algebra.lie.engel | 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

210657c4

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

44e2ae8c

bump to nightly-2024-04-06-08

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

e34029c9

Diff

@@ -130,7 +130,7 @@ theorem lcs_le_lcs_of_is_nilpotent_span_sup_eq_top {n i j : ℕ}
     exact le_sup_of_le_left hIM
   · simp only [LieIdeal.lcs_succ, i.add_succ l, lie_top_eq_of_span_sup_eq_top hxI, sup_le_iff]
     refine' ⟨(Submodule.map_mono ih).trans _, le_sup_of_le_right _⟩
-    · rw [Submodule.map_sup, ← Submodule.map_comp, ← LinearMap.mul_eq_comp, ← pow_succ, ←
+    · rw [Submodule.map_sup, ← Submodule.map_comp, ← LinearMap.mul_eq_comp, ← pow_succ', ←
         I.lcs_succ]
       exact sup_le_sup_left coe_map_to_endomorphism_le _
     · refine' le_trans (mono_lie_right _ _ I _) (mono_lie_right _ _ I hIM)

44e2ae8c

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -88,7 +88,7 @@ variable {I : LieIdeal R L} {x : L} (hxI : (R ∙ x) ⊔ I = ⊤)
 theorem exists_smul_add_of_span_sup_eq_top (y : L) : ∃ t : R, ∃ z ∈ I, y = t • x + z :=
   by
   have hy : y ∈ (⊤ : Submodule R L) := Submodule.mem_top
-  simp only [← hxI, Submodule.mem_sup, Submodule.mem_span_singleton] at hy 
+  simp only [← hxI, Submodule.mem_sup, Submodule.mem_span_singleton] at hy
   obtain ⟨-, ⟨t, rfl⟩, z, hz, rfl⟩ := hy
   exact ⟨t, z, hz, rfl⟩
 #align lie_submodule.exists_smul_add_of_span_sup_eq_top LieSubmodule.exists_smul_add_of_span_sup_eq_top

44e2ae8c

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,8 +3,8 @@ 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.Nilpotent
-import Mathbin.Algebra.Lie.Normalizer
+import Algebra.Lie.Nilpotent
+import Algebra.Lie.Normalizer
 
 #align_import algebra.lie.engel from "leanprover-community/mathlib"@"44e2ae8cffc713925494e4975ee31ec1d06929b3"

44e2ae8c

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,15 +2,12 @@
 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.engel
-! leanprover-community/mathlib commit 44e2ae8cffc713925494e4975ee31ec1d06929b3
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.Lie.Nilpotent
 import Mathbin.Algebra.Lie.Normalizer
 
+#align_import algebra.lie.engel from "leanprover-community/mathlib"@"44e2ae8cffc713925494e4975ee31ec1d06929b3"
+
 /-!
 # Engel's theorem

44e2ae8c

bump to nightly-2023-06-14-03

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

f4ed04bb

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.engel
-! leanprover-community/mathlib commit 210657c4ea4a4a7b234392f70a3a2a83346dfa90
+! leanprover-community/mathlib commit 44e2ae8cffc713925494e4975ee31ec1d06929b3
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.Algebra.Lie.Normalizer
 /-!
 # Engel's theorem
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file contains a proof of Engel's theorem providing necessary and sufficient conditions for Lie
 algebras and Lie modules to be nilpotent.

210657c4

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -78,16 +78,13 @@ variable [CommRing R] [LieRing L] [LieAlgebra R L] [LieRing L₂] [LieAlgebra R
 
 variable [AddCommGroup M] [Module R M] [LieRingModule L M] [LieModule R L M]
 
-include R L
-
 namespace LieSubmodule
 
 open LieModule
 
 variable {I : LieIdeal R L} {x : L} (hxI : (R ∙ x) ⊔ I = ⊤)
 
-include hxI
-
+#print LieSubmodule.exists_smul_add_of_span_sup_eq_top /-
 theorem exists_smul_add_of_span_sup_eq_top (y : L) : ∃ t : R, ∃ z ∈ I, y = t • x + z :=
   by
   have hy : y ∈ (⊤ : Submodule R L) := Submodule.mem_top
@@ -95,7 +92,9 @@ theorem exists_smul_add_of_span_sup_eq_top (y : L) : ∃ t : R, ∃ z ∈ I, y =
   obtain ⟨-, ⟨t, rfl⟩, z, hz, rfl⟩ := hy
   exact ⟨t, z, hz, rfl⟩
 #align lie_submodule.exists_smul_add_of_span_sup_eq_top LieSubmodule.exists_smul_add_of_span_sup_eq_top
+-/
 
+#print LieSubmodule.lie_top_eq_of_span_sup_eq_top /-
 theorem lie_top_eq_of_span_sup_eq_top (N : LieSubmodule R L M) :
     (↑⁅(⊤ : LieIdeal R L), N⁆ : Submodule R M) =
       (N : Submodule R M).map (toEndomorphism R L M x) ⊔ (↑⁅I, N⁆ : Submodule R M) :=
@@ -112,7 +111,9 @@ theorem lie_top_eq_of_span_sup_eq_top (N : LieSubmodule R L M) :
   · rcases hz with (⟨m, hm, rfl⟩ | ⟨y, hy, m, hm, rfl⟩)
     exacts [⟨x, m, hm, rfl⟩, ⟨y, m, hm, rfl⟩]
 #align lie_submodule.lie_top_eq_of_span_sup_eq_top LieSubmodule.lie_top_eq_of_span_sup_eq_top
+-/
 
+#print LieSubmodule.lcs_le_lcs_of_is_nilpotent_span_sup_eq_top /-
 theorem lcs_le_lcs_of_is_nilpotent_span_sup_eq_top {n i j : ℕ}
     (hxn : toEndomorphism R L M x ^ n = 0) (hIM : lowerCentralSeries R L M i ≤ I.lcs M j) :
     lowerCentralSeries R L M (i + n) ≤ I.lcs M (j + 1) :=
@@ -135,7 +136,9 @@ theorem lcs_le_lcs_of_is_nilpotent_span_sup_eq_top {n i j : ℕ}
     · refine' le_trans (mono_lie_right _ _ I _) (mono_lie_right _ _ I hIM)
       exact antitone_lower_central_series R L M le_self_add
 #align lie_submodule.lcs_le_lcs_of_is_nilpotent_span_sup_eq_top LieSubmodule.lcs_le_lcs_of_is_nilpotent_span_sup_eq_top
+-/
 
+#print LieSubmodule.isNilpotentOfIsNilpotentSpanSupEqTop /-
 theorem isNilpotentOfIsNilpotentSpanSupEqTop (hnp : IsNilpotent <| toEndomorphism R L M x)
     (hIM : IsNilpotent R I M) : IsNilpotent R L M :=
   by
@@ -152,6 +155,7 @@ theorem isNilpotentOfIsNilpotentSpanSupEqTop (hnp : IsNilpotent <| toEndomorphis
   · simp
   · exact (l.succ_mul n).symm ▸ lcs_le_lcs_of_is_nilpotent_span_sup_eq_top hxI hn ih
 #align lie_submodule.is_nilpotent_of_is_nilpotent_span_sup_eq_top LieSubmodule.isNilpotentOfIsNilpotentSpanSupEqTop
+-/
 
 end LieSubmodule
 
@@ -177,6 +181,7 @@ def LieAlgebra.IsEngelian : Prop :=
 
 variable {R L}
 
+#print LieAlgebra.isEngelian_of_subsingleton /-
 theorem LieAlgebra.isEngelian_of_subsingleton [Subsingleton L] : LieAlgebra.IsEngelian R L :=
   by
   intro M _i1 _i2 _i3 _i4 h
@@ -185,7 +190,9 @@ theorem LieAlgebra.isEngelian_of_subsingleton [Subsingleton L] : LieAlgebra.IsEn
   haveI := (LieSubmodule.subsingleton_iff R L L).mpr inferInstance
   apply Subsingleton.elim
 #align lie_algebra.is_engelian_of_subsingleton LieAlgebra.isEngelian_of_subsingleton
+-/
 
+#print Function.Surjective.isEngelian /-
 theorem Function.Surjective.isEngelian {f : L →ₗ⁅R⁆ L₂} (hf : Function.Surjective f)
     (h : LieAlgebra.IsEngelian.{u₁, u₂, u₄} R L) : LieAlgebra.IsEngelian.{u₁, u₃, u₄} R L₂ :=
   by
@@ -198,6 +205,7 @@ theorem Function.Surjective.isEngelian {f : L →ₗ⁅R⁆ L₂} (hf : Function
   apply hf.lie_module_is_nilpotent surj_id
   simp
 #align function.surjective.is_engelian Function.Surjective.isEngelian
+-/
 
 #print LieEquiv.isEngelian_iff /-
 theorem LieEquiv.isEngelian_iff (e : L ≃ₗ⁅R⁆ L₂) :
@@ -206,6 +214,7 @@ theorem LieEquiv.isEngelian_iff (e : L ≃ₗ⁅R⁆ L₂) :
 #align lie_equiv.is_engelian_iff LieEquiv.isEngelian_iff
 -/
 
+#print LieAlgebra.exists_engelian_lieSubalgebra_of_lt_normalizer /-
 theorem LieAlgebra.exists_engelian_lieSubalgebra_of_lt_normalizer {K : LieSubalgebra R L}
     (hK₁ : LieAlgebra.IsEngelian.{u₁, u₂, u₄} R K) (hK₂ : K < K.normalizer) :
     ∃ (K' : LieSubalgebra R L) (hK' : LieAlgebra.IsEngelian.{u₁, u₂, u₄} R K'), K < K' :=
@@ -235,11 +244,13 @@ theorem LieAlgebra.exists_engelian_lieSubalgebra_of_lt_normalizer {K : LieSubalg
   have hI₃ : LieAlgebra.IsEngelian R I := e.is_engelian_iff.mp hK₁
   exact LieSubmodule.isNilpotentOfIsNilpotentSpanSupEqTop hI₂ (h _) (hI₃ _ fun x => h x)
 #align lie_algebra.exists_engelian_lie_subalgebra_of_lt_normalizer LieAlgebra.exists_engelian_lieSubalgebra_of_lt_normalizer
+-/
 
 attribute [local instance] LieSubalgebra.subsingleton_bot
 
 variable [IsNoetherian R L]
 
+#print LieAlgebra.isEngelian_of_isNoetherian /-
 /-- *Engel's theorem*.
 
 Note that this implies all traditional forms of Engel's theorem via
@@ -289,6 +300,7 @@ theorem LieAlgebra.isEngelian_of_isNoetherian : LieAlgebra.IsEngelian R L :=
     exact hK₂ K' hK'₁ hK'₂
   exact hK₃ ▸ hK₁
 #align lie_algebra.is_engelian_of_is_noetherian LieAlgebra.isEngelian_of_isNoetherian
+-/
 
 #print LieModule.isNilpotent_iff_forall /-
 /-- Engel's theorem. -/
@@ -301,11 +313,13 @@ theorem LieModule.isNilpotent_iff_forall :
 #align lie_module.is_nilpotent_iff_forall LieModule.isNilpotent_iff_forall
 -/
 
+#print LieAlgebra.isNilpotent_iff_forall /-
 /-- Engel's theorem. -/
 theorem LieAlgebra.isNilpotent_iff_forall :
     LieAlgebra.IsNilpotent R L ↔ ∀ x, IsNilpotent <| LieAlgebra.ad R L x :=
   LieModule.isNilpotent_iff_forall
 #align lie_algebra.is_nilpotent_iff_forall LieAlgebra.isNilpotent_iff_forall
+-/
 
 end LieAlgebra

210657c4

bump to nightly-2023-06-12-17

mathlib commit https://github.com/leanprover-community/mathlib/commit/ccdbfb6e5614667af5aa3ab2d50885e0ef44a46f

ae53e046

Diff

@@ -161,6 +161,7 @@ open LieModule hiding IsNilpotent
 
 variable (R L)
 
+#print LieAlgebra.IsEngelian /-
 /-- A Lie algebra `L` is said to be Engelian if a sufficient condition for any `L`-Lie module `M` to
 be nilpotent is that the image of the map `L → End(M)` consists of nilpotent elements.
 
@@ -172,6 +173,7 @@ def LieAlgebra.IsEngelian : Prop :=
       ∀ [LieModule R L M],
         ∀ h : ∀ x : L, IsNilpotent (to_endomorphism R L M x), LieModule.IsNilpotent R L M
 #align lie_algebra.is_engelian LieAlgebra.IsEngelian
+-/
 
 variable {R L}
 
@@ -197,10 +199,12 @@ theorem Function.Surjective.isEngelian {f : L →ₗ⁅R⁆ L₂} (hf : Function
   simp
 #align function.surjective.is_engelian Function.Surjective.isEngelian
 
+#print LieEquiv.isEngelian_iff /-
 theorem LieEquiv.isEngelian_iff (e : L ≃ₗ⁅R⁆ L₂) :
     LieAlgebra.IsEngelian.{u₁, u₂, u₄} R L ↔ LieAlgebra.IsEngelian.{u₁, u₃, u₄} R L₂ :=
   ⟨e.Surjective.IsEngelian, e.symm.Surjective.IsEngelian⟩
 #align lie_equiv.is_engelian_iff LieEquiv.isEngelian_iff
+-/
 
 theorem LieAlgebra.exists_engelian_lieSubalgebra_of_lt_normalizer {K : LieSubalgebra R L}
     (hK₁ : LieAlgebra.IsEngelian.{u₁, u₂, u₄} R K) (hK₂ : K < K.normalizer) :
@@ -286,6 +290,7 @@ theorem LieAlgebra.isEngelian_of_isNoetherian : LieAlgebra.IsEngelian R L :=
   exact hK₃ ▸ hK₁
 #align lie_algebra.is_engelian_of_is_noetherian LieAlgebra.isEngelian_of_isNoetherian
 
+#print LieModule.isNilpotent_iff_forall /-
 /-- Engel's theorem. -/
 theorem LieModule.isNilpotent_iff_forall :
     LieModule.IsNilpotent R L M ↔ ∀ x, IsNilpotent <| toEndomorphism R L M x :=
@@ -294,6 +299,7 @@ theorem LieModule.isNilpotent_iff_forall :
     obtain ⟨k, hk⟩ := nilpotent_endo_of_nilpotent_module R L M
     exact fun x => ⟨k, hk x⟩, fun h => LieAlgebra.isEngelian_of_isNoetherian M h⟩
 #align lie_module.is_nilpotent_iff_forall LieModule.isNilpotent_iff_forall
+-/
 
 /-- Engel's theorem. -/
 theorem LieAlgebra.isNilpotent_iff_forall :

210657c4

bump to nightly-2023-06-04-18

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

3fb4268b

Diff

@@ -250,7 +250,7 @@ theorem LieAlgebra.isEngelian_of_isNoetherian : LieAlgebra.IsEngelian R L :=
   · rintro ⟨-, ⟨y, rfl⟩⟩
     simp [h]
   change LieModule.IsNilpotent R L' M
-  let s := { K : LieSubalgebra R L' | LieAlgebra.IsEngelian R K }
+  let s := {K : LieSubalgebra R L' | LieAlgebra.IsEngelian R K}
   have hs : s.nonempty := ⟨⊥, LieAlgebra.isEngelian_of_subsingleton⟩
   suffices ⊤ ∈ s by
     rw [← is_nilpotent_of_top_iff]
@@ -266,7 +266,7 @@ theorem LieAlgebra.isEngelian_of_isNoetherian : LieAlgebra.IsEngelian R L :=
     have : Nontrivial (L' ⧸ K.to_lie_submodule) :=
       by
       replace hK₂ : K.to_lie_submodule ≠ ⊤ := by
-        rwa [Ne.def, ← LieSubmodule.coe_to_submodule_eq_iff, K.coe_to_lie_submodule,
+        rwa [Ne.def, ← LieSubmodule.coe_toSubmodule_eq_iff, K.coe_to_lie_submodule,
           LieSubmodule.top_coeSubmodule, ← LieSubalgebra.top_coe_submodule,
           K.coe_to_submodule_eq_iff]
       exact Submodule.Quotient.nontrivial_of_lt_top _ hK₂.lt_top

210657c4

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -91,7 +91,7 @@ include hxI
 theorem exists_smul_add_of_span_sup_eq_top (y : L) : ∃ t : R, ∃ z ∈ I, y = t • x + z :=
   by
   have hy : y ∈ (⊤ : Submodule R L) := Submodule.mem_top
-  simp only [← hxI, Submodule.mem_sup, Submodule.mem_span_singleton] at hy
+  simp only [← hxI, Submodule.mem_sup, Submodule.mem_span_singleton] at hy 
   obtain ⟨-, ⟨t, rfl⟩, z, hz, rfl⟩ := hy
   exact ⟨t, z, hz, rfl⟩
 #align lie_submodule.exists_smul_add_of_span_sup_eq_top LieSubmodule.exists_smul_add_of_span_sup_eq_top
@@ -110,7 +110,7 @@ theorem lie_top_eq_of_span_sup_eq_top (N : LieSubmodule R L M) :
       ⟨t • ⁅x, n⁆, Submodule.subset_span ⟨t • n, N.smul_mem' t hn, lie_smul t x n⟩, ⁅z, n⁆,
         Submodule.subset_span ⟨z, hz, n, hn, rfl⟩, by simp⟩
   · rcases hz with (⟨m, hm, rfl⟩ | ⟨y, hy, m, hm, rfl⟩)
-    exacts[⟨x, m, hm, rfl⟩, ⟨y, m, hm, rfl⟩]
+    exacts [⟨x, m, hm, rfl⟩, ⟨y, m, hm, rfl⟩]
 #align lie_submodule.lie_top_eq_of_span_sup_eq_top LieSubmodule.lie_top_eq_of_span_sup_eq_top
 
 theorem lcs_le_lcs_of_is_nilpotent_span_sup_eq_top {n i j : ℕ}
@@ -204,7 +204,7 @@ theorem LieEquiv.isEngelian_iff (e : L ≃ₗ⁅R⁆ L₂) :
 
 theorem LieAlgebra.exists_engelian_lieSubalgebra_of_lt_normalizer {K : LieSubalgebra R L}
     (hK₁ : LieAlgebra.IsEngelian.{u₁, u₂, u₄} R K) (hK₂ : K < K.normalizer) :
-    ∃ (K' : LieSubalgebra R L)(hK' : LieAlgebra.IsEngelian.{u₁, u₂, u₄} R K'), K < K' :=
+    ∃ (K' : LieSubalgebra R L) (hK' : LieAlgebra.IsEngelian.{u₁, u₂, u₄} R K'), K < K' :=
   by
   obtain ⟨x, hx₁, hx₂⟩ := SetLike.exists_of_lt hK₂
   let K' : LieSubalgebra R L :=

210657c4

bump to nightly-2023-06-01-04

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

4d9eaa85

Diff

@@ -143,7 +143,7 @@ theorem isNilpotentOfIsNilpotentSpanSupEqTop (hnp : IsNilpotent <| toEndomorphis
   obtain ⟨k, hk⟩ := hIM
   have hk' : I.lcs M k = ⊥ := by
     simp only [← coe_to_submodule_eq_iff, I.coe_lcs_eq, hk, bot_coe_submodule]
-  suffices ∀ l, lower_central_series R L M (l * n) ≤ I.lcs M l
+  suffices ∀ l, lowerCentralSeries R L M (l * n) ≤ I.lcs M l
     by
     use k * n
     simpa [hk'] using this k

210657c4

bump to nightly-2023-04-02-02

mathlib commit https://github.com/leanprover-community/mathlib/commit/88fcb83fe7996142dfcfe7368d31304a9adc874a

a22ad38d

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.engel
-! leanprover-community/mathlib commit 938fead7abdc0cbbca8eba7a1052865a169dc102
+! leanprover-community/mathlib commit 210657c4ea4a4a7b234392f70a3a2a83346dfa90
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -278,14 +278,11 @@ theorem LieAlgebra.isEngelian_of_isNoetherian : LieAlgebra.IsEngelian R L :=
     exact nontrivial_max_triv_of_is_nilpotent R K (L' ⧸ K.to_lie_submodule)
   haveI _i5 : IsNoetherian R L' :=
     isNoetherian_of_surjective L _ (LinearMap.range_rangeRestrict (to_endomorphism R L M))
-  obtain ⟨K, hK₁, hK₂⟩ :=
-    well_founded.well_founded_iff_has_max'.mp (LieSubalgebra.wellFounded_of_noetherian R L') s hs
+  obtain ⟨K, hK₁, hK₂⟩ := (LieSubalgebra.wellFounded_of_noetherian R L').has_min s hs
   have hK₃ : K = ⊤ := by
     by_contra contra
     obtain ⟨K', hK'₁, hK'₂⟩ := this K hK₁ contra
-    specialize hK₂ K' hK'₁ (le_of_lt hK'₂)
-    replace hK'₂ := (ne_of_lt hK'₂).symm
-    contradiction
+    exact hK₂ K' hK'₁ hK'₂
   exact hK₃ ▸ hK₁
 #align lie_algebra.is_engelian_of_is_noetherian LieAlgebra.isEngelian_of_isNoetherian

938fead7

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

210657c4

chore: backports from #11997, adaptations for nightly-2024-04-07 (#12176)

These are changes from #11997, the latest adaptation PR for nightly-2024-04-07, which can be made directly on master.

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

02293f49

Diff

@@ -241,7 +241,7 @@ theorem LieAlgebra.isEngelian_of_isNoetherian [IsNoetherian R L] : LieAlgebra.Is
     rintro K (hK₁ : LieAlgebra.IsEngelian R K) hK₂
     apply LieAlgebra.exists_engelian_lieSubalgebra_of_lt_normalizer hK₁
     apply lt_of_le_of_ne K.le_normalizer
-    rw [Ne.def, eq_comm, K.normalizer_eq_self_iff, ← Ne.def, ←
+    rw [Ne, eq_comm, K.normalizer_eq_self_iff, ← Ne, ←
       LieSubmodule.nontrivial_iff_ne_bot R K]
     have : Nontrivial (L' ⧸ K.toLieSubmodule) := by
       replace hK₂ : K.toLieSubmodule ≠ ⊤ := by

210657c4

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

1b40c7bc

Diff

@@ -245,7 +245,7 @@ theorem LieAlgebra.isEngelian_of_isNoetherian [IsNoetherian R L] : LieAlgebra.Is
       LieSubmodule.nontrivial_iff_ne_bot R K]
     have : Nontrivial (L' ⧸ K.toLieSubmodule) := by
       replace hK₂ : K.toLieSubmodule ≠ ⊤ := by
-        rwa [Ne.def, ← LieSubmodule.coe_toSubmodule_eq_iff, K.coe_toLieSubmodule,
+        rwa [Ne, ← LieSubmodule.coe_toSubmodule_eq_iff, K.coe_toLieSubmodule,
           LieSubmodule.top_coeSubmodule, ← LieSubalgebra.top_coe_submodule,
           K.coe_to_submodule_eq_iff]
       exact Submodule.Quotient.nontrivial_of_lt_top _ hK₂.lt_top

210657c4

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

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

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

where the latter is more natural

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

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

but it seems to no longer apply.

Remarks on the PR :

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

9a3feeae

Diff

@@ -118,7 +118,7 @@ theorem lcs_le_lcs_of_is_nilpotent_span_sup_eq_top {n i j : ℕ}
     exact le_sup_of_le_left hIM
   · simp only [LieIdeal.lcs_succ, i.add_succ l, lie_top_eq_of_span_sup_eq_top hxI, sup_le_iff]
     refine' ⟨(Submodule.map_mono ih).trans _, le_sup_of_le_right _⟩
-    · rw [Submodule.map_sup, ← Submodule.map_comp, ← LinearMap.mul_eq_comp, ← pow_succ, ←
+    · rw [Submodule.map_sup, ← Submodule.map_comp, ← LinearMap.mul_eq_comp, ← pow_succ', ←
         I.lcs_succ]
       exact sup_le_sup_left coe_map_toEndomorphism_le _
     · refine' le_trans (mono_lie_right _ _ I _) (mono_lie_right _ _ I hIM)

210657c4

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

@@ -70,9 +70,7 @@ into a single statement about nilpotency of Lie modules. This is not usually emp
 universe u₁ u₂ u₃ u₄
 
 variable {R : Type u₁} {L : Type u₂} {L₂ : Type u₃} {M : Type u₄}
-
 variable [CommRing R] [LieRing L] [LieAlgebra R L] [LieRing L₂] [LieAlgebra R L₂]
-
 variable [AddCommGroup M] [Module R M] [LieRingModule L M] [LieModule R L M]
 
 namespace LieSubmodule

210657c4

chore: classify was simp porting notes (#10746)

Classifies by adding issue number (#10745) to porting notes claiming was simp.

71e045ac

Diff

@@ -181,7 +181,7 @@ theorem Function.Surjective.isEngelian {f : L →ₗ⁅R⁆ L₂} (hf : Function
   have surj_id : Function.Surjective (LinearMap.id : M →ₗ[R] M) := Function.surjective_id
   haveI : LieModule.IsNilpotent R L M := h M hnp
   apply hf.lieModuleIsNilpotent surj_id
-  -- Porting note: was `simp`
+  -- porting note (#10745): was `simp`
   intros; simp only [LinearMap.id_coe, id_eq]; rfl
 #align function.surjective.is_engelian Function.Surjective.isEngelian

210657c4

chore: remove stream-of-consciousness uses of have, replace and suffices (#10640)

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>

a13e8040

Diff

@@ -229,8 +229,8 @@ theorem LieAlgebra.isEngelian_of_isNoetherian [IsNoetherian R L] : LieAlgebra.Is
   intro M _i1 _i2 _i3 _i4 h
   rw [← isNilpotent_range_toEndomorphism_iff]
   let L' := (toEndomorphism R L M).range
-  replace h : ∀ y : L', _root_.IsNilpotent (y : Module.End R M)
-  · rintro ⟨-, ⟨y, rfl⟩⟩
+  replace h : ∀ y : L', _root_.IsNilpotent (y : Module.End R M) := by
+    rintro ⟨-, ⟨y, rfl⟩⟩
     simp [h]
   change LieModule.IsNilpotent R L' M
   let s := {K : LieSubalgebra R L' | LieAlgebra.IsEngelian R K}

210657c4

chore(*): use α → β instead of ∀ _ : α, β (#9529)

5618e431

Diff

@@ -158,10 +158,8 @@ be nilpotent is that the image of the map `L → End(M)` consists of nilpotent e
 Engel's theorem `LieAlgebra.isEngelian_of_isNoetherian` states that any Noetherian Lie algebra is
 Engelian. -/
 def LieAlgebra.IsEngelian : Prop :=
-  ∀ (M : Type u₄) [AddCommGroup M],
-    ∀ [Module R M] [LieRingModule L M],
-      ∀ [LieModule R L M],
-        ∀ _ : ∀ x : L, _root_.IsNilpotent (toEndomorphism R L M x), LieModule.IsNilpotent R L M
+  ∀ (M : Type u₄) [AddCommGroup M] [Module R M] [LieRingModule L M] [LieModule R L M],
+    (∀ x : L, _root_.IsNilpotent (toEndomorphism R L M x)) → LieModule.IsNilpotent R L M
 #align lie_algebra.is_engelian LieAlgebra.IsEngelian
 
 variable {R L}

210657c4

feat: remove IsNoetherian R L hypothesis from proof that zero-weight space of a Lie module is nilpotent (#7295)

This is possible thanks to the commit: 63ca289d

766dbabf

Diff

@@ -222,14 +222,12 @@ theorem LieAlgebra.exists_engelian_lieSubalgebra_of_lt_normalizer {K : LieSubalg
 
 attribute [local instance] LieSubalgebra.subsingleton_bot
 
-variable [IsNoetherian R L]
-
 /-- *Engel's theorem*.
 
 Note that this implies all traditional forms of Engel's theorem via
 `LieModule.nontrivial_max_triv_of_isNilpotent`, `LieModule.isNilpotent_iff_forall`,
 `LieAlgebra.isNilpotent_iff_forall`. -/
-theorem LieAlgebra.isEngelian_of_isNoetherian : LieAlgebra.IsEngelian R L := by
+theorem LieAlgebra.isEngelian_of_isNoetherian [IsNoetherian R L] : LieAlgebra.IsEngelian R L := by
   intro M _i1 _i2 _i3 _i4 h
   rw [← isNilpotent_range_toEndomorphism_iff]
   let L' := (toEndomorphism R L M).range
@@ -283,15 +281,22 @@ theorem LieAlgebra.isEngelian_of_isNoetherian : LieAlgebra.IsEngelian R L := by
   exact hK₃ ▸ hK₁
 #align lie_algebra.is_engelian_of_is_noetherian LieAlgebra.isEngelian_of_isNoetherian
 
-/-- Engel's theorem. -/
-theorem LieModule.isNilpotent_iff_forall :
+/-- Engel's theorem.
+
+See also `LieModule.isNilpotent_iff_forall'` which assumes that `M` is Noetherian instead of `L`. -/
+theorem LieModule.isNilpotent_iff_forall [IsNoetherian R L] :
     LieModule.IsNilpotent R L M ↔ ∀ x, _root_.IsNilpotent <| toEndomorphism R L M x :=
   ⟨fun _ ↦ isNilpotent_toEndomorphism_of_isNilpotent R L M,
    fun h => LieAlgebra.isEngelian_of_isNoetherian M h⟩
 #align lie_module.is_nilpotent_iff_forall LieModule.isNilpotent_iff_forall
 
 /-- Engel's theorem. -/
-theorem LieAlgebra.isNilpotent_iff_forall :
+theorem LieModule.isNilpotent_iff_forall' [IsNoetherian R M] :
+    LieModule.IsNilpotent R L M ↔ ∀ x, _root_.IsNilpotent <| toEndomorphism R L M x := by
+  rw [← isNilpotent_range_toEndomorphism_iff, LieModule.isNilpotent_iff_forall]; simp
+
+/-- Engel's theorem. -/
+theorem LieAlgebra.isNilpotent_iff_forall [IsNoetherian R L] :
     LieAlgebra.IsNilpotent R L ↔ ∀ x, _root_.IsNilpotent <| LieAlgebra.ad R L x :=
   LieModule.isNilpotent_iff_forall
 #align lie_algebra.is_nilpotent_iff_forall LieAlgebra.isNilpotent_iff_forall

210657c4

feat: define the trace / killing forms on a Lie algebra (#6308)

23eea437

Diff

@@ -286,10 +286,8 @@ theorem LieAlgebra.isEngelian_of_isNoetherian : LieAlgebra.IsEngelian R L := by
 /-- Engel's theorem. -/
 theorem LieModule.isNilpotent_iff_forall :
     LieModule.IsNilpotent R L M ↔ ∀ x, _root_.IsNilpotent <| toEndomorphism R L M x :=
-  ⟨by
-    intro h
-    obtain ⟨k, hk⟩ := nilpotent_endo_of_nilpotent_module R L M
-    exact fun x => ⟨k, hk x⟩, fun h => LieAlgebra.isEngelian_of_isNoetherian M h⟩
+  ⟨fun _ ↦ isNilpotent_toEndomorphism_of_isNilpotent R L M,
+   fun h => LieAlgebra.isEngelian_of_isNoetherian M h⟩
 #align lie_module.is_nilpotent_iff_forall LieModule.isNilpotent_iff_forall
 
 /-- Engel's theorem. -/

210657c4

chore: fix grammar mistakes (#6121)

a16538af

Diff

@@ -23,7 +23,7 @@ Engel's theorem is true for any coefficients (i.e., it is really a theorem about
 we work with coefficients in any commutative ring `R` throughout.
 
 On the other hand, Engel's theorem is not true for infinite-dimensional Lie algebras and so a
-finite-dimensionality assumption is required. We prove the theorem subject to the the assumption
+finite-dimensionality assumption is required. We prove the theorem subject to the assumption
 that the Lie algebra is Noetherian as an `R`-module, though actually we only need the slightly
 weaker property that the relation `>` is well-founded on the complete lattice of Lie subalgebras.

210657c4

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

@@ -2,15 +2,12 @@
 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.engel
-! leanprover-community/mathlib commit 210657c4ea4a4a7b234392f70a3a2a83346dfa90
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Algebra.Lie.Nilpotent
 import Mathlib.Algebra.Lie.Normalizer
 
+#align_import algebra.lie.engel from "leanprover-community/mathlib"@"210657c4ea4a4a7b234392f70a3a2a83346dfa90"
+
 /-!
 # Engel's theorem

210657c4

feat: port Algebra.Lie.Engel (#4926)

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au>

eba2601f

`algebra.lie.engel` ⟷ `Mathlib.Algebra.Lie.Engel`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 10 + 533

algebra.lie.engel ⟷ Mathlib.Algebra.Lie.Engel

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 10 + 533

`algebra.lie.engel` ⟷ `Mathlib.Algebra.Lie.Engel`