ring_theory.derivation.lie
⟷
Mathlib.RingTheory.Derivation.Lie
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.
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mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -3,8 +3,8 @@ Copyright © 2020 Nicolò Cavalleri. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Nicolò Cavalleri, Andrew Yang
-/
-import Mathbin.Algebra.Lie.OfAssociative
-import Mathbin.RingTheory.Derivation.Basic
+import Algebra.Lie.OfAssociative
+import RingTheory.Derivation.Basic
#align_import ring_theory.derivation.lie from "leanprover-community/mathlib"@"5c1efce12ba86d4901463f61019832f6a4b1a0d0"
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,15 +2,12 @@
Copyright © 2020 Nicolò Cavalleri. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Nicolò Cavalleri, Andrew Yang
-
-! This file was ported from Lean 3 source module ring_theory.derivation.lie
-! leanprover-community/mathlib commit 5c1efce12ba86d4901463f61019832f6a4b1a0d0
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.Algebra.Lie.OfAssociative
import Mathbin.RingTheory.Derivation.Basic
+#align_import ring_theory.derivation.lie from "leanprover-community/mathlib"@"5c1efce12ba86d4901463f61019832f6a4b1a0d0"
+
/-!
# Results
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
@@ -44,14 +44,18 @@ instance : Bracket (Derivation R A A) (Derivation R A A) :=
coe_fn_coe, LinearMap.sub_apply]
ring⟩
+#print Derivation.commutator_coe_linear_map /-
@[simp]
theorem commutator_coe_linear_map : ↑⁅D1, D2⁆ = ⁅(D1 : Module.End R A), (D2 : Module.End R A)⁆ :=
rfl
#align derivation.commutator_coe_linear_map Derivation.commutator_coe_linear_map
+-/
+#print Derivation.commutator_apply /-
theorem commutator_apply : ⁅D1, D2⁆ a = D1 (D2 a) - D2 (D1 a) :=
rfl
#align derivation.commutator_apply Derivation.commutator_apply
+-/
instance : LieRing (Derivation R A A)
where
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: Nicolò Cavalleri, Andrew Yang
! This file was ported from Lean 3 source module ring_theory.derivation.lie
-! leanprover-community/mathlib commit b608348ffaeb7f557f2fd46876037abafd326ff3
+! leanprover-community/mathlib commit 5c1efce12ba86d4901463f61019832f6a4b1a0d0
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
@@ -14,6 +14,9 @@ import Mathbin.RingTheory.Derivation.Basic
/-!
# Results
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
- `derivation.lie_algebra`: The `R`-derivations from `A` to `A` form an lie algebra over `R`.
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/34ebaffc1d1e8e783fc05438ec2e70af87275ac9
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)
@@ -19,9 +19,7 @@ import Mathlib.RingTheory.Derivation.Basic
namespace Derivation
variable {R : Type*} [CommRing R]
-
variable {A : Type*} [CommRing A] [Algebra R A]
-
variable (D : Derivation R A A) {D1 D2 : Derivation R A A} (a : A)
section LieStructures
@@ -52,7 +52,7 @@ instance : LieRing (Derivation R A A) where
lie_self d := by ext a; simp only [commutator_apply, add_apply, map_add]; ring_nf; simp
leibniz_lie d e f := by ext a; simp only [commutator_apply, add_apply, sub_apply, map_sub]; ring
-instance instLieAlgebra: LieAlgebra R (Derivation R A A) :=
+instance instLieAlgebra : LieAlgebra R (Derivation R A A) :=
{ Derivation.instModule with
lie_smul := fun r d e => by
ext a; simp only [commutator_apply, map_smul, smul_sub, smul_apply] }
Type _
and Sort _
(#6499)
We remove all possible occurences of Type _
and Sort _
in favor of Type*
and Sort*
.
This has nice performance benefits.
@@ -18,9 +18,9 @@ import Mathlib.RingTheory.Derivation.Basic
namespace Derivation
-variable {R : Type _} [CommRing R]
+variable {R : Type*} [CommRing R]
-variable {A : Type _} [CommRing A] [Algebra R A]
+variable {A : Type*} [CommRing A] [Algebra R A]
variable (D : Derivation R A A) {D1 D2 : Derivation R A A} (a : A)
@@ -2,15 +2,12 @@
Copyright © 2020 Nicolò Cavalleri. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Nicolò Cavalleri, Andrew Yang
-
-! This file was ported from Lean 3 source module ring_theory.derivation.lie
-! leanprover-community/mathlib commit b608348ffaeb7f557f2fd46876037abafd326ff3
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.Algebra.Lie.OfAssociative
import Mathlib.RingTheory.Derivation.Basic
+#align_import ring_theory.derivation.lie from "leanprover-community/mathlib"@"b608348ffaeb7f557f2fd46876037abafd326ff3"
+
/-!
# Results
The unported dependencies are