algebra.lie.normalizer | 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

938fead7

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

6b31d1ee

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -174,7 +174,7 @@ variable {H}
 theorem lie_mem_sup_of_mem_normalizer {x y z : L} (hx : x ∈ H.normalizer) (hy : y ∈ (R ∙ x) ⊔ ↑H)
     (hz : z ∈ (R ∙ x) ⊔ ↑H) : ⁅y, z⁆ ∈ (R ∙ x) ⊔ ↑H :=
   by
-  rw [Submodule.mem_sup] at hy hz 
+  rw [Submodule.mem_sup] at hy hz
   obtain ⟨u₁, hu₁, v, hv : v ∈ H, rfl⟩ := hy
   obtain ⟨u₂, hu₂, w, hw : w ∈ H, rfl⟩ := hz
   obtain ⟨t, rfl⟩ := submodule.mem_span_singleton.mp hu₁
@@ -220,7 +220,7 @@ theorem normalizer_eq_self_iff :
     rw [← h, H.mem_normalizer_iff']
     intro y hy
     replace hx : ⁅_, LieSubmodule.Quotient.mk' _ x⁆ = 0 := hx ⟨y, hy⟩
-    rwa [← LieModuleHom.map_lie, LieSubmodule.Quotient.mk_eq_zero] at hx 
+    rwa [← LieModuleHom.map_lie, LieSubmodule.Quotient.mk_eq_zero] at hx
   · let y := LieSubmodule.Quotient.mk' H.to_lie_submodule x
     have hy : y ∈ LieModule.maxTrivSubmodule R H (L ⧸ H.to_lie_submodule) :=
       by

6b31d1ee

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) 2022 Oliver Nash. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Oliver Nash
 -/
-import Mathbin.Algebra.Lie.Abelian
-import Mathbin.Algebra.Lie.IdealOperations
-import Mathbin.Algebra.Lie.Quotient
+import Algebra.Lie.Abelian
+import Algebra.Lie.IdealOperations
+import Algebra.Lie.Quotient
 
 #align_import algebra.lie.normalizer from "leanprover-community/mathlib"@"6b31d1eebd64eab86d5bd9936bfaada6ca8b5842"

6b31d1ee

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) 2022 Oliver Nash. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Oliver Nash
-
-! This file was ported from Lean 3 source module algebra.lie.normalizer
-! leanprover-community/mathlib commit 6b31d1eebd64eab86d5bd9936bfaada6ca8b5842
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.Lie.Abelian
 import Mathbin.Algebra.Lie.IdealOperations
 import Mathbin.Algebra.Lie.Quotient
 
+#align_import algebra.lie.normalizer from "leanprover-community/mathlib"@"6b31d1eebd64eab86d5bd9936bfaada6ca8b5842"
+
 /-!
 # The normalizer of a Lie submodules and subalgebras.

6b31d1ee

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -65,21 +65,28 @@ def normalizer : LieSubmodule R L M
 #align lie_submodule.normalizer LieSubmodule.normalizer
 -/
 
+#print LieSubmodule.mem_normalizer /-
 @[simp]
 theorem mem_normalizer (m : M) : m ∈ N.normalizer ↔ ∀ x : L, ⁅x, m⁆ ∈ N :=
   Iff.rfl
 #align lie_submodule.mem_normalizer LieSubmodule.mem_normalizer
+-/
 
+#print LieSubmodule.le_normalizer /-
 theorem le_normalizer : N ≤ N.normalizer := by
   intro m hm
   rw [mem_normalizer]
   exact fun x => N.lie_mem hm
 #align lie_submodule.le_normalizer LieSubmodule.le_normalizer
+-/
 
+#print LieSubmodule.normalizer_inf /-
 theorem normalizer_inf : (N₁ ⊓ N₂).normalizer = N₁.normalizer ⊓ N₂.normalizer := by ext;
   simp [← forall_and]
 #align lie_submodule.normalizer_inf LieSubmodule.normalizer_inf
+-/
 
+#print LieSubmodule.monotone_normalizer /-
 @[mono]
 theorem monotone_normalizer : Monotone (normalizer : LieSubmodule R L M → LieSubmodule R L M) :=
   by
@@ -87,27 +94,36 @@ theorem monotone_normalizer : Monotone (normalizer : LieSubmodule R L M → LieS
   rw [mem_normalizer] at hm ⊢
   exact fun x => h (hm x)
 #align lie_submodule.monotone_normalizer LieSubmodule.monotone_normalizer
+-/
 
+#print LieSubmodule.comap_normalizer /-
 @[simp]
 theorem comap_normalizer (f : M' →ₗ⁅R,L⁆ M) : N.normalizer.comap f = (N.comap f).normalizer := by
   ext; simp
 #align lie_submodule.comap_normalizer LieSubmodule.comap_normalizer
+-/
 
+#print LieSubmodule.top_lie_le_iff_le_normalizer /-
 theorem top_lie_le_iff_le_normalizer (N' : LieSubmodule R L M) :
     ⁅(⊤ : LieIdeal R L), N⁆ ≤ N' ↔ N ≤ N'.normalizer := by rw [lie_le_iff]; tauto
 #align lie_submodule.top_lie_le_iff_le_normalizer LieSubmodule.top_lie_le_iff_le_normalizer
+-/
 
+#print LieSubmodule.gc_top_lie_normalizer /-
 theorem gc_top_lie_normalizer :
     GaloisConnection (fun N : LieSubmodule R L M => ⁅(⊤ : LieIdeal R L), N⁆) normalizer :=
   top_lie_le_iff_le_normalizer
 #align lie_submodule.gc_top_lie_normalizer LieSubmodule.gc_top_lie_normalizer
+-/
 
 variable (R L M)
 
+#print LieSubmodule.normalizer_bot_eq_maxTrivSubmodule /-
 theorem normalizer_bot_eq_maxTrivSubmodule :
     (⊥ : LieSubmodule R L M).normalizer = LieModule.maxTrivSubmodule R L M :=
   rfl
 #align lie_submodule.normalizer_bot_eq_max_triv_submodule LieSubmodule.normalizer_bot_eq_maxTrivSubmodule
+-/
 
 end LieSubmodule
 
@@ -142,9 +158,11 @@ theorem mem_normalizer_iff (x : L) : x ∈ H.normalizer ↔ ∀ y : L, y ∈ H 
 #align lie_subalgebra.mem_normalizer_iff LieSubalgebra.mem_normalizer_iff
 -/
 
+#print LieSubalgebra.le_normalizer /-
 theorem le_normalizer : H ≤ H.normalizer :=
   H.toLieSubmodule.le_normalizer
 #align lie_subalgebra.le_normalizer LieSubalgebra.le_normalizer
+-/
 
 #print LieSubalgebra.coe_normalizer_eq_normalizer /-
 theorem coe_normalizer_eq_normalizer :
@@ -155,6 +173,7 @@ theorem coe_normalizer_eq_normalizer :
 
 variable {H}
 
+#print LieSubalgebra.lie_mem_sup_of_mem_normalizer /-
 theorem lie_mem_sup_of_mem_normalizer {x y z : L} (hx : x ∈ H.normalizer) (hy : y ∈ (R ∙ x) ⊔ ↑H)
     (hz : z ∈ (R ∙ x) ⊔ ↑H) : ⁅y, z⁆ ∈ (R ∙ x) ⊔ ↑H :=
   by
@@ -169,6 +188,7 @@ theorem lie_mem_sup_of_mem_normalizer {x y z : L} (hx : x ∈ H.normalizer) (hy
   refine' H.add_mem (H.smul_mem s _) (H.add_mem (H.smul_mem t _) (H.lie_mem hv hw))
   exacts [(H.mem_normalizer_iff' x).mp hx v hv, (H.mem_normalizer_iff x).mp hx w hw]
 #align lie_subalgebra.lie_mem_sup_of_mem_normalizer LieSubalgebra.lie_mem_sup_of_mem_normalizer
+-/
 
 #print LieSubalgebra.ideal_in_normalizer /-
 /-- A Lie subalgebra is an ideal of its normalizer. -/
@@ -179,6 +199,7 @@ theorem ideal_in_normalizer {x y : L} (hx : x ∈ H.normalizer) (hy : y ∈ H) :
 #align lie_subalgebra.ideal_in_normalizer LieSubalgebra.ideal_in_normalizer
 -/
 
+#print LieSubalgebra.exists_nested_lieIdeal_ofLe_normalizer /-
 /-- A Lie subalgebra `H` is an ideal of any Lie subalgebra `K` containing `H` and contained in the
 normalizer of `H`. -/
 theorem exists_nested_lieIdeal_ofLe_normalizer {K : LieSubalgebra R L} (h₁ : H ≤ K)
@@ -187,6 +208,7 @@ theorem exists_nested_lieIdeal_ofLe_normalizer {K : LieSubalgebra R L} (h₁ : H
   rw [exists_nested_lie_ideal_coe_eq_iff]
   exact fun x y hx hy => ideal_in_normalizer (h₂ hx) hy
 #align lie_subalgebra.exists_nested_lie_ideal_of_le_normalizer LieSubalgebra.exists_nested_lieIdeal_ofLe_normalizer
+-/
 
 variable (H)

6b31d1ee

bump to nightly-2023-06-10-03

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

e13a28eb

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Oliver Nash
 
 ! This file was ported from Lean 3 source module algebra.lie.normalizer
-! leanprover-community/mathlib commit 938fead7abdc0cbbca8eba7a1052865a169dc102
+! leanprover-community/mathlib commit 6b31d1eebd64eab86d5bd9936bfaada6ca8b5842
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -15,6 +15,9 @@ import Mathbin.Algebra.Lie.Quotient
 /-!
 # The normalizer of a Lie submodules and subalgebras.
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 Given a Lie module `M` over a Lie subalgebra `L`, the normalizer of a Lie submodule `N ⊆ M` is
 the Lie submodule with underlying set `{ m | ∀ (x : L), ⁅x, m⁆ ∈ N }`.

938fead7

bump to nightly-2023-06-08-11

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

7d7c0aca

Diff

@@ -50,6 +50,7 @@ namespace LieSubmodule
 
 variable (N : LieSubmodule R L M) {N₁ N₂ : LieSubmodule R L M}
 
+#print LieSubmodule.normalizer /-
 /-- The normalizer of a Lie submodule. -/
 def normalizer : LieSubmodule R L M
     where
@@ -59,6 +60,7 @@ def normalizer : LieSubmodule R L M
   smul_mem' t m hm x := by rw [lie_smul]; exact N.smul_mem' t (hm x)
   lie_mem x m hm y := by rw [leibniz_lie]; exact N.add_mem' (hm ⁅y, x⁆) (N.lie_mem (hm y))
 #align lie_submodule.normalizer LieSubmodule.normalizer
+-/
 
 @[simp]
 theorem mem_normalizer (m : M) : m ∈ N.normalizer ↔ ∀ x : L, ⁅x, m⁆ ∈ N :=
@@ -110,6 +112,7 @@ namespace LieSubalgebra
 
 variable (H : LieSubalgebra R L)
 
+#print LieSubalgebra.normalizer /-
 /-- Regarding a Lie subalgebra `H ⊆ L` as a module over itself, its normalizer is in fact a Lie
 subalgebra. -/
 def normalizer : LieSubalgebra R L :=
@@ -119,26 +122,33 @@ def normalizer : LieSubalgebra R L :=
       rw [coe_bracket_of_module, mem_to_lie_submodule, leibniz_lie, ← lie_skew y, ← sub_eq_add_neg]
       exact H.sub_mem (hz ⟨_, hy x⟩) (hy ⟨_, hz x⟩) }
 #align lie_subalgebra.normalizer LieSubalgebra.normalizer
+-/
 
+#print LieSubalgebra.mem_normalizer_iff' /-
 theorem mem_normalizer_iff' (x : L) : x ∈ H.normalizer ↔ ∀ y : L, y ∈ H → ⁅y, x⁆ ∈ H := by
   rw [Subtype.forall']; rfl
 #align lie_subalgebra.mem_normalizer_iff' LieSubalgebra.mem_normalizer_iff'
+-/
 
+#print LieSubalgebra.mem_normalizer_iff /-
 theorem mem_normalizer_iff (x : L) : x ∈ H.normalizer ↔ ∀ y : L, y ∈ H → ⁅x, y⁆ ∈ H :=
   by
   rw [mem_normalizer_iff']
   refine' forall₂_congr fun y hy => _
   rw [← lie_skew, neg_mem_iff]
 #align lie_subalgebra.mem_normalizer_iff LieSubalgebra.mem_normalizer_iff
+-/
 
 theorem le_normalizer : H ≤ H.normalizer :=
   H.toLieSubmodule.le_normalizer
 #align lie_subalgebra.le_normalizer LieSubalgebra.le_normalizer
 
+#print LieSubalgebra.coe_normalizer_eq_normalizer /-
 theorem coe_normalizer_eq_normalizer :
     (H.toLieSubmodule.normalizer : Submodule R L) = H.normalizer :=
   rfl
 #align lie_subalgebra.coe_normalizer_eq_normalizer LieSubalgebra.coe_normalizer_eq_normalizer
+-/
 
 variable {H}
 
@@ -157,12 +167,14 @@ theorem lie_mem_sup_of_mem_normalizer {x y z : L} (hx : x ∈ H.normalizer) (hy
   exacts [(H.mem_normalizer_iff' x).mp hx v hv, (H.mem_normalizer_iff x).mp hx w hw]
 #align lie_subalgebra.lie_mem_sup_of_mem_normalizer LieSubalgebra.lie_mem_sup_of_mem_normalizer
 
+#print LieSubalgebra.ideal_in_normalizer /-
 /-- A Lie subalgebra is an ideal of its normalizer. -/
 theorem ideal_in_normalizer {x y : L} (hx : x ∈ H.normalizer) (hy : y ∈ H) : ⁅x, y⁆ ∈ H :=
   by
   rw [← lie_skew, neg_mem_iff]
   exact hx ⟨y, hy⟩
 #align lie_subalgebra.ideal_in_normalizer LieSubalgebra.ideal_in_normalizer
+-/
 
 /-- A Lie subalgebra `H` is an ideal of any Lie subalgebra `K` containing `H` and contained in the
 normalizer of `H`. -/
@@ -175,6 +187,7 @@ theorem exists_nested_lieIdeal_ofLe_normalizer {K : LieSubalgebra R L} (h₁ : H
 
 variable (H)
 
+#print LieSubalgebra.normalizer_eq_self_iff /-
 theorem normalizer_eq_self_iff :
     H.normalizer = H ↔ (LieModule.maxTrivSubmodule R H <| L ⧸ H.toLieSubmodule) = ⊥ :=
   by
@@ -195,6 +208,7 @@ theorem normalizer_eq_self_iff :
       exact (H.mem_normalizer_iff' x).mp hx z hz
     simpa using h y hy
 #align lie_subalgebra.normalizer_eq_self_iff LieSubalgebra.normalizer_eq_self_iff
+-/
 
 end LieSubalgebra

938fead7

bump to nightly-2023-06-04-18

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

3fb4268b

Diff

@@ -53,7 +53,7 @@ variable (N : LieSubmodule R L M) {N₁ N₂ : LieSubmodule R L M}
 /-- The normalizer of a Lie submodule. -/
 def normalizer : LieSubmodule R L M
     where
-  carrier := { m | ∀ x : L, ⁅x, m⁆ ∈ N }
+  carrier := {m | ∀ x : L, ⁅x, m⁆ ∈ N}
   add_mem' m₁ m₂ hm₁ hm₂ x := by rw [lie_add]; exact N.add_mem' (hm₁ x) (hm₂ x)
   zero_mem' x := by simp
   smul_mem' t m hm x := by rw [lie_smul]; exact N.smul_mem' t (hm x)

938fead7

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -79,7 +79,7 @@ theorem normalizer_inf : (N₁ ⊓ N₂).normalizer = N₁.normalizer ⊓ N₂.n
 theorem monotone_normalizer : Monotone (normalizer : LieSubmodule R L M → LieSubmodule R L M) :=
   by
   intro N₁ N₂ h m hm
-  rw [mem_normalizer] at hm⊢
+  rw [mem_normalizer] at hm ⊢
   exact fun x => h (hm x)
 #align lie_submodule.monotone_normalizer LieSubmodule.monotone_normalizer
 
@@ -145,7 +145,7 @@ variable {H}
 theorem lie_mem_sup_of_mem_normalizer {x y z : L} (hx : x ∈ H.normalizer) (hy : y ∈ (R ∙ x) ⊔ ↑H)
     (hz : z ∈ (R ∙ x) ⊔ ↑H) : ⁅y, z⁆ ∈ (R ∙ x) ⊔ ↑H :=
   by
-  rw [Submodule.mem_sup] at hy hz
+  rw [Submodule.mem_sup] at hy hz 
   obtain ⟨u₁, hu₁, v, hv : v ∈ H, rfl⟩ := hy
   obtain ⟨u₂, hu₂, w, hw : w ∈ H, rfl⟩ := hz
   obtain ⟨t, rfl⟩ := submodule.mem_span_singleton.mp hu₁
@@ -154,7 +154,7 @@ theorem lie_mem_sup_of_mem_normalizer {x y z : L} (hx : x ∈ H.normalizer) (hy
   simp only [LieSubalgebra.mem_coe_submodule, smul_lie, add_lie, zero_add, lie_add, smul_zero,
     lie_smul, lie_self]
   refine' H.add_mem (H.smul_mem s _) (H.add_mem (H.smul_mem t _) (H.lie_mem hv hw))
-  exacts[(H.mem_normalizer_iff' x).mp hx v hv, (H.mem_normalizer_iff x).mp hx w hw]
+  exacts [(H.mem_normalizer_iff' x).mp hx v hv, (H.mem_normalizer_iff x).mp hx w hw]
 #align lie_subalgebra.lie_mem_sup_of_mem_normalizer LieSubalgebra.lie_mem_sup_of_mem_normalizer
 
 /-- A Lie subalgebra is an ideal of its normalizer. -/
@@ -185,7 +185,7 @@ theorem normalizer_eq_self_iff :
     rw [← h, H.mem_normalizer_iff']
     intro y hy
     replace hx : ⁅_, LieSubmodule.Quotient.mk' _ x⁆ = 0 := hx ⟨y, hy⟩
-    rwa [← LieModuleHom.map_lie, LieSubmodule.Quotient.mk_eq_zero] at hx
+    rwa [← LieModuleHom.map_lie, LieSubmodule.Quotient.mk_eq_zero] at hx 
   · let y := LieSubmodule.Quotient.mk' H.to_lie_submodule x
     have hy : y ∈ LieModule.maxTrivSubmodule R H (L ⧸ H.to_lie_submodule) :=
       by

938fead7

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -54,16 +54,10 @@ variable (N : LieSubmodule R L M) {N₁ N₂ : LieSubmodule R L M}
 def normalizer : LieSubmodule R L M
     where
   carrier := { m | ∀ x : L, ⁅x, m⁆ ∈ N }
-  add_mem' m₁ m₂ hm₁ hm₂ x := by
-    rw [lie_add]
-    exact N.add_mem' (hm₁ x) (hm₂ x)
+  add_mem' m₁ m₂ hm₁ hm₂ x := by rw [lie_add]; exact N.add_mem' (hm₁ x) (hm₂ x)
   zero_mem' x := by simp
-  smul_mem' t m hm x := by
-    rw [lie_smul]
-    exact N.smul_mem' t (hm x)
-  lie_mem x m hm y := by
-    rw [leibniz_lie]
-    exact N.add_mem' (hm ⁅y, x⁆) (N.lie_mem (hm y))
+  smul_mem' t m hm x := by rw [lie_smul]; exact N.smul_mem' t (hm x)
+  lie_mem x m hm y := by rw [leibniz_lie]; exact N.add_mem' (hm ⁅y, x⁆) (N.lie_mem (hm y))
 #align lie_submodule.normalizer LieSubmodule.normalizer
 
 @[simp]
@@ -77,9 +71,7 @@ theorem le_normalizer : N ≤ N.normalizer := by
   exact fun x => N.lie_mem hm
 #align lie_submodule.le_normalizer LieSubmodule.le_normalizer
 
-theorem normalizer_inf : (N₁ ⊓ N₂).normalizer = N₁.normalizer ⊓ N₂.normalizer :=
-  by
-  ext
+theorem normalizer_inf : (N₁ ⊓ N₂).normalizer = N₁.normalizer ⊓ N₂.normalizer := by ext;
   simp [← forall_and]
 #align lie_submodule.normalizer_inf LieSubmodule.normalizer_inf
 
@@ -92,17 +84,12 @@ theorem monotone_normalizer : Monotone (normalizer : LieSubmodule R L M → LieS
 #align lie_submodule.monotone_normalizer LieSubmodule.monotone_normalizer
 
 @[simp]
-theorem comap_normalizer (f : M' →ₗ⁅R,L⁆ M) : N.normalizer.comap f = (N.comap f).normalizer :=
-  by
-  ext
-  simp
+theorem comap_normalizer (f : M' →ₗ⁅R,L⁆ M) : N.normalizer.comap f = (N.comap f).normalizer := by
+  ext; simp
 #align lie_submodule.comap_normalizer LieSubmodule.comap_normalizer
 
 theorem top_lie_le_iff_le_normalizer (N' : LieSubmodule R L M) :
-    ⁅(⊤ : LieIdeal R L), N⁆ ≤ N' ↔ N ≤ N'.normalizer :=
-  by
-  rw [lie_le_iff]
-  tauto
+    ⁅(⊤ : LieIdeal R L), N⁆ ≤ N' ↔ N ≤ N'.normalizer := by rw [lie_le_iff]; tauto
 #align lie_submodule.top_lie_le_iff_le_normalizer LieSubmodule.top_lie_le_iff_le_normalizer
 
 theorem gc_top_lie_normalizer :
@@ -133,10 +120,8 @@ def normalizer : LieSubalgebra R L :=
       exact H.sub_mem (hz ⟨_, hy x⟩) (hy ⟨_, hz x⟩) }
 #align lie_subalgebra.normalizer LieSubalgebra.normalizer
 
-theorem mem_normalizer_iff' (x : L) : x ∈ H.normalizer ↔ ∀ y : L, y ∈ H → ⁅y, x⁆ ∈ H :=
-  by
-  rw [Subtype.forall']
-  rfl
+theorem mem_normalizer_iff' (x : L) : x ∈ H.normalizer ↔ ∀ y : L, y ∈ H → ⁅y, x⁆ ∈ H := by
+  rw [Subtype.forall']; rfl
 #align lie_subalgebra.mem_normalizer_iff' LieSubalgebra.mem_normalizer_iff'
 
 theorem mem_normalizer_iff (x : L) : x ∈ H.normalizer ↔ ∀ y : L, y ∈ H → ⁅x, y⁆ ∈ H :=

938fead7

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

938fead7

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

@@ -36,11 +36,8 @@ lie algebra, normalizer
 
 
 variable {R L M M' : Type*}
-
 variable [CommRing R] [LieRing L] [LieAlgebra R L]
-
 variable [AddCommGroup M] [Module R M] [LieRingModule L M] [LieModule R L M]
-
 variable [AddCommGroup M'] [Module R M'] [LieRingModule L M'] [LieModule R L M']
 
 namespace LieSubmodule

938fead7

chore: prepare Lean version bump with explicit simp (#10999)

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

38bce757

Diff

@@ -203,7 +203,7 @@ theorem normalizer_eq_self_iff :
       rw [← LieModuleHom.map_lie, LieSubmodule.Quotient.mk_eq_zero, coe_bracket_of_module,
         Submodule.coe_mk, mem_toLieSubmodule]
       exact (H.mem_normalizer_iff' x).mp hx z hz
-    simpa using h y hy
+    simpa [y] using h y hy
 #align lie_subalgebra.normalizer_eq_self_iff LieSubalgebra.normalizer_eq_self_iff
 
 end LieSubalgebra

938fead7

feat: further theory about the Killing form of Lie algebras (#6737)

e92aa3c8

Diff

@@ -47,7 +47,9 @@ namespace LieSubmodule
 
 variable (N : LieSubmodule R L M) {N₁ N₂ : LieSubmodule R L M}
 
-/-- The normalizer of a Lie submodule. -/
+/-- The normalizer of a Lie submodule.
+
+See also `LieSubmodule.idealizer`. -/
 def normalizer : LieSubmodule R L M where
   carrier := {m | ∀ x : L, ⁅x, m⁆ ∈ N}
   add_mem' hm₁ hm₂ x := by rw [lie_add]; exact N.add_mem' (hm₁ x) (hm₂ x)
@@ -61,6 +63,7 @@ theorem mem_normalizer (m : M) : m ∈ N.normalizer ↔ ∀ x : L, ⁅x, m⁆ 
   Iff.rfl
 #align lie_submodule.mem_normalizer LieSubmodule.mem_normalizer
 
+@[simp]
 theorem le_normalizer : N ≤ N.normalizer := by
   intro m hm
   rw [mem_normalizer]
@@ -92,13 +95,30 @@ theorem gc_top_lie_normalizer :
   top_lie_le_iff_le_normalizer
 #align lie_submodule.gc_top_lie_normalizer LieSubmodule.gc_top_lie_normalizer
 
-variable (R L M)
-
+variable (R L M) in
 theorem normalizer_bot_eq_maxTrivSubmodule :
     (⊥ : LieSubmodule R L M).normalizer = LieModule.maxTrivSubmodule R L M :=
   rfl
 #align lie_submodule.normalizer_bot_eq_max_triv_submodule LieSubmodule.normalizer_bot_eq_maxTrivSubmodule
 
+/-- The idealizer of a Lie submodule.
+
+See also `LieSubmodule.normalizer`. -/
+def idealizer : LieIdeal R L where
+  carrier := {x : L | ∀ m : M, ⁅x, m⁆ ∈ N}
+  add_mem' := fun {x} {y} hx hy m ↦ by rw [add_lie]; exact N.add_mem (hx m) (hy m)
+  zero_mem' := by simp
+  smul_mem' := fun t {x} hx m ↦ by rw [smul_lie]; exact N.smul_mem t (hx m)
+  lie_mem := fun {x} {y} hy m ↦ by rw [lie_lie]; exact sub_mem (N.lie_mem (hy m)) (hy ⁅x, m⁆)
+
+@[simp]
+lemma mem_idealizer {x : L} : x ∈ N.idealizer ↔ ∀ m : M, ⁅x, m⁆ ∈ N := Iff.rfl
+
+@[simp]
+lemma _root_.LieIdeal.idealizer_eq_normalizer (I : LieIdeal R L) :
+    I.idealizer = I.normalizer := by
+  ext x; exact forall_congr' fun y ↦ by simp only [← lie_skew x y, neg_mem_iff]
+
 end LieSubmodule
 
 namespace LieSubalgebra

938fead7

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

@@ -35,7 +35,7 @@ lie algebra, normalizer
 -/
 
 
-variable {R L M M' : Type _}
+variable {R L M M' : Type*}
 
 variable [CommRing R] [LieRing L] [LieAlgebra R L]

938fead7

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) 2022 Oliver Nash. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Oliver Nash
-
-! This file was ported from Lean 3 source module algebra.lie.normalizer
-! leanprover-community/mathlib commit 938fead7abdc0cbbca8eba7a1052865a169dc102
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Algebra.Lie.Abelian
 import Mathlib.Algebra.Lie.IdealOperations
 import Mathlib.Algebra.Lie.Quotient
 
+#align_import algebra.lie.normalizer from "leanprover-community/mathlib"@"938fead7abdc0cbbca8eba7a1052865a169dc102"
+
 /-!
 # The normalizer of Lie submodules and subalgebras.

938fead7

feat: port Algebra.Lie.Normalizer (#4843)

84610768

`algebra.lie.normalizer` ⟷ `Mathlib.Algebra.Lie.Normalizer`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 8 + 472

algebra.lie.normalizer ⟷ Mathlib.Algebra.Lie.Normalizer

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 8 + 472

`algebra.lie.normalizer` ⟷ `Mathlib.Algebra.Lie.Normalizer`