≃ₗᵢ⋆[𝕜] NormedSpace.Dual 𝕜 E :=
         have h₂ : ℓ z * ⟪z, x⟫ = ℓ x * ⟪z, z⟫ :=
           haveI h₃ :=
             calc
-              0 = ⟪z, ℓ z • x - ℓ x • z⟫ :=
-                by
-                rw [(Y.mem_orthogonal' z).mp hz]
-                exact h₁
+              0 = ⟪z, ℓ z • x - ℓ x • z⟫ := by rw [(Y.mem_orthogonal' z).mp hz]; exact h₁
               _ = ⟪z, ℓ z • x⟫ - ⟪z, ℓ x • z⟫ := by rw [inner_sub_right]
               _ = ℓ z * ⟪z, x⟫ - ℓ x * ⟪z, z⟫ := by simp [inner_smul_right]

0b7c740e

bump to nightly-2023-05-28-03

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

6c6011cf

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Frédéric Dupuis
 
 ! This file was ported from Lean 3 source module analysis.inner_product_space.dual
-! leanprover-community/mathlib commit 46b633fd842bef9469441c0209906f6dddd2b4f5
+! leanprover-community/mathlib commit 0b7c740e25651db0ba63648fbae9f9d6f941e31b
 ! 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.NormedSpace.Star.Basic
 /-!
 # The Fréchet-Riesz representation theorem
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 We consider an inner product space `E` over `𝕜`, which is either `ℝ` or `ℂ`. We define
 `to_dual_map`, a conjugate-linear isometric embedding of `E` into its dual, which maps an element
 `x` of the space to `λ y, ⟪x, y⟫`.
@@ -60,6 +63,7 @@ local notation "⟪" x ", " y "⟫" => @inner 𝕜 E _ x y
 -- mathport name: «expr †»
 local postfix:90 "†" => starRingEnd _
 
+#print InnerProductSpace.toDualMap /-
 /-- An element `x` of an inner product space `E` induces an element of the dual space `dual 𝕜 E`,
 the map `λ y, ⟪x, y⟫`; moreover this operation is a conjugate-linear isometric embedding of `E`
 into `dual 𝕜 E`.
@@ -69,20 +73,30 @@ see `to_dual`.
 def toDualMap : E →ₗᵢ⋆[𝕜] NormedSpace.Dual 𝕜 E :=
   { innerSL 𝕜 with norm_map' := innerSL_apply_norm _ }
 #align inner_product_space.to_dual_map InnerProductSpace.toDualMap
+-/
 
 variable {E}
 
+/- warning: inner_product_space.to_dual_map_apply -> InnerProductSpace.toDualMap_apply is a dubious translation:
+<too large>
+Case conversion may be inaccurate. Consider using '#align inner_product_space.to_dual_map_apply InnerProductSpace.toDualMap_applyₓ'. -/
 @[simp]
 theorem toDualMap_apply {x y : E} : toDualMap 𝕜 E x y = ⟪x, y⟫ :=
   rfl
 #align inner_product_space.to_dual_map_apply InnerProductSpace.toDualMap_apply
 
+/- warning: inner_product_space.innerSL_norm -> InnerProductSpace.innerSL_norm is a dubious translation:
+<too large>
+Case conversion may be inaccurate. Consider using '#align inner_product_space.innerSL_norm InnerProductSpace.innerSL_normₓ'. -/
 theorem innerSL_norm [Nontrivial E] : ‖(innerSL 𝕜 : E →L⋆[𝕜] E →L[𝕜] 𝕜)‖ = 1 :=
   show ‖(toDualMap 𝕜 E).toContinuousLinearMap‖ = 1 from LinearIsometry.norm_toContinuousLinearMap _
 #align inner_product_space.innerSL_norm InnerProductSpace.innerSL_norm
 
 variable {𝕜}
 
+/- warning: inner_product_space.ext_inner_left_basis -> InnerProductSpace.ext_inner_left_basis is a dubious translation:
+<too large>
+Case conversion may be inaccurate. Consider using '#align inner_product_space.ext_inner_left_basis InnerProductSpace.ext_inner_left_basisₓ'. -/
 theorem ext_inner_left_basis {ι : Type _} {x y : E} (b : Basis ι 𝕜 E)
     (h : ∀ i : ι, ⟪b i, x⟫ = ⟪b i, y⟫) : x = y :=
   by
@@ -95,6 +109,9 @@ theorem ext_inner_left_basis {ι : Type _} {x y : E} (b : Basis ι 𝕜 E)
   exact congr_arg conj (h i)
 #align inner_product_space.ext_inner_left_basis InnerProductSpace.ext_inner_left_basis
 
+/- warning: inner_product_space.ext_inner_right_basis -> InnerProductSpace.ext_inner_right_basis is a dubious translation:
+<too large>
+Case conversion may be inaccurate. Consider using '#align inner_product_space.ext_inner_right_basis InnerProductSpace.ext_inner_right_basisₓ'. -/
 theorem ext_inner_right_basis {ι : Type _} {x y : E} (b : Basis ι 𝕜 E)
     (h : ∀ i : ι, ⟪x, b i⟫ = ⟪y, b i⟫) : x = y :=
   by
@@ -106,6 +123,7 @@ theorem ext_inner_right_basis {ι : Type _} {x y : E} (b : Basis ι 𝕜 E)
 
 variable (𝕜) (E) [CompleteSpace E]
 
+#print InnerProductSpace.toDual /-
 /-- Fréchet-Riesz representation: any `ℓ` in the dual of a Hilbert space `E` is of the form
 `λ u, ⟪y, u⟫` for some `y : E`, i.e. `to_dual_map` is surjective.
 -/
@@ -152,14 +170,21 @@ def toDual : E ≃ₗᵢ⋆[𝕜] NormedSpace.Dual 𝕜 E :=
             
         exact h₄)
 #align inner_product_space.to_dual InnerProductSpace.toDual
+-/
 
 variable {𝕜} {E}
 
+/- warning: inner_product_space.to_dual_apply -> InnerProductSpace.toDual_apply is a dubious translation:
+<too large>
+Case conversion may be inaccurate. Consider using '#align inner_product_space.to_dual_apply InnerProductSpace.toDual_applyₓ'. -/
 @[simp]
 theorem toDual_apply {x y : E} : toDual 𝕜 E x y = ⟪x, y⟫ :=
   rfl
 #align inner_product_space.to_dual_apply InnerProductSpace.toDual_apply
 
+/- warning: inner_product_space.to_dual_symm_apply -> InnerProductSpace.toDual_symm_apply is a dubious translation:
+<too large>
+Case conversion may be inaccurate. Consider using '#align inner_product_space.to_dual_symm_apply InnerProductSpace.toDual_symm_applyₓ'. -/
 @[simp]
 theorem toDual_symm_apply {x : E} {y : NormedSpace.Dual 𝕜 E} : ⟪(toDual 𝕜 E).symm y, x⟫ = y x :=
   by
@@ -169,6 +194,7 @@ theorem toDual_symm_apply {x : E} {y : NormedSpace.Dual 𝕜 E} : ⟪(toDual 
 
 variable {E 𝕜}
 
+#print InnerProductSpace.continuousLinearMapOfBilin /-
 /-- Maps a bounded sesquilinear form to its continuous linear map,
 given by interpreting the form as a map `B : E →L⋆[𝕜] normed_space.dual 𝕜 E`
 and dualizing the result using `to_dual`.
@@ -176,17 +202,24 @@ and dualizing the result using `to_dual`.
 def continuousLinearMapOfBilin (B : E →L⋆[𝕜] E →L[𝕜] 𝕜) : E →L[𝕜] E :=
   comp (toDual 𝕜 E).symm.toContinuousLinearEquiv.toContinuousLinearMap B
 #align inner_product_space.continuous_linear_map_of_bilin InnerProductSpace.continuousLinearMapOfBilin
+-/
 
 -- mathport name: «expr ♯»
 local postfix:1024 "♯" => continuousLinearMapOfBilin
 
 variable (B : E →L⋆[𝕜] E →L[𝕜] 𝕜)
 
+/- warning: inner_product_space.continuous_linear_map_of_bilin_apply -> InnerProductSpace.continuousLinearMapOfBilin_apply is a dubious translation:
+<too large>
+Case conversion may be inaccurate. Consider using '#align inner_product_space.continuous_linear_map_of_bilin_apply InnerProductSpace.continuousLinearMapOfBilin_applyₓ'. -/
 @[simp]
 theorem continuousLinearMapOfBilin_apply (v w : E) : ⟪B♯ v, w⟫ = B v w := by
   simp [continuous_linear_map_of_bilin]
 #align inner_product_space.continuous_linear_map_of_bilin_apply InnerProductSpace.continuousLinearMapOfBilin_apply
 
+/- warning: inner_product_space.unique_continuous_linear_map_of_bilin -> InnerProductSpace.unique_continuousLinearMapOfBilin is a dubious translation:
+<too large>
+Case conversion may be inaccurate. Consider using '#align inner_product_space.unique_continuous_linear_map_of_bilin InnerProductSpace.unique_continuousLinearMapOfBilinₓ'. -/
 theorem unique_continuousLinearMapOfBilin {v f : E} (is_lax_milgram : ∀ w, ⟪f, w⟫ = B v w) :
     f = B♯ v := by
   refine' ext_inner_right 𝕜 _

46b633fd

bump to nightly-2023-03-26-02

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

ca5de00c

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Frédéric Dupuis
 
 ! This file was ported from Lean 3 source module analysis.inner_product_space.dual
-! 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.
 -/
@@ -52,7 +52,7 @@ open IsROrC ContinuousLinearMap
 
 variable (𝕜 : Type _)
 
-variable (E : Type _) [IsROrC 𝕜] [InnerProductSpace 𝕜 E]
+variable (E : Type _) [IsROrC 𝕜] [NormedAddCommGroup E] [InnerProductSpace 𝕜 E]
 
 -- mathport name: «expr⟪ , ⟫»
 local notation "⟪" x ", " y "⟫" => @inner 𝕜 E _ x y

c78cad35

bump to nightly-2023-03-20-03

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

2e1f2c13

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Frédéric Dupuis
 
 ! This file was ported from Lean 3 source module analysis.inner_product_space.dual
-! leanprover-community/mathlib commit a37865088599172dc923253bb7b31998297d9c8a
+! leanprover-community/mathlib commit c78cad350eb321c81e1eacf68d14e3d3ba1e17f7
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -67,7 +67,7 @@ If `E` is complete, this operation is surjective, hence a conjugate-linear isome
 see `to_dual`.
 -/
 def toDualMap : E →ₗᵢ⋆[𝕜] NormedSpace.Dual 𝕜 E :=
-  { innerSL with norm_map' := fun _ => innerSL_apply_norm }
+  { innerSL 𝕜 with norm_map' := innerSL_apply_norm _ }
 #align inner_product_space.to_dual_map InnerProductSpace.toDualMap
 
 variable {E}
@@ -77,7 +77,7 @@ theorem toDualMap_apply {x y : E} : toDualMap 𝕜 E x y = ⟪x, y⟫ :=
   rfl
 #align inner_product_space.to_dual_map_apply InnerProductSpace.toDualMap_apply
 
-theorem innerSL_norm [Nontrivial E] : ‖(innerSL : E →L⋆[𝕜] E →L[𝕜] 𝕜)‖ = 1 :=
+theorem innerSL_norm [Nontrivial E] : ‖(innerSL 𝕜 : E →L⋆[𝕜] E →L[𝕜] 𝕜)‖ = 1 :=
   show ‖(toDualMap 𝕜 E).toContinuousLinearMap‖ = 1 from LinearIsometry.norm_toContinuousLinearMap _
 #align inner_product_space.innerSL_norm InnerProductSpace.innerSL_norm

a3786508

bump to nightly-2023-03-16-03

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

8ae28b0b

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Frédéric Dupuis
 
 ! This file was ported from Lean 3 source module analysis.inner_product_space.dual
-! leanprover-community/mathlib commit 3fc0b254310908f70a1a75f01147d52e53e9f8a2
+! leanprover-community/mathlib commit a37865088599172dc923253bb7b31998297d9c8a
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -148,12 +148,7 @@ def toDual : E ≃ₗᵢ⋆[𝕜] NormedSpace.Dual 𝕜 E :=
             ⟪(ℓ z† / ⟪z, z⟫) • z, x⟫ = ℓ z / ⟪z, z⟫ * ⟪z, x⟫ := by simp [inner_smul_left, conj_conj]
             _ = ℓ z * ⟪z, x⟫ / ⟪z, z⟫ := by rw [← div_mul_eq_mul_div]
             _ = ℓ x * ⟪z, z⟫ / ⟪z, z⟫ := by rw [h₂]
-            _ = ℓ x :=
-              by
-              have : ⟪z, z⟫ ≠ 0 := by
-                change z = 0 → False at z_ne_0
-                rwa [← inner_self_eq_zero] at z_ne_0
-              field_simp [this]
+            _ = ℓ x := by field_simp [inner_self_ne_zero.2 z_ne_0]
             
         exact h₄)
 #align inner_product_space.to_dual InnerProductSpace.toDual

3fc0b254

bump to nightly-2023-03-15-03

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

4e269297

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Frédéric Dupuis
 
 ! This file was ported from Lean 3 source module analysis.inner_product_space.dual
-! leanprover-community/mathlib commit a148d797a1094ab554ad4183a4ad6f130358ef64
+! leanprover-community/mathlib commit 3fc0b254310908f70a1a75f01147d52e53e9f8a2
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -90,8 +90,8 @@ theorem ext_inner_left_basis {ι : Type _} {x y : E} (b : Basis ι 𝕜 E)
   refine' (Function.Injective.eq_iff ContinuousLinearMap.coe_injective).mp (Basis.ext b _)
   intro i
   simp only [to_dual_map_apply, ContinuousLinearMap.coe_coe]
-  rw [← inner_conj_sym]
-  nth_rw_rhs 1 [← inner_conj_sym]
+  rw [← inner_conj_symm]
+  nth_rw_rhs 1 [← inner_conj_symm]
   exact congr_arg conj (h i)
 #align inner_product_space.ext_inner_left_basis InnerProductSpace.ext_inner_left_basis
 
@@ -99,8 +99,8 @@ theorem ext_inner_right_basis {ι : Type _} {x y : E} (b : Basis ι 𝕜 E)
     (h : ∀ i : ι, ⟪x, b i⟫ = ⟪y, b i⟫) : x = y :=
   by
   refine' ext_inner_left_basis b fun i => _
-  rw [← inner_conj_sym]
-  nth_rw_rhs 1 [← inner_conj_sym]
+  rw [← inner_conj_symm]
+  nth_rw_rhs 1 [← inner_conj_symm]
   exact congr_arg conj (h i)
 #align inner_product_space.ext_inner_right_basis InnerProductSpace.ext_inner_right_basis

a148d797

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

46b633fd

chore: Rename IsROrC to RCLike (#10819)

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.

43618f93

Diff

@@ -46,10 +46,10 @@ universe u v
 
 namespace InnerProductSpace
 
-open IsROrC ContinuousLinearMap
+open RCLike ContinuousLinearMap
 
 variable (𝕜 : Type*)
-variable (E : Type*) [IsROrC 𝕜] [NormedAddCommGroup E] [InnerProductSpace 𝕜 E]
+variable (E : Type*) [RCLike 𝕜] [NormedAddCommGroup E] [InnerProductSpace 𝕜 E]
 
 local notation "⟪" x ", " y "⟫" => @inner 𝕜 E _ x y

46b633fd

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

Empty lines were removed by executing the following Python script twice

import os
import re


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

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

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

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

75c86f04

Diff

@@ -49,7 +49,6 @@ namespace InnerProductSpace
 open IsROrC ContinuousLinearMap
 
 variable (𝕜 : Type*)
-
 variable (E : Type*) [IsROrC 𝕜] [NormedAddCommGroup E] [InnerProductSpace 𝕜 E]
 
 local notation "⟪" x ", " y "⟫" => @inner 𝕜 E _ x y
@@ -101,7 +100,6 @@ theorem ext_inner_right_basis {ι : Type*} {x y : E} (b : Basis ι 𝕜 E)
 #align inner_product_space.ext_inner_right_basis InnerProductSpace.ext_inner_right_basis
 
 variable (𝕜) (E)
-
 variable [CompleteSpace E]
 
 /-- Fréchet-Riesz representation: any `ℓ` in the dual of a Hilbert space `E` is of the form

46b633fd

chore: scope open Classical (#11199)

We remove all but one open Classicals, instead preferring to use open scoped Classical. The only real side-effect this led to is moving a couple declarations to use Exists.choose instead of Classical.choose.

The first few commits are explicitly labelled regex replaces for ease of review.

c747be0a

Diff

@@ -39,7 +39,8 @@ dual, Fréchet-Riesz
 
 noncomputable section
 
-open Classical ComplexConjugate
+open scoped Classical
+open ComplexConjugate
 
 universe u v

46b633fd

feat (NormedSpace.Dual): make Dual reducible (#6998)

Following LinearAlgebra.Dual this makes NormedSpace.Dual reducible.

a4810ea0

Diff

@@ -174,7 +174,8 @@ variable (B : E →L⋆[𝕜] E →L[𝕜] 𝕜)
 
 @[simp]
 theorem continuousLinearMapOfBilin_apply (v w : E) : ⟪B♯ v, w⟫ = B v w := by
-  simp [continuousLinearMapOfBilin]
+  rw [continuousLinearMapOfBilin, coe_comp', ContinuousLinearEquiv.coe_coe,
+    LinearIsometryEquiv.coe_toContinuousLinearEquiv, Function.comp_apply, toDual_symm_apply]
 #align inner_product_space.continuous_linear_map_of_bilin_apply InnerProductSpace.continuousLinearMapOfBilin_apply
 
 theorem unique_continuousLinearMapOfBilin {v f : E} (is_lax_milgram : ∀ w, ⟪f, w⟫ = B v w) :

46b633fd

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

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

This has nice performance benefits.

32de3f67

Diff

@@ -47,9 +47,9 @@ namespace InnerProductSpace
 
 open IsROrC ContinuousLinearMap
 
-variable (𝕜 : Type _)
+variable (𝕜 : Type*)
 
-variable (E : Type _) [IsROrC 𝕜] [NormedAddCommGroup E] [InnerProductSpace 𝕜 E]
+variable (E : Type*) [IsROrC 𝕜] [NormedAddCommGroup E] [InnerProductSpace 𝕜 E]
 
 local notation "⟪" x ", " y "⟫" => @inner 𝕜 E _ x y
 
@@ -79,7 +79,7 @@ set_option linter.uppercaseLean3 false in
 
 variable {𝕜}
 
-theorem ext_inner_left_basis {ι : Type _} {x y : E} (b : Basis ι 𝕜 E)
+theorem ext_inner_left_basis {ι : Type*} {x y : E} (b : Basis ι 𝕜 E)
     (h : ∀ i : ι, ⟪b i, x⟫ = ⟪b i, y⟫) : x = y := by
   apply (toDualMap 𝕜 E).map_eq_iff.mp
   refine' (Function.Injective.eq_iff ContinuousLinearMap.coe_injective).mp (Basis.ext b _)
@@ -91,7 +91,7 @@ theorem ext_inner_left_basis {ι : Type _} {x y : E} (b : Basis ι 𝕜 E)
   exact congr_arg conj (h i)
 #align inner_product_space.ext_inner_left_basis InnerProductSpace.ext_inner_left_basis
 
-theorem ext_inner_right_basis {ι : Type _} {x y : E} (b : Basis ι 𝕜 E)
+theorem ext_inner_right_basis {ι : Type*} {x y : E} (b : Basis ι 𝕜 E)
     (h : ∀ i : ι, ⟪x, b i⟫ = ⟪y, b i⟫) : x = y := by
   refine' ext_inner_left_basis b fun i => _
   rw [← inner_conj_symm]

46b633fd

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

depends on: #5966

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

89aa3a3b

Diff

@@ -2,16 +2,13 @@
 Copyright (c) 2020 Frédéric Dupuis. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Frédéric Dupuis
-
-! This file was ported from Lean 3 source module analysis.inner_product_space.dual
-! 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.Dual
 import Mathlib.Analysis.NormedSpace.Star.Basic
 
+#align_import analysis.inner_product_space.dual from "leanprover-community/mathlib"@"46b633fd842bef9469441c0209906f6dddd2b4f5"
+
 /-!
 # The Fréchet-Riesz representation theorem

46b633fd

feat: port Analysis.InnerProductSpace.Dual (#4402)

91459584

`analysis.inner_product_space.dual` ⟷ `Mathlib.Analysis.InnerProductSpace.Dual`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 12 + 874

analysis.inner_product_space.dual ⟷ Mathlib.Analysis.InnerProductSpace.Dual

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 12 + 874

`analysis.inner_product_space.dual` ⟷ `Mathlib.Analysis.InnerProductSpace.Dual`