geometry.manifold.algebra.left_invariant_derivation ⟷ Mathlib.Geometry.Manifold.Algebra.LeftInvariantDerivation

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

@@ -323,7 +323,7 @@ instance : Bracket (LeftInvariantDerivation I G) (LeftInvariantDerivation I G)
       have hX := Derivation.congr_fun (left_invariant' g X) (Y f)
       have hY := Derivation.congr_fun (left_invariant' g Y) (X f)
       rw [apply_hfdifferential, apply_fdifferential, Derivation.evalAt_apply] at hX hY ⊢
-      rw [comp_L] at hX hY 
+      rw [comp_L] at hX hY
       rw [Derivation.commutator_apply, SmoothMap.coe_sub, Pi.sub_apply, coe_derivation]
       rw [coe_derivation] at hX hY ⊢
       rw [hX, hY]

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
 -/
-import Mathbin.RingTheory.Derivation.Lie
-import Mathbin.Geometry.Manifold.DerivationBundle
+import RingTheory.Derivation.Lie
+import Geometry.Manifold.DerivationBundle
 
 #align_import geometry.manifold.algebra.left_invariant_derivation from "leanprover-community/mathlib"@"2fe465deb81bcd7ccafa065bb686888a82f15372"
 

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
-
-! This file was ported from Lean 3 source module geometry.manifold.algebra.left_invariant_derivation
-! leanprover-community/mathlib commit 2fe465deb81bcd7ccafa065bb686888a82f15372
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.RingTheory.Derivation.Lie
 import Mathbin.Geometry.Manifold.DerivationBundle
 
+#align_import geometry.manifold.algebra.left_invariant_derivation from "leanprover-community/mathlib"@"2fe465deb81bcd7ccafa065bb686888a82f15372"
+
 /-!
 
 # Left invariant derivations

mathlib commit https://github.com/leanprover-community/mathlib/commit/2fe465deb81bcd7ccafa065bb686888a82f15372

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Nicolò Cavalleri
 
 ! This file was ported from Lean 3 source module geometry.manifold.algebra.left_invariant_derivation
-! leanprover-community/mathlib commit b608348ffaeb7f557f2fd46876037abafd326ff3
+! leanprover-community/mathlib commit 2fe465deb81bcd7ccafa065bb686888a82f15372
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -15,6 +15,9 @@ import Mathbin.Geometry.Manifold.DerivationBundle
 
 # Left invariant derivations
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 In this file we define the concept of left invariant derivation for a Lie group. The concept is
 analogous to the more classical concept of left invariant vector fields, and it holds that the
 derivation associated to a vector field is left invariant iff the field is.

mathlib commit https://github.com/leanprover-community/mathlib/commit/8905e5ed90859939681a725b00f6063e65096d95

@@ -38,6 +38,7 @@ variable {𝕜 : Type _} [NontriviallyNormedField 𝕜] {E : Type _} [NormedAddC
 private def disable_has_sizeof {α} : SizeOf α :=
   ⟨fun _ => 0⟩
 
+#print LeftInvariantDerivation /-
 /-- Left-invariant global derivations.
 
 A global derivation is left-invariant if it is equal to its pullback along left multiplication by
@@ -49,6 +50,7 @@ structure LeftInvariantDerivation extends Derivation 𝕜 C^∞⟮I, G; 𝕜⟯
       𝒅ₕ (smoothLeftMul_one I g) (Derivation.evalAt 1 to_derivation) =
         Derivation.evalAt g to_derivation
 #align left_invariant_derivation LeftInvariantDerivation
+-/
 
 variable {I G}
 
@@ -63,9 +65,11 @@ instance : CoeFun (LeftInvariantDerivation I G) fun _ => C^∞⟮I, G; 𝕜⟯ 
 variable {M : Type _} [TopologicalSpace M] [ChartedSpace H M] {x : M} {r : 𝕜}
   {X Y : LeftInvariantDerivation I G} {f f' : C^∞⟮I, G; 𝕜⟯}
 
+#print LeftInvariantDerivation.toFun_eq_coe /-
 theorem toFun_eq_coe : X.toFun = ⇑X :=
   rfl
 #align left_invariant_derivation.to_fun_eq_coe LeftInvariantDerivation.toFun_eq_coe
+-/
 
 theorem coe_to_linearMap : ⇑(X : C^∞⟮I, G; 𝕜⟯ →ₗ[𝕜] C^∞⟮I, G; 𝕜⟯) = X :=
   rfl
@@ -76,64 +80,86 @@ theorem toDerivation_eq_coe : X.toDerivation = X :=
   rfl
 #align left_invariant_derivation.to_derivation_eq_coe LeftInvariantDerivation.toDerivation_eq_coe
 
+#print LeftInvariantDerivation.coe_injective /-
 theorem coe_injective :
     @Function.Injective (LeftInvariantDerivation I G) (_ → C^⊤⟮I, G; 𝕜⟯) coeFn := fun X Y h => by
   cases X; cases Y; congr; exact Derivation.coe_injective h
 #align left_invariant_derivation.coe_injective LeftInvariantDerivation.coe_injective
+-/
 
+#print LeftInvariantDerivation.ext /-
 @[ext]
 theorem ext (h : ∀ f, X f = Y f) : X = Y :=
   coe_injective <| funext h
 #align left_invariant_derivation.ext LeftInvariantDerivation.ext
+-/
 
 variable (X Y f)
 
+#print LeftInvariantDerivation.coe_derivation /-
 theorem coe_derivation :
     ⇑(X : Derivation 𝕜 C^∞⟮I, G; 𝕜⟯ C^∞⟮I, G; 𝕜⟯) = (X : C^∞⟮I, G; 𝕜⟯ → C^∞⟮I, G; 𝕜⟯) :=
   rfl
 #align left_invariant_derivation.coe_derivation LeftInvariantDerivation.coe_derivation
+-/
 
-theorem coe_derivation_injective :
+#print LeftInvariantDerivation.toDerivation_injective /-
+theorem toDerivation_injective :
     Function.Injective
       (coe : LeftInvariantDerivation I G → Derivation 𝕜 C^∞⟮I, G; 𝕜⟯ C^∞⟮I, G; 𝕜⟯) :=
   fun X Y h => by cases X; cases Y; congr; exact h
-#align left_invariant_derivation.coe_derivation_injective LeftInvariantDerivation.coe_derivation_injective
+#align left_invariant_derivation.coe_derivation_injective LeftInvariantDerivation.toDerivation_injective
+-/
 
+#print LeftInvariantDerivation.left_invariant' /-
 /-- Premature version of the lemma. Prefer using `left_invariant` instead. -/
 theorem left_invariant' :
     𝒅ₕ (smoothLeftMul_one I g) (Derivation.evalAt (1 : G) ↑X) = Derivation.evalAt g ↑X :=
   left_invariant'' X g
 #align left_invariant_derivation.left_invariant' LeftInvariantDerivation.left_invariant'
+-/
 
+#print LeftInvariantDerivation.map_add /-
 @[simp]
 theorem map_add : X (f + f') = X f + X f' :=
   Derivation.map_add X f f'
 #align left_invariant_derivation.map_add LeftInvariantDerivation.map_add
+-/
 
+#print LeftInvariantDerivation.map_zero /-
 @[simp]
 theorem map_zero : X 0 = 0 :=
   Derivation.map_zero X
 #align left_invariant_derivation.map_zero LeftInvariantDerivation.map_zero
+-/
 
+#print LeftInvariantDerivation.map_neg /-
 @[simp]
 theorem map_neg : X (-f) = -X f :=
   Derivation.map_neg X f
 #align left_invariant_derivation.map_neg LeftInvariantDerivation.map_neg
+-/
 
+#print LeftInvariantDerivation.map_sub /-
 @[simp]
 theorem map_sub : X (f - f') = X f - X f' :=
   Derivation.map_sub X f f'
 #align left_invariant_derivation.map_sub LeftInvariantDerivation.map_sub
+-/
 
+#print LeftInvariantDerivation.map_smul /-
 @[simp]
 theorem map_smul : X (r • f) = r • X f :=
   Derivation.map_smul X r f
 #align left_invariant_derivation.map_smul LeftInvariantDerivation.map_smul
+-/
 
+#print LeftInvariantDerivation.leibniz /-
 @[simp]
 theorem leibniz : X (f * f') = f • X f' + f' • X f :=
   X.leibniz' _ _
 #align left_invariant_derivation.leibniz LeftInvariantDerivation.leibniz
+-/
 
 instance : Zero (LeftInvariantDerivation I G) :=
   ⟨⟨0, fun g => by simp only [LinearMap.map_zero, Derivation.coe_zero]⟩⟩
@@ -151,44 +177,60 @@ instance : Neg (LeftInvariantDerivation I G) where neg X := ⟨-X, fun g => by s
 instance : Sub (LeftInvariantDerivation I G)
     where sub X Y := ⟨X - Y, fun g => by simp [left_invariant']⟩
 
+#print LeftInvariantDerivation.coe_add /-
 @[simp]
 theorem coe_add : ⇑(X + Y) = X + Y :=
   rfl
 #align left_invariant_derivation.coe_add LeftInvariantDerivation.coe_add
+-/
 
+#print LeftInvariantDerivation.coe_zero /-
 @[simp]
 theorem coe_zero : ⇑(0 : LeftInvariantDerivation I G) = 0 :=
   rfl
 #align left_invariant_derivation.coe_zero LeftInvariantDerivation.coe_zero
+-/
 
+#print LeftInvariantDerivation.coe_neg /-
 @[simp]
 theorem coe_neg : ⇑(-X) = -X :=
   rfl
 #align left_invariant_derivation.coe_neg LeftInvariantDerivation.coe_neg
+-/
 
+#print LeftInvariantDerivation.coe_sub /-
 @[simp]
 theorem coe_sub : ⇑(X - Y) = X - Y :=
   rfl
 #align left_invariant_derivation.coe_sub LeftInvariantDerivation.coe_sub
+-/
 
+#print LeftInvariantDerivation.lift_add /-
 @[simp, norm_cast]
 theorem lift_add : (↑(X + Y) : Derivation 𝕜 C^∞⟮I, G; 𝕜⟯ C^∞⟮I, G; 𝕜⟯) = X + Y :=
   rfl
 #align left_invariant_derivation.lift_add LeftInvariantDerivation.lift_add
+-/
 
+#print LeftInvariantDerivation.lift_zero /-
 @[simp, norm_cast]
 theorem lift_zero :
     (↑(0 : LeftInvariantDerivation I G) : Derivation 𝕜 C^∞⟮I, G; 𝕜⟯ C^∞⟮I, G; 𝕜⟯) = 0 :=
   rfl
 #align left_invariant_derivation.lift_zero LeftInvariantDerivation.lift_zero
+-/
 
+#print LeftInvariantDerivation.hasNatScalar /-
 instance hasNatScalar : SMul ℕ (LeftInvariantDerivation I G)
     where smul r X := ⟨r • X, fun g => by simp_rw [LinearMap.map_smul_of_tower, left_invariant']⟩
 #align left_invariant_derivation.has_nat_scalar LeftInvariantDerivation.hasNatScalar
+-/
 
+#print LeftInvariantDerivation.hasIntScalar /-
 instance hasIntScalar : SMul ℤ (LeftInvariantDerivation I G)
     where smul r X := ⟨r • X, fun g => by simp_rw [LinearMap.map_smul_of_tower, left_invariant']⟩
 #align left_invariant_derivation.has_int_scalar LeftInvariantDerivation.hasIntScalar
+-/
 
 instance : AddCommGroup (LeftInvariantDerivation I G) :=
   coe_injective.AddCommGroup _ coe_zero coe_add coe_neg coe_sub (fun _ _ => rfl) fun _ _ => rfl
@@ -198,29 +240,36 @@ instance : SMul 𝕜 (LeftInvariantDerivation I G)
 
 variable (r X)
 
+#print LeftInvariantDerivation.coe_smul /-
 @[simp]
 theorem coe_smul : ⇑(r • X) = r • X :=
   rfl
 #align left_invariant_derivation.coe_smul LeftInvariantDerivation.coe_smul
+-/
 
+#print LeftInvariantDerivation.lift_smul /-
 @[simp]
 theorem lift_smul (k : 𝕜) : (↑(k • X) : Derivation 𝕜 C^∞⟮I, G; 𝕜⟯ C^∞⟮I, G; 𝕜⟯) = k • X :=
   rfl
 #align left_invariant_derivation.lift_smul LeftInvariantDerivation.lift_smul
+-/
 
 variable (I G)
 
+#print LeftInvariantDerivation.coeFnAddMonoidHom /-
 /-- The coercion to function is a monoid homomorphism. -/
 @[simps]
 def coeFnAddMonoidHom : LeftInvariantDerivation I G →+ C^∞⟮I, G; 𝕜⟯ → C^∞⟮I, G; 𝕜⟯ :=
   ⟨fun X => X.toDerivation.toFun, coe_zero, coe_add⟩
 #align left_invariant_derivation.coe_fn_add_monoid_hom LeftInvariantDerivation.coeFnAddMonoidHom
+-/
 
 variable {I G}
 
 instance : Module 𝕜 (LeftInvariantDerivation I G) :=
   coe_injective.Module _ (coeFnAddMonoidHom I G) coe_smul
 
+#print LeftInvariantDerivation.evalAt /-
 /-- Evaluation at a point for left invariant derivation. Same thing as for generic global
 derivations (`derivation.eval_at`). -/
 def evalAt : LeftInvariantDerivation I G →ₗ[𝕜] PointDerivation I g
@@ -229,31 +278,42 @@ def evalAt : LeftInvariantDerivation I G →ₗ[𝕜] PointDerivation I g
   map_add' X Y := rfl
   map_smul' k X := rfl
 #align left_invariant_derivation.eval_at LeftInvariantDerivation.evalAt
+-/
 
+#print LeftInvariantDerivation.evalAt_apply /-
 theorem evalAt_apply : evalAt g X f = (X f) g :=
   rfl
 #align left_invariant_derivation.eval_at_apply LeftInvariantDerivation.evalAt_apply
+-/
 
+#print LeftInvariantDerivation.evalAt_coe /-
 @[simp]
 theorem evalAt_coe : Derivation.evalAt g ↑X = evalAt g X :=
   rfl
 #align left_invariant_derivation.eval_at_coe LeftInvariantDerivation.evalAt_coe
+-/
 
+#print LeftInvariantDerivation.left_invariant /-
 theorem left_invariant : 𝒅ₕ (smoothLeftMul_one I g) (evalAt (1 : G) X) = evalAt g X :=
   X.left_invariant'' g
 #align left_invariant_derivation.left_invariant LeftInvariantDerivation.left_invariant
+-/
 
+#print LeftInvariantDerivation.evalAt_mul /-
 theorem evalAt_mul : evalAt (g * h) X = 𝒅ₕ (L_apply I g h) (evalAt h X) := by ext f;
   rw [← left_invariant, apply_hfdifferential, apply_hfdifferential, L_mul, fdifferential_comp,
     apply_fdifferential, LinearMap.comp_apply, apply_fdifferential, ← apply_hfdifferential,
     left_invariant]
 #align left_invariant_derivation.eval_at_mul LeftInvariantDerivation.evalAt_mul
+-/
 
+#print LeftInvariantDerivation.comp_L /-
 theorem comp_L : (X f).comp (𝑳 I g) = X (f.comp (𝑳 I g)) := by
   ext h <;>
     rw [ContMDiffMap.comp_apply, L_apply, ← eval_at_apply, eval_at_mul, apply_hfdifferential,
       apply_fdifferential, eval_at_apply]
 #align left_invariant_derivation.comp_L LeftInvariantDerivation.comp_L
+-/
 
 instance : Bracket (LeftInvariantDerivation I G) (LeftInvariantDerivation I G)
     where bracket X Y :=
@@ -269,6 +329,7 @@ instance : Bracket (LeftInvariantDerivation I G) (LeftInvariantDerivation I G)
       rw [hX, hY]
       rfl⟩
 
+#print LeftInvariantDerivation.commutator_coe_derivation /-
 @[simp]
 theorem commutator_coe_derivation :
     ⇑⁅X, Y⁆ =
@@ -276,10 +337,13 @@ theorem commutator_coe_derivation :
         Derivation 𝕜 C^∞⟮I, G; 𝕜⟯ C^∞⟮I, G; 𝕜⟯) :=
   rfl
 #align left_invariant_derivation.commutator_coe_derivation LeftInvariantDerivation.commutator_coe_derivation
+-/
 
+#print LeftInvariantDerivation.commutator_apply /-
 theorem commutator_apply : ⁅X, Y⁆ f = X (Y f) - Y (X f) :=
   rfl
 #align left_invariant_derivation.commutator_apply LeftInvariantDerivation.commutator_apply
+-/
 
 instance : LieRing (LeftInvariantDerivation I G)
     where

mathlib commit https://github.com/leanprover-community/mathlib/commit/fdc286cc6967a012f41b87f76dcd2797b53152af

@@ -31,7 +31,7 @@ open scoped LieGroup Manifold Derivation
 
 variable {𝕜 : Type _} [NontriviallyNormedField 𝕜] {E : Type _} [NormedAddCommGroup E]
   [NormedSpace 𝕜 E] {H : Type _} [TopologicalSpace H] (I : ModelWithCorners 𝕜 E H) (G : Type _)
-  [TopologicalSpace G] [ChartedSpace H G] [Monoid G] [HasSmoothMul I G] (g h : G)
+  [TopologicalSpace G] [ChartedSpace H G] [Monoid G] [SmoothMul I G] (g h : G)
 
 -- Generate trivial has_sizeof instance. It prevents weird type class inference timeout problems
 @[local nolint instance_priority, local instance 10000]

mathlib commit https://github.com/leanprover-community/mathlib/commit/93f880918cb51905fd51b76add8273cbc27718ab

@@ -251,7 +251,7 @@ theorem evalAt_mul : evalAt (g * h) X = 𝒅ₕ (L_apply I g h) (evalAt h X) :=
 
 theorem comp_L : (X f).comp (𝑳 I g) = X (f.comp (𝑳 I g)) := by
   ext h <;>
-    rw [ContMdiffMap.comp_apply, L_apply, ← eval_at_apply, eval_at_mul, apply_hfdifferential,
+    rw [ContMDiffMap.comp_apply, L_apply, ← eval_at_apply, eval_at_mul, apply_hfdifferential,
       apply_fdifferential, eval_at_apply]
 #align left_invariant_derivation.comp_L LeftInvariantDerivation.comp_L
 

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

@@ -4,10 +4,11 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Nicolò Cavalleri
 
 ! This file was ported from Lean 3 source module geometry.manifold.algebra.left_invariant_derivation
-! leanprover-community/mathlib commit d1bd9c5df2867c1cb463bc6364446d57bdd9f7f1
+! leanprover-community/mathlib commit b608348ffaeb7f557f2fd46876037abafd326ff3
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
+import Mathbin.RingTheory.Derivation.Lie
 import Mathbin.Geometry.Manifold.DerivationBundle
 
 /-!

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

@@ -77,7 +77,7 @@ theorem toDerivation_eq_coe : X.toDerivation = X :=
 
 theorem coe_injective :
     @Function.Injective (LeftInvariantDerivation I G) (_ → C^⊤⟮I, G; 𝕜⟯) coeFn := fun X Y h => by
-  cases X; cases Y; congr ; exact Derivation.coe_injective h
+  cases X; cases Y; congr; exact Derivation.coe_injective h
 #align left_invariant_derivation.coe_injective LeftInvariantDerivation.coe_injective
 
 @[ext]
@@ -95,7 +95,7 @@ theorem coe_derivation :
 theorem coe_derivation_injective :
     Function.Injective
       (coe : LeftInvariantDerivation I G → Derivation 𝕜 C^∞⟮I, G; 𝕜⟯ C^∞⟮I, G; 𝕜⟯) :=
-  fun X Y h => by cases X; cases Y; congr ; exact h
+  fun X Y h => by cases X; cases Y; congr; exact h
 #align left_invariant_derivation.coe_derivation_injective LeftInvariantDerivation.coe_derivation_injective
 
 /-- Premature version of the lemma. Prefer using `left_invariant` instead. -/
@@ -261,10 +261,10 @@ instance : Bracket (LeftInvariantDerivation I G) (LeftInvariantDerivation I G)
       ext f
       have hX := Derivation.congr_fun (left_invariant' g X) (Y f)
       have hY := Derivation.congr_fun (left_invariant' g Y) (X f)
-      rw [apply_hfdifferential, apply_fdifferential, Derivation.evalAt_apply] at hX hY⊢
-      rw [comp_L] at hX hY
+      rw [apply_hfdifferential, apply_fdifferential, Derivation.evalAt_apply] at hX hY ⊢
+      rw [comp_L] at hX hY 
       rw [Derivation.commutator_apply, SmoothMap.coe_sub, Pi.sub_apply, coe_derivation]
-      rw [coe_derivation] at hX hY⊢
+      rw [coe_derivation] at hX hY ⊢
       rw [hX, hY]
       rfl⟩
 

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

@@ -26,7 +26,7 @@ implementing one of the possible definitions of the Lie algebra attached to a Li
 
 noncomputable section
 
-open LieGroup Manifold Derivation
+open scoped LieGroup Manifold Derivation
 
 variable {𝕜 : Type _} [NontriviallyNormedField 𝕜] {E : Type _} [NormedAddCommGroup E]
   [NormedSpace 𝕜 E] {H : Type _} [TopologicalSpace H] (I : ModelWithCorners 𝕜 E H) (G : Type _)

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

@@ -76,12 +76,8 @@ theorem toDerivation_eq_coe : X.toDerivation = X :=
 #align left_invariant_derivation.to_derivation_eq_coe LeftInvariantDerivation.toDerivation_eq_coe
 
 theorem coe_injective :
-    @Function.Injective (LeftInvariantDerivation I G) (_ → C^⊤⟮I, G; 𝕜⟯) coeFn := fun X Y h =>
-  by
-  cases X
-  cases Y
-  congr
-  exact Derivation.coe_injective h
+    @Function.Injective (LeftInvariantDerivation I G) (_ → C^⊤⟮I, G; 𝕜⟯) coeFn := fun X Y h => by
+  cases X; cases Y; congr ; exact Derivation.coe_injective h
 #align left_invariant_derivation.coe_injective LeftInvariantDerivation.coe_injective
 
 @[ext]
@@ -99,11 +95,7 @@ theorem coe_derivation :
 theorem coe_derivation_injective :
     Function.Injective
       (coe : LeftInvariantDerivation I G → Derivation 𝕜 C^∞⟮I, G; 𝕜⟯ C^∞⟮I, G; 𝕜⟯) :=
-  fun X Y h => by
-  cases X
-  cases Y
-  congr
-  exact h
+  fun X Y h => by cases X; cases Y; congr ; exact h
 #align left_invariant_derivation.coe_derivation_injective LeftInvariantDerivation.coe_derivation_injective
 
 /-- Premature version of the lemma. Prefer using `left_invariant` instead. -/
@@ -250,9 +242,7 @@ theorem left_invariant : 𝒅ₕ (smoothLeftMul_one I g) (evalAt (1 : G) X) = ev
   X.left_invariant'' g
 #align left_invariant_derivation.left_invariant LeftInvariantDerivation.left_invariant
 
-theorem evalAt_mul : evalAt (g * h) X = 𝒅ₕ (L_apply I g h) (evalAt h X) :=
-  by
-  ext f
+theorem evalAt_mul : evalAt (g * h) X = 𝒅ₕ (L_apply I g h) (evalAt h X) := by ext f;
   rw [← left_invariant, apply_hfdifferential, apply_hfdifferential, L_mul, fdifferential_comp,
     apply_fdifferential, LinearMap.comp_apply, apply_fdifferential, ← apply_hfdifferential,
     left_invariant]
@@ -293,27 +283,22 @@ theorem commutator_apply : ⁅X, Y⁆ f = X (Y f) - Y (X f) :=
 instance : LieRing (LeftInvariantDerivation I G)
     where
   add_lie X Y Z := by
-    ext1
+    ext1;
     simp only [commutator_apply, coe_add, Pi.add_apply, LinearMap.map_add,
       LeftInvariantDerivation.map_add]
     ring
   lie_add X Y Z := by
-    ext1
+    ext1;
     simp only [commutator_apply, coe_add, Pi.add_apply, LinearMap.map_add,
       LeftInvariantDerivation.map_add]
     ring
-  lie_self X := by
-    ext1
-    simp only [commutator_apply, sub_self]
-    rfl
+  lie_self X := by ext1; simp only [commutator_apply, sub_self]; rfl
   leibniz_lie X Y Z := by
-    ext1
-    simp only [commutator_apply, coe_add, coe_sub, map_sub, Pi.add_apply]
+    ext1; simp only [commutator_apply, coe_add, coe_sub, map_sub, Pi.add_apply]
     ring
 
 instance : LieAlgebra 𝕜 (LeftInvariantDerivation I G)
-    where lie_smul r Y Z := by
-    ext1
+    where lie_smul r Y Z := by ext1;
     simp only [commutator_apply, map_smul, smul_sub, coe_smul, Pi.smul_apply]
 
 end LeftInvariantDerivation

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

@@ -36,7 +36,6 @@ variable {𝕜 : Type _} [NontriviallyNormedField 𝕜] {E : Type _} [NormedAddC
 @[local nolint instance_priority, local instance 10000]
 private def disable_has_sizeof {α} : SizeOf α :=
   ⟨fun _ => 0⟩
-#align disable_has_sizeof disable_has_sizeof
 
 /-- Left-invariant global derivations.
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/09079525fd01b3dda35e96adaa08d2f943e1648c

@@ -33,7 +33,7 @@ variable {𝕜 : Type _} [NontriviallyNormedField 𝕜] {E : Type _} [NormedAddC
   [TopologicalSpace G] [ChartedSpace H G] [Monoid G] [HasSmoothMul I G] (g h : G)
 
 -- Generate trivial has_sizeof instance. It prevents weird type class inference timeout problems
-@[local nolint instance_priority, local instance]
+@[local nolint instance_priority, local instance 10000]
 private def disable_has_sizeof {α} : SizeOf α :=
   ⟨fun _ => 0⟩
 #align disable_has_sizeof disable_has_sizeof

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

Reference the newly created issues #12094 and #12096, as well as the pre-existing #5171. Change all references to #10927 to #5171. Some of these changes were not labelled as "porting note"; change this for good measure.

@@ -31,6 +31,7 @@ variable {𝕜 : Type*} [NontriviallyNormedField 𝕜] {E : Type*} [NormedAddCom
   [TopologicalSpace G] [ChartedSpace H G] [Monoid G] [SmoothMul I G] (g h : G)
 
 -- Generate trivial has_sizeof instance. It prevents weird type class inference timeout problems
+-- Porting note(#12096): removed @[nolint instance_priority], linter not ported yet
 -- @[local nolint instance_priority, local instance 10000]
 -- private def disable_has_sizeof {α} : SizeOf α :=
 --   ⟨fun _ => 0⟩

The FunLike hierarchy is very big and gets scanned through each time we need a coercion (via the CoeFun instance). It looks like unbundled inheritance suits Lean 4 better here. The only class that still extends FunLike is EquivLike, since that has a custom coe_injective' field that is easier to implement. All other classes should take FunLike or EquivLike as a parameter.

Zulip thread

Important changes

Previously, morphism classes would be Type-valued and extend FunLike:

/-- `MyHomClass F A B` states that `F` is a type of `MyClass.op`-preserving morphisms.
You should extend this class when you extend `MyHom`. -/
class MyHomClass (F : Type*) (A B : outParam <| Type*) [MyClass A] [MyClass B]
  extends FunLike F A B :=
(map_op : ∀ (f : F) (x y : A), f (MyClass.op x y) = MyClass.op (f x) (f y))

After this PR, they should be Prop-valued and take FunLike as a parameter:

/-- `MyHomClass F A B` states that `F` is a type of `MyClass.op`-preserving morphisms.
You should extend this class when you extend `MyHom`. -/
class MyHomClass (F : Type*) (A B : outParam <| Type*) [MyClass A] [MyClass B]
  [FunLike F A B] : Prop :=
(map_op : ∀ (f : F) (x y : A), f (MyClass.op x y) = MyClass.op (f x) (f y))

(Note that A B stay marked as outParam even though they are not purely required to be so due to the FunLike parameter already filling them in. This is required to see through type synonyms, which is important in the category theory library. Also, I think keeping them as outParam is slightly faster.)

Similarly, MyEquivClass should take EquivLike as a parameter.

As a result, every mention of [MyHomClass F A B] should become [FunLike F A B] [MyHomClass F A B].

Remaining issues

Slower (failing) search

While overall this gives some great speedups, there are some cases that are noticeably slower. In particular, a failing application of a lemma such as map_mul is more expensive. This is due to suboptimal processing of arguments. For example:

variable [FunLike F M N] [Mul M] [Mul N] (f : F) (x : M) (y : M)

theorem map_mul [MulHomClass F M N] : f (x * y) = f x * f y

example [AddHomClass F A B] : f (x * y) = f x * f y := map_mul f _ _

Before this PR, applying map_mul f gives the goals [Mul ?M] [Mul ?N] [MulHomClass F ?M ?N]. Since M and N are out_params, [MulHomClass F ?M ?N] is synthesized first, supplies values for ?M and ?N and then the Mul M and Mul N instances can be found.

After this PR, the goals become [FunLike F ?M ?N] [Mul ?M] [Mul ?N] [MulHomClass F ?M ?N]. Now [FunLike F ?M ?N] is synthesized first, supplies values for ?M and ?N and then the Mul M and Mul N instances can be found, before trying MulHomClass F M N which fails. Since the Mul hierarchy is very big, this can be slow to fail, especially when there is no such Mul instance.

A long-term but harder to achieve solution would be to specify the order in which instance goals get solved. For example, we'd like to change the arguments to map_mul to look like [FunLike F M N] [Mul M] [Mul N] [highPriority <| MulHomClass F M N] because MulHomClass fails or succeeds much faster than the others.

As a consequence, the simpNF linter is much slower since by design it tries and fails to apply many map_ lemmas. The same issue occurs a few times in existing calls to simp [map_mul], where map_mul is tried "too soon" and fails. Thanks to the speedup of leanprover/lean4#2478 the impact is very limited, only in files that already were close to the timeout.

simp not firing sometimes

This affects map_smulₛₗ and related definitions. For simp lemmas Lean apparently uses a slightly different mechanism to find instances, so that rw can find every argument to map_smulₛₗ successfully but simp can't: leanprover/lean4#3701.

Missing instances due to unification failing

Especially in the category theory library, we might sometimes have a type A which is also accessible as a synonym (Bundled A hA).1. Instance synthesis doesn't always work if we have f : A →* B but x * y : (Bundled A hA).1 or vice versa. This seems to be mostly fixed by keeping A B as outParams in MulHomClass F A B. (Presumably because Lean will do a definitional check A =?= (Bundled A hA).1 instead of using the syntax in the discrimination tree.)

Workaround for issues

The timeouts can be worked around for now by specifying which map_mul we mean, either as map_mul f for some explicit f, or as e.g. MonoidHomClass.map_mul.

map_smulₛₗ not firing as simp lemma can be worked around by going back to the pre-FunLike situation and making LinearMap.map_smulₛₗ a simp lemma instead of the generic map_smulₛₗ. Writing simp [map_smulₛₗ _] also works.

Co-authored-by: Matthew Ballard <matt@mrb.email> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Scott Morrison <scott@tqft.net> Co-authored-by: Anne Baanen <Vierkantor@users.noreply.github.com>

@@ -60,15 +60,14 @@ theorem toDerivation_injective :
   fun X Y h => by cases X; cases Y; congr
 #align left_invariant_derivation.coe_derivation_injective LeftInvariantDerivation.toDerivation_injective
 
-instance : LinearMapClass (LeftInvariantDerivation I G) 𝕜 C^∞⟮I, G; 𝕜⟯ C^∞⟮I, G; 𝕜⟯ where
+instance : FunLike (LeftInvariantDerivation I G) C^∞⟮I, G; 𝕜⟯ C^∞⟮I, G; 𝕜⟯ where
   coe f := f.toDerivation
   coe_injective' _ _ h := toDerivation_injective <| DFunLike.ext' h
+
+instance : LinearMapClass (LeftInvariantDerivation I G) 𝕜 C^∞⟮I, G; 𝕜⟯ C^∞⟮I, G; 𝕜⟯ where
   map_add f := map_add f.1
   map_smulₛₗ f := map_smul f.1.1
 
-instance : CoeFun (LeftInvariantDerivation I G) fun _ => C^∞⟮I, G; 𝕜⟯ → C^∞⟮I, G; 𝕜⟯ :=
-  ⟨DFunLike.coe⟩
-
 variable {M : Type*} [TopologicalSpace M] [ChartedSpace H M] {x : M} {r : 𝕜}
   {X Y : LeftInvariantDerivation I G} {f f' : C^∞⟮I, G; 𝕜⟯}
 
@@ -140,18 +139,10 @@ instance : Add (LeftInvariantDerivation I G) where
       simp only [map_add, Derivation.coe_add, left_invariant', Pi.add_apply]⟩
 
 instance : Neg (LeftInvariantDerivation I G) where
-  neg X := ⟨-X, fun g => by
-    -- porting note: was simp [left_invariant']
-    -- `rw` fails without detailed type annotations too; also it needs a lot of time
-    rw [map_neg (Derivation.evalAt (𝕜 := 𝕜) (1 : G)), map_neg (𝒅ₕ (smoothLeftMul_one I g)),
-      left_invariant', map_neg (Derivation.evalAt (𝕜 := 𝕜) g)]⟩
+  neg X := ⟨-X, fun g => by simp [left_invariant']⟩
 
 instance : Sub (LeftInvariantDerivation I G) where
-  sub X Y := ⟨X - Y, fun g => by
-    -- porting note: was simp [left_invariant']
-    -- `rw` fails without detailed type annotations too; also it needs a lot of time
-    rw [map_sub (Derivation.evalAt (𝕜 := 𝕜) (1 : G)), map_sub (𝒅ₕ (smoothLeftMul_one I g)),
-      map_sub (Derivation.evalAt (𝕜 := 𝕜) g), left_invariant', left_invariant']⟩
+  sub X Y := ⟨X - Y, fun g => by simp [left_invariant']⟩
 
 @[simp]
 theorem coe_add : ⇑(X + Y) = X + Y :=

This prepares for the introduction of a non-dependent synonym of FunLike, which helps a lot with keeping #8386 readable.

This is entirely search-and-replace in 680197f combined with manual fixes in 4145626, e900597 and b8428f8. The commands that generated this change:

sed -i 's/\bFunLike\b/DFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\btoFunLike\b/toDFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/import Mathlib.Data.DFunLike/import Mathlib.Data.FunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\bHom_FunLike\b/Hom_DFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean     
sed -i 's/\binstFunLike\b/instDFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\bfunLike\b/instDFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\btoo many metavariables to apply `fun_like.has_coe_to_fun`/too many metavariables to apply `DFunLike.hasCoeToFun`/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean

Co-authored-by: Anne Baanen <Vierkantor@users.noreply.github.com>

@@ -62,12 +62,12 @@ theorem toDerivation_injective :
 
 instance : LinearMapClass (LeftInvariantDerivation I G) 𝕜 C^∞⟮I, G; 𝕜⟯ C^∞⟮I, G; 𝕜⟯ where
   coe f := f.toDerivation
-  coe_injective' _ _ h := toDerivation_injective <| FunLike.ext' h
+  coe_injective' _ _ h := toDerivation_injective <| DFunLike.ext' h
   map_add f := map_add f.1
   map_smulₛₗ f := map_smul f.1.1
 
 instance : CoeFun (LeftInvariantDerivation I G) fun _ => C^∞⟮I, G; 𝕜⟯ → C^∞⟮I, G; 𝕜⟯ :=
-  ⟨FunLike.coe⟩
+  ⟨DFunLike.coe⟩
 
 variable {M : Type*} [TopologicalSpace M] [ChartedSpace H M] {x : M} {r : 𝕜}
   {X Y : LeftInvariantDerivation I G} {f f' : C^∞⟮I, G; 𝕜⟯}
@@ -82,12 +82,12 @@ theorem toFun_eq_coe : X.toFun = ⇑X :=
 #noalign left_invariant_derivation.to_derivation_eq_coe
 
 theorem coe_injective :
-    @Function.Injective (LeftInvariantDerivation I G) (_ → C^∞⟮I, G; 𝕜⟯) FunLike.coe :=
-  FunLike.coe_injective
+    @Function.Injective (LeftInvariantDerivation I G) (_ → C^∞⟮I, G; 𝕜⟯) DFunLike.coe :=
+  DFunLike.coe_injective
 #align left_invariant_derivation.coe_injective LeftInvariantDerivation.coe_injective
 
 @[ext]
-theorem ext (h : ∀ f, X f = Y f) : X = Y := FunLike.ext _ _ h
+theorem ext (h : ∀ f, X f = Y f) : X = Y := DFunLike.ext _ _ h
 #align left_invariant_derivation.ext LeftInvariantDerivation.ext
 
 variable (X Y f)
@@ -215,7 +215,7 @@ variable (I G)
 /-- The coercion to function is a monoid homomorphism. -/
 @[simps]
 def coeFnAddMonoidHom : LeftInvariantDerivation I G →+ C^∞⟮I, G; 𝕜⟯ → C^∞⟮I, G; 𝕜⟯ :=
-  ⟨⟨FunLike.coe, coe_zero⟩, coe_add⟩
+  ⟨⟨DFunLike.coe, coe_zero⟩, coe_add⟩
 #align left_invariant_derivation.coe_fn_add_monoid_hom LeftInvariantDerivation.coeFnAddMonoidHom
 
 variable {I G}

Due to recent changes in core we can reduce or remove many set_option maxHeartbeats statements.

I have tried to be careful to not leave anything too close to the line, so don't be surprised if some of these can still be reduced further.

This reduces us from 96 maxHeartbeats statements to 44. (There are 10 false positives in meta or testing code.)

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

@@ -146,7 +146,6 @@ instance : Neg (LeftInvariantDerivation I G) where
     rw [map_neg (Derivation.evalAt (𝕜 := 𝕜) (1 : G)), map_neg (𝒅ₕ (smoothLeftMul_one I g)),
       left_invariant', map_neg (Derivation.evalAt (𝕜 := 𝕜) g)]⟩
 
-set_option maxHeartbeats 300000 in
 instance : Sub (LeftInvariantDerivation I G) where
   sub X Y := ⟨X - Y, fun g => by
     -- porting note: was simp [left_invariant']

This reverts commit f3695eb2.

@@ -251,7 +251,8 @@ theorem evalAt_mul : evalAt (g * h) X = 𝒅ₕ (L_apply I g h) (evalAt h X) :=
     apply_fdifferential]
   -- Porting note: more agressive here
   erw [LinearMap.comp_apply]
-  rw [apply_fdifferential, ← apply_hfdifferential, left_invariant]
+  -- This used to be `rw`, but we need `erw` after leanprover/lean4#2644
+  erw [apply_fdifferential, ← apply_hfdifferential, left_invariant]
 #align left_invariant_derivation.eval_at_mul LeftInvariantDerivation.evalAt_mul
 
 theorem comp_L : (X f).comp (𝑳 I g) = X (f.comp (𝑳 I g)) := by

This reverts commit 26eb2b0a.

@@ -251,8 +251,7 @@ theorem evalAt_mul : evalAt (g * h) X = 𝒅ₕ (L_apply I g h) (evalAt h X) :=
     apply_fdifferential]
   -- Porting note: more agressive here
   erw [LinearMap.comp_apply]
-  -- This used to be `rw`, but we need `erw` after leanprover/lean4#2644
-  erw [apply_fdifferential, ← apply_hfdifferential, left_invariant]
+  rw [apply_fdifferential, ← apply_hfdifferential, left_invariant]
 #align left_invariant_derivation.eval_at_mul LeftInvariantDerivation.evalAt_mul
 
 theorem comp_L : (X f).comp (𝑳 I g) = X (f.comp (𝑳 I g)) := by

This includes all the changes from #7606.

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

@@ -251,7 +251,8 @@ theorem evalAt_mul : evalAt (g * h) X = 𝒅ₕ (L_apply I g h) (evalAt h X) :=
     apply_fdifferential]
   -- Porting note: more agressive here
   erw [LinearMap.comp_apply]
-  rw [apply_fdifferential, ← apply_hfdifferential, left_invariant]
+  -- This used to be `rw`, but we need `erw` after leanprover/lean4#2644
+  erw [apply_fdifferential, ← apply_hfdifferential, left_invariant]
 #align left_invariant_derivation.eval_at_mul LeftInvariantDerivation.evalAt_mul
 
 theorem comp_L : (X f).comp (𝑳 I g) = X (f.comp (𝑳 I g)) := by

We clean up heart beat bumps after #6474.

@@ -139,7 +139,6 @@ instance : Add (LeftInvariantDerivation I G) where
     ⟨X + Y, fun g => by
       simp only [map_add, Derivation.coe_add, left_invariant', Pi.add_apply]⟩
 
-set_option maxHeartbeats 400000 in
 instance : Neg (LeftInvariantDerivation I G) where
   neg X := ⟨-X, fun g => by
     -- porting note: was simp [left_invariant']
@@ -147,7 +146,7 @@ instance : Neg (LeftInvariantDerivation I G) where
     rw [map_neg (Derivation.evalAt (𝕜 := 𝕜) (1 : G)), map_neg (𝒅ₕ (smoothLeftMul_one I g)),
       left_invariant', map_neg (Derivation.evalAt (𝕜 := 𝕜) g)]⟩
 
-set_option maxHeartbeats 400000 in
+set_option maxHeartbeats 300000 in
 instance : Sub (LeftInvariantDerivation I G) where
   sub X Y := ⟨X - Y, fun g => by
     -- porting note: was simp [left_invariant']
@@ -262,7 +261,6 @@ theorem comp_L : (X f).comp (𝑳 I g) = X (f.comp (𝑳 I g)) := by
 set_option linter.uppercaseLean3 false in
 #align left_invariant_derivation.comp_L LeftInvariantDerivation.comp_L
 
-set_option maxHeartbeats 400000 in
 instance : Bracket (LeftInvariantDerivation I G) (LeftInvariantDerivation I G) where
   bracket X Y :=
     ⟨⁅(X : Derivation 𝕜 C^∞⟮I, G; 𝕜⟯ C^∞⟮I, G; 𝕜⟯), Y⁆, fun g => by

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

This has nice performance benefits.

@@ -26,8 +26,8 @@ noncomputable section
 
 open scoped LieGroup Manifold Derivation
 
-variable {𝕜 : Type _} [NontriviallyNormedField 𝕜] {E : Type _} [NormedAddCommGroup E]
-  [NormedSpace 𝕜 E] {H : Type _} [TopologicalSpace H] (I : ModelWithCorners 𝕜 E H) (G : Type _)
+variable {𝕜 : Type*} [NontriviallyNormedField 𝕜] {E : Type*} [NormedAddCommGroup E]
+  [NormedSpace 𝕜 E] {H : Type*} [TopologicalSpace H] (I : ModelWithCorners 𝕜 E H) (G : Type*)
   [TopologicalSpace G] [ChartedSpace H G] [Monoid G] [SmoothMul I G] (g h : G)
 
 -- Generate trivial has_sizeof instance. It prevents weird type class inference timeout problems
@@ -69,7 +69,7 @@ instance : LinearMapClass (LeftInvariantDerivation I G) 𝕜 C^∞⟮I, G; 𝕜
 instance : CoeFun (LeftInvariantDerivation I G) fun _ => C^∞⟮I, G; 𝕜⟯ → C^∞⟮I, G; 𝕜⟯ :=
   ⟨FunLike.coe⟩
 
-variable {M : Type _} [TopologicalSpace M] [ChartedSpace H M] {x : M} {r : 𝕜}
+variable {M : Type*} [TopologicalSpace M] [ChartedSpace H M] {x : M} {r : 𝕜}
   {X Y : LeftInvariantDerivation I G} {f f' : C^∞⟮I, G; 𝕜⟯}
 
 theorem toFun_eq_coe : X.toFun = ⇑X :=

• depends on: #5966

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

@@ -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
-
-! This file was ported from Lean 3 source module geometry.manifold.algebra.left_invariant_derivation
-! 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.RingTheory.Derivation.Lie
 import Mathlib.Geometry.Manifold.DerivationBundle
 
+#align_import geometry.manifold.algebra.left_invariant_derivation from "leanprover-community/mathlib"@"b608348ffaeb7f557f2fd46876037abafd326ff3"
+
 /-!
 
 # Left invariant derivations

Co-authored-by: Parcly Taxel <reddeloostw@gmail.com> Co-authored-by: Matthew Ballard <matt@mrb.email>