geometry.manifold.algebra.lie_group ⟷ Mathlib.Geometry.Manifold.Algebra.LieGroup

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

@@ -3,7 +3,7 @@ Copyright © 2020 Nicolò Cavalleri. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Nicolò Cavalleri
 -/
-import Mathbin.Geometry.Manifold.Algebra.Monoid
+import Geometry.Manifold.Algebra.Monoid
 
 #align_import geometry.manifold.algebra.lie_group from "leanprover-community/mathlib"@"30faa0c3618ce1472bf6305ae0e3fa56affa3f95"
 

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

@@ -2,14 +2,11 @@
 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.lie_group
-! leanprover-community/mathlib commit 30faa0c3618ce1472bf6305ae0e3fa56affa3f95
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Geometry.Manifold.Algebra.Monoid
 
+#align_import geometry.manifold.algebra.lie_group from "leanprover-community/mathlib"@"30faa0c3618ce1472bf6305ae0e3fa56affa3f95"
+
 /-!
 # Lie groups
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/8b981918a93bc45a8600de608cde7944a80d92b9

@@ -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.lie_group
-! leanprover-community/mathlib commit f9ec187127cc5b381dfcf5f4a22dacca4c20b63d
+! leanprover-community/mathlib commit 30faa0c3618ce1472bf6305ae0e3fa56affa3f95
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -13,6 +13,9 @@ import Mathbin.Geometry.Manifold.Algebra.Monoid
 /-!
 # Lie groups
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 A Lie group is a group that is also a smooth manifold, in which the group operations of
 multiplication and inversion are smooth maps. Smoothness of the group multiplication means that
 multiplication is a smooth mapping of the product manifold `G` × `G` into `G`.

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

@@ -51,7 +51,7 @@ open scoped Manifold
 the addition and negation operations are smooth. -/
 class LieAddGroup {𝕜 : Type _} [NontriviallyNormedField 𝕜] {H : Type _} [TopologicalSpace H]
     {E : Type _} [NormedAddCommGroup E] [NormedSpace 𝕜 E] (I : ModelWithCorners 𝕜 E H) (G : Type _)
-    [AddGroup G] [TopologicalSpace G] [ChartedSpace H G] extends HasSmoothAdd I G : Prop where
+    [AddGroup G] [TopologicalSpace G] [ChartedSpace H G] extends SmoothAdd I G : Prop where
   smooth_neg : Smooth I I fun a : G => -a
 #align lie_add_group LieAddGroup
 -/
@@ -63,7 +63,7 @@ the multiplication and inverse operations are smooth. -/
 @[to_additive]
 class LieGroup {𝕜 : Type _} [NontriviallyNormedField 𝕜] {H : Type _} [TopologicalSpace H]
     {E : Type _} [NormedAddCommGroup E] [NormedSpace 𝕜 E] (I : ModelWithCorners 𝕜 E H) (G : Type _)
-    [Group G] [TopologicalSpace G] [ChartedSpace H G] extends HasSmoothMul I G : Prop where
+    [Group G] [TopologicalSpace G] [ChartedSpace H G] extends SmoothMul I G : Prop where
   smooth_inv : Smooth I I fun a : G => a⁻¹
 #align lie_group LieGroup
 #align lie_add_group LieAddGroup
@@ -258,7 +258,7 @@ instance {𝕜 : Type _} [NontriviallyNormedField 𝕜] {H : Type _} [Topologica
     [NormedAddCommGroup E'] [NormedSpace 𝕜 E'] {H' : Type _} [TopologicalSpace H']
     {I' : ModelWithCorners 𝕜 E' H'} {G' : Type _} [TopologicalSpace G'] [ChartedSpace H' G']
     [Group G'] [LieGroup I' G'] : LieGroup (I.Prod I') (G × G') :=
-  { HasSmoothMul.prod _ _ _ _ with smooth_inv := smooth_fst.inv.prod_mk smooth_snd.inv }
+  { SmoothMul.prod _ _ _ _ with smooth_inv := smooth_fst.inv.prod_mk smooth_snd.inv }
 
 end ProdLieGroup
 

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

@@ -45,6 +45,7 @@ noncomputable section
 
 open scoped Manifold
 
+#print LieAddGroup /-
 -- See note [Design choices about smooth algebraic structures]
 /-- A Lie (additive) group is a group and a smooth manifold at the same time in which
 the addition and negation operations are smooth. -/
@@ -53,7 +54,9 @@ class LieAddGroup {𝕜 : Type _} [NontriviallyNormedField 𝕜] {H : Type _} [T
     [AddGroup G] [TopologicalSpace G] [ChartedSpace H G] extends HasSmoothAdd I G : Prop where
   smooth_neg : Smooth I I fun a : G => -a
 #align lie_add_group LieAddGroup
+-/
 
+#print LieGroup /-
 -- See note [Design choices about smooth algebraic structures]
 /-- A Lie group is a group and a smooth manifold at the same time in which
 the multiplication and inverse operations are smooth. -/
@@ -64,6 +67,7 @@ class LieGroup {𝕜 : Type _} [NontriviallyNormedField 𝕜] {H : Type _} [Topo
   smooth_inv : Smooth I I fun a : G => a⁻¹
 #align lie_group LieGroup
 #align lie_add_group LieAddGroup
+-/
 
 section LieGroup
 
@@ -81,12 +85,15 @@ section
 
 variable (I)
 
+#print smooth_inv /-
 @[to_additive]
 theorem smooth_inv : Smooth I I fun x : G => x⁻¹ :=
   LieGroup.smooth_inv
 #align smooth_inv smooth_inv
 #align smooth_neg smooth_neg
+-/
 
+#print topologicalGroup_of_lieGroup /-
 /-- A Lie group is a topological group. This is not an instance for technical reasons,
 see note [Design choices about smooth algebraic structures]. -/
 @[to_additive
@@ -94,63 +101,81 @@ see note [Design choices about smooth algebraic structures]. -/
 theorem topologicalGroup_of_lieGroup : TopologicalGroup G :=
   { continuousMul_of_smooth I with continuous_inv := (smooth_inv I).Continuous }
 #align topological_group_of_lie_group topologicalGroup_of_lieGroup
-#align topological_add_group_of_lie_add_group topological_add_group_of_lie_add_group
+#align topological_add_group_of_lie_add_group topologicalAddGroup_of_lieAddGroup
+-/
 
 end
 
+#print ContMDiffWithinAt.inv /-
 @[to_additive]
 theorem ContMDiffWithinAt.inv {f : M → G} {s : Set M} {x₀ : M}
     (hf : ContMDiffWithinAt I' I n f s x₀) : ContMDiffWithinAt I' I n (fun x => (f x)⁻¹) s x₀ :=
   ((smooth_inv I).of_le le_top).ContMDiffAt.ContMDiffWithinAt.comp x₀ hf <| Set.mapsTo_univ _ _
 #align cont_mdiff_within_at.inv ContMDiffWithinAt.inv
 #align cont_mdiff_within_at.neg ContMDiffWithinAt.neg
+-/
 
+#print ContMDiffAt.inv /-
 @[to_additive]
 theorem ContMDiffAt.inv {f : M → G} {x₀ : M} (hf : ContMDiffAt I' I n f x₀) :
     ContMDiffAt I' I n (fun x => (f x)⁻¹) x₀ :=
   ((smooth_inv I).of_le le_top).ContMDiffAt.comp x₀ hf
 #align cont_mdiff_at.inv ContMDiffAt.inv
 #align cont_mdiff_at.neg ContMDiffAt.neg
+-/
 
+#print ContMDiffOn.inv /-
 @[to_additive]
 theorem ContMDiffOn.inv {f : M → G} {s : Set M} (hf : ContMDiffOn I' I n f s) :
     ContMDiffOn I' I n (fun x => (f x)⁻¹) s := fun x hx => (hf x hx).inv
 #align cont_mdiff_on.inv ContMDiffOn.inv
 #align cont_mdiff_on.neg ContMDiffOn.neg
+-/
 
+#print ContMDiff.inv /-
 @[to_additive]
 theorem ContMDiff.inv {f : M → G} (hf : ContMDiff I' I n f) : ContMDiff I' I n fun x => (f x)⁻¹ :=
   fun x => (hf x).inv
 #align cont_mdiff.inv ContMDiff.inv
 #align cont_mdiff.neg ContMDiff.neg
+-/
 
+#print SmoothWithinAt.inv /-
 @[to_additive]
 theorem SmoothWithinAt.inv {f : M → G} {s : Set M} {x₀ : M} (hf : SmoothWithinAt I' I f s x₀) :
     SmoothWithinAt I' I (fun x => (f x)⁻¹) s x₀ :=
   hf.inv
 #align smooth_within_at.inv SmoothWithinAt.inv
 #align smooth_within_at.neg SmoothWithinAt.neg
+-/
 
+#print SmoothAt.inv /-
 @[to_additive]
 theorem SmoothAt.inv {f : M → G} {x₀ : M} (hf : SmoothAt I' I f x₀) :
     SmoothAt I' I (fun x => (f x)⁻¹) x₀ :=
   hf.inv
 #align smooth_at.inv SmoothAt.inv
 #align smooth_at.neg SmoothAt.neg
+-/
 
+#print SmoothOn.inv /-
 @[to_additive]
 theorem SmoothOn.inv {f : M → G} {s : Set M} (hf : SmoothOn I' I f s) :
     SmoothOn I' I (fun x => (f x)⁻¹) s :=
   hf.inv
 #align smooth_on.inv SmoothOn.inv
 #align smooth_on.neg SmoothOn.neg
+-/
 
+#print Smooth.inv /-
 @[to_additive]
 theorem Smooth.inv {f : M → G} (hf : Smooth I' I f) : Smooth I' I fun x => (f x)⁻¹ :=
   hf.inv
 #align smooth.inv Smooth.inv
 #align smooth.neg Smooth.neg
+-/
 
+#print ContMDiffWithinAt.div /-
 @[to_additive]
 theorem ContMDiffWithinAt.div {f g : M → G} {s : Set M} {x₀ : M}
     (hf : ContMDiffWithinAt I' I n f s x₀) (hg : ContMDiffWithinAt I' I n g s x₀) :
@@ -158,53 +183,68 @@ theorem ContMDiffWithinAt.div {f g : M → G} {s : Set M} {x₀ : M}
   exact hf.mul hg.inv
 #align cont_mdiff_within_at.div ContMDiffWithinAt.div
 #align cont_mdiff_within_at.sub ContMDiffWithinAt.sub
+-/
 
+#print ContMDiffAt.div /-
 @[to_additive]
 theorem ContMDiffAt.div {f g : M → G} {x₀ : M} (hf : ContMDiffAt I' I n f x₀)
     (hg : ContMDiffAt I' I n g x₀) : ContMDiffAt I' I n (fun x => f x / g x) x₀ := by
   simp_rw [div_eq_mul_inv]; exact hf.mul hg.inv
 #align cont_mdiff_at.div ContMDiffAt.div
 #align cont_mdiff_at.sub ContMDiffAt.sub
+-/
 
+#print ContMDiffOn.div /-
 @[to_additive]
 theorem ContMDiffOn.div {f g : M → G} {s : Set M} (hf : ContMDiffOn I' I n f s)
     (hg : ContMDiffOn I' I n g s) : ContMDiffOn I' I n (fun x => f x / g x) s := by
   simp_rw [div_eq_mul_inv]; exact hf.mul hg.inv
 #align cont_mdiff_on.div ContMDiffOn.div
 #align cont_mdiff_on.sub ContMDiffOn.sub
+-/
 
+#print ContMDiff.div /-
 @[to_additive]
 theorem ContMDiff.div {f g : M → G} (hf : ContMDiff I' I n f) (hg : ContMDiff I' I n g) :
     ContMDiff I' I n fun x => f x / g x := by simp_rw [div_eq_mul_inv]; exact hf.mul hg.inv
 #align cont_mdiff.div ContMDiff.div
 #align cont_mdiff.sub ContMDiff.sub
+-/
 
+#print SmoothWithinAt.div /-
 @[to_additive]
 theorem SmoothWithinAt.div {f g : M → G} {s : Set M} {x₀ : M} (hf : SmoothWithinAt I' I f s x₀)
     (hg : SmoothWithinAt I' I g s x₀) : SmoothWithinAt I' I (fun x => f x / g x) s x₀ :=
   hf.div hg
 #align smooth_within_at.div SmoothWithinAt.div
 #align smooth_within_at.sub SmoothWithinAt.sub
+-/
 
+#print SmoothAt.div /-
 @[to_additive]
 theorem SmoothAt.div {f g : M → G} {x₀ : M} (hf : SmoothAt I' I f x₀) (hg : SmoothAt I' I g x₀) :
     SmoothAt I' I (fun x => f x / g x) x₀ :=
   hf.div hg
 #align smooth_at.div SmoothAt.div
 #align smooth_at.sub SmoothAt.sub
+-/
 
+#print SmoothOn.div /-
 @[to_additive]
 theorem SmoothOn.div {f g : M → G} {s : Set M} (hf : SmoothOn I' I f s) (hg : SmoothOn I' I g s) :
     SmoothOn I' I (f / g) s :=
   hf.div hg
 #align smooth_on.div SmoothOn.div
 #align smooth_on.sub SmoothOn.sub
+-/
 
+#print Smooth.div /-
 @[to_additive]
 theorem Smooth.div {f g : M → G} (hf : Smooth I' I f) (hg : Smooth I' I g) : Smooth I' I (f / g) :=
   hf.div hg
 #align smooth.div Smooth.div
 #align smooth.sub Smooth.sub
+-/
 
 end LieGroup
 
@@ -225,11 +265,13 @@ end ProdLieGroup
 /-! ### Normed spaces are Lie groups -/
 
 
-instance normedSpace_lieAddGroup {𝕜 : Type _} [NontriviallyNormedField 𝕜] {E : Type _}
+#print normedSpaceLieAddGroup /-
+instance normedSpaceLieAddGroup {𝕜 : Type _} [NontriviallyNormedField 𝕜] {E : Type _}
     [NormedAddCommGroup E] [NormedSpace 𝕜 E] : LieAddGroup 𝓘(𝕜, E) E :=
   {
     model_space_smooth with
     smooth_add := smooth_iff.2 ⟨continuous_add, fun x y => contDiff_add.ContDiffOn⟩
     smooth_neg := smooth_iff.2 ⟨continuous_neg, fun x y => contDiff_neg.ContDiffOn⟩ }
-#align normed_space_lie_add_group normedSpace_lieAddGroup
+#align normed_space_lie_add_group normedSpaceLieAddGroup
+-/
 

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

@@ -225,11 +225,11 @@ end ProdLieGroup
 /-! ### Normed spaces are Lie groups -/
 
 
-instance normedSpaceLieAddGroup {𝕜 : Type _} [NontriviallyNormedField 𝕜] {E : Type _}
+instance normedSpace_lieAddGroup {𝕜 : Type _} [NontriviallyNormedField 𝕜] {E : Type _}
     [NormedAddCommGroup E] [NormedSpace 𝕜 E] : LieAddGroup 𝓘(𝕜, E) E :=
   {
     model_space_smooth with
     smooth_add := smooth_iff.2 ⟨continuous_add, fun x y => contDiff_add.ContDiffOn⟩
     smooth_neg := smooth_iff.2 ⟨continuous_neg, fun x y => contDiff_neg.ContDiffOn⟩ }
-#align normed_space_lie_add_group normedSpaceLieAddGroup
+#align normed_space_lie_add_group normedSpace_lieAddGroup
 

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

@@ -99,30 +99,30 @@ theorem topologicalGroup_of_lieGroup : TopologicalGroup G :=
 end
 
 @[to_additive]
-theorem ContMdiffWithinAt.inv {f : M → G} {s : Set M} {x₀ : M}
-    (hf : ContMdiffWithinAt I' I n f s x₀) : ContMdiffWithinAt I' I n (fun x => (f x)⁻¹) s x₀ :=
-  ((smooth_inv I).of_le le_top).ContMdiffAt.ContMdiffWithinAt.comp x₀ hf <| Set.mapsTo_univ _ _
-#align cont_mdiff_within_at.inv ContMdiffWithinAt.inv
-#align cont_mdiff_within_at.neg ContMdiffWithinAt.neg
+theorem ContMDiffWithinAt.inv {f : M → G} {s : Set M} {x₀ : M}
+    (hf : ContMDiffWithinAt I' I n f s x₀) : ContMDiffWithinAt I' I n (fun x => (f x)⁻¹) s x₀ :=
+  ((smooth_inv I).of_le le_top).ContMDiffAt.ContMDiffWithinAt.comp x₀ hf <| Set.mapsTo_univ _ _
+#align cont_mdiff_within_at.inv ContMDiffWithinAt.inv
+#align cont_mdiff_within_at.neg ContMDiffWithinAt.neg
 
 @[to_additive]
-theorem ContMdiffAt.inv {f : M → G} {x₀ : M} (hf : ContMdiffAt I' I n f x₀) :
-    ContMdiffAt I' I n (fun x => (f x)⁻¹) x₀ :=
-  ((smooth_inv I).of_le le_top).ContMdiffAt.comp x₀ hf
-#align cont_mdiff_at.inv ContMdiffAt.inv
-#align cont_mdiff_at.neg ContMdiffAt.neg
+theorem ContMDiffAt.inv {f : M → G} {x₀ : M} (hf : ContMDiffAt I' I n f x₀) :
+    ContMDiffAt I' I n (fun x => (f x)⁻¹) x₀ :=
+  ((smooth_inv I).of_le le_top).ContMDiffAt.comp x₀ hf
+#align cont_mdiff_at.inv ContMDiffAt.inv
+#align cont_mdiff_at.neg ContMDiffAt.neg
 
 @[to_additive]
-theorem ContMdiffOn.inv {f : M → G} {s : Set M} (hf : ContMdiffOn I' I n f s) :
-    ContMdiffOn I' I n (fun x => (f x)⁻¹) s := fun x hx => (hf x hx).inv
-#align cont_mdiff_on.inv ContMdiffOn.inv
-#align cont_mdiff_on.neg ContMdiffOn.neg
+theorem ContMDiffOn.inv {f : M → G} {s : Set M} (hf : ContMDiffOn I' I n f s) :
+    ContMDiffOn I' I n (fun x => (f x)⁻¹) s := fun x hx => (hf x hx).inv
+#align cont_mdiff_on.inv ContMDiffOn.inv
+#align cont_mdiff_on.neg ContMDiffOn.neg
 
 @[to_additive]
-theorem ContMdiff.inv {f : M → G} (hf : ContMdiff I' I n f) : ContMdiff I' I n fun x => (f x)⁻¹ :=
+theorem ContMDiff.inv {f : M → G} (hf : ContMDiff I' I n f) : ContMDiff I' I n fun x => (f x)⁻¹ :=
   fun x => (hf x).inv
-#align cont_mdiff.inv ContMdiff.inv
-#align cont_mdiff.neg ContMdiff.neg
+#align cont_mdiff.inv ContMDiff.inv
+#align cont_mdiff.neg ContMDiff.neg
 
 @[to_additive]
 theorem SmoothWithinAt.inv {f : M → G} {s : Set M} {x₀ : M} (hf : SmoothWithinAt I' I f s x₀) :
@@ -152,32 +152,32 @@ theorem Smooth.inv {f : M → G} (hf : Smooth I' I f) : Smooth I' I fun x => (f
 #align smooth.neg Smooth.neg
 
 @[to_additive]
-theorem ContMdiffWithinAt.div {f g : M → G} {s : Set M} {x₀ : M}
-    (hf : ContMdiffWithinAt I' I n f s x₀) (hg : ContMdiffWithinAt I' I n g s x₀) :
-    ContMdiffWithinAt I' I n (fun x => f x / g x) s x₀ := by simp_rw [div_eq_mul_inv];
+theorem ContMDiffWithinAt.div {f g : M → G} {s : Set M} {x₀ : M}
+    (hf : ContMDiffWithinAt I' I n f s x₀) (hg : ContMDiffWithinAt I' I n g s x₀) :
+    ContMDiffWithinAt I' I n (fun x => f x / g x) s x₀ := by simp_rw [div_eq_mul_inv];
   exact hf.mul hg.inv
-#align cont_mdiff_within_at.div ContMdiffWithinAt.div
-#align cont_mdiff_within_at.sub ContMdiffWithinAt.sub
+#align cont_mdiff_within_at.div ContMDiffWithinAt.div
+#align cont_mdiff_within_at.sub ContMDiffWithinAt.sub
 
 @[to_additive]
-theorem ContMdiffAt.div {f g : M → G} {x₀ : M} (hf : ContMdiffAt I' I n f x₀)
-    (hg : ContMdiffAt I' I n g x₀) : ContMdiffAt I' I n (fun x => f x / g x) x₀ := by
+theorem ContMDiffAt.div {f g : M → G} {x₀ : M} (hf : ContMDiffAt I' I n f x₀)
+    (hg : ContMDiffAt I' I n g x₀) : ContMDiffAt I' I n (fun x => f x / g x) x₀ := by
   simp_rw [div_eq_mul_inv]; exact hf.mul hg.inv
-#align cont_mdiff_at.div ContMdiffAt.div
-#align cont_mdiff_at.sub ContMdiffAt.sub
+#align cont_mdiff_at.div ContMDiffAt.div
+#align cont_mdiff_at.sub ContMDiffAt.sub
 
 @[to_additive]
-theorem ContMdiffOn.div {f g : M → G} {s : Set M} (hf : ContMdiffOn I' I n f s)
-    (hg : ContMdiffOn I' I n g s) : ContMdiffOn I' I n (fun x => f x / g x) s := by
+theorem ContMDiffOn.div {f g : M → G} {s : Set M} (hf : ContMDiffOn I' I n f s)
+    (hg : ContMDiffOn I' I n g s) : ContMDiffOn I' I n (fun x => f x / g x) s := by
   simp_rw [div_eq_mul_inv]; exact hf.mul hg.inv
-#align cont_mdiff_on.div ContMdiffOn.div
-#align cont_mdiff_on.sub ContMdiffOn.sub
+#align cont_mdiff_on.div ContMDiffOn.div
+#align cont_mdiff_on.sub ContMDiffOn.sub
 
 @[to_additive]
-theorem ContMdiff.div {f g : M → G} (hf : ContMdiff I' I n f) (hg : ContMdiff I' I n g) :
-    ContMdiff I' I n fun x => f x / g x := by simp_rw [div_eq_mul_inv]; exact hf.mul hg.inv
-#align cont_mdiff.div ContMdiff.div
-#align cont_mdiff.sub ContMdiff.sub
+theorem ContMDiff.div {f g : M → G} (hf : ContMDiff I' I n f) (hg : ContMDiff I' I n g) :
+    ContMDiff I' I n fun x => f x / g x := by simp_rw [div_eq_mul_inv]; exact hf.mul hg.inv
+#align cont_mdiff.div ContMDiff.div
+#align cont_mdiff.sub ContMDiff.sub
 
 @[to_additive]
 theorem SmoothWithinAt.div {f g : M → G} {s : Set M} {x₀ : M} (hf : SmoothWithinAt I' I f s x₀)

mathlib commit https://github.com/leanprover-community/mathlib/commit/9f55d0d4363ae59948c33864cbc52e0b12e0e8ce

@@ -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.lie_group
-! leanprover-community/mathlib commit d1bd9c5df2867c1cb463bc6364446d57bdd9f7f1
+! leanprover-community/mathlib commit f9ec187127cc5b381dfcf5f4a22dacca4c20b63d
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -75,6 +75,7 @@ variable {𝕜 : Type _} [NontriviallyNormedField 𝕜] {H : Type _} [Topologica
   {I' : ModelWithCorners 𝕜 E' H'} {M : Type _} [TopologicalSpace M] [ChartedSpace H' M]
   {E'' : Type _} [NormedAddCommGroup E''] [NormedSpace 𝕜 E''] {H'' : Type _} [TopologicalSpace H'']
   {I'' : ModelWithCorners 𝕜 E'' H''} {M' : Type _} [TopologicalSpace M'] [ChartedSpace H'' M']
+  {n : ℕ∞}
 
 section
 
@@ -98,31 +99,113 @@ theorem topologicalGroup_of_lieGroup : TopologicalGroup G :=
 end
 
 @[to_additive]
-theorem Smooth.inv {f : M → G} (hf : Smooth I' I f) : Smooth I' I fun x => (f x)⁻¹ :=
-  (smooth_inv I).comp hf
-#align smooth.inv Smooth.inv
-#align smooth.neg Smooth.neg
+theorem ContMdiffWithinAt.inv {f : M → G} {s : Set M} {x₀ : M}
+    (hf : ContMdiffWithinAt I' I n f s x₀) : ContMdiffWithinAt I' I n (fun x => (f x)⁻¹) s x₀ :=
+  ((smooth_inv I).of_le le_top).ContMdiffAt.ContMdiffWithinAt.comp x₀ hf <| Set.mapsTo_univ _ _
+#align cont_mdiff_within_at.inv ContMdiffWithinAt.inv
+#align cont_mdiff_within_at.neg ContMdiffWithinAt.neg
+
+@[to_additive]
+theorem ContMdiffAt.inv {f : M → G} {x₀ : M} (hf : ContMdiffAt I' I n f x₀) :
+    ContMdiffAt I' I n (fun x => (f x)⁻¹) x₀ :=
+  ((smooth_inv I).of_le le_top).ContMdiffAt.comp x₀ hf
+#align cont_mdiff_at.inv ContMdiffAt.inv
+#align cont_mdiff_at.neg ContMdiffAt.neg
+
+@[to_additive]
+theorem ContMdiffOn.inv {f : M → G} {s : Set M} (hf : ContMdiffOn I' I n f s) :
+    ContMdiffOn I' I n (fun x => (f x)⁻¹) s := fun x hx => (hf x hx).inv
+#align cont_mdiff_on.inv ContMdiffOn.inv
+#align cont_mdiff_on.neg ContMdiffOn.neg
+
+@[to_additive]
+theorem ContMdiff.inv {f : M → G} (hf : ContMdiff I' I n f) : ContMdiff I' I n fun x => (f x)⁻¹ :=
+  fun x => (hf x).inv
+#align cont_mdiff.inv ContMdiff.inv
+#align cont_mdiff.neg ContMdiff.neg
+
+@[to_additive]
+theorem SmoothWithinAt.inv {f : M → G} {s : Set M} {x₀ : M} (hf : SmoothWithinAt I' I f s x₀) :
+    SmoothWithinAt I' I (fun x => (f x)⁻¹) s x₀ :=
+  hf.inv
+#align smooth_within_at.inv SmoothWithinAt.inv
+#align smooth_within_at.neg SmoothWithinAt.neg
+
+@[to_additive]
+theorem SmoothAt.inv {f : M → G} {x₀ : M} (hf : SmoothAt I' I f x₀) :
+    SmoothAt I' I (fun x => (f x)⁻¹) x₀ :=
+  hf.inv
+#align smooth_at.inv SmoothAt.inv
+#align smooth_at.neg SmoothAt.neg
 
 @[to_additive]
 theorem SmoothOn.inv {f : M → G} {s : Set M} (hf : SmoothOn I' I f s) :
     SmoothOn I' I (fun x => (f x)⁻¹) s :=
-  (smooth_inv I).comp_smoothOn hf
+  hf.inv
 #align smooth_on.inv SmoothOn.inv
 #align smooth_on.neg SmoothOn.neg
 
 @[to_additive]
-theorem Smooth.div {f g : M → G} (hf : Smooth I' I f) (hg : Smooth I' I g) : Smooth I' I (f / g) :=
-  by rw [div_eq_mul_inv]; exact ((smooth_mul I).comp (hf.prod_mk hg.inv) : _)
-#align smooth.div Smooth.div
-#align smooth.sub Smooth.sub
+theorem Smooth.inv {f : M → G} (hf : Smooth I' I f) : Smooth I' I fun x => (f x)⁻¹ :=
+  hf.inv
+#align smooth.inv Smooth.inv
+#align smooth.neg Smooth.neg
+
+@[to_additive]
+theorem ContMdiffWithinAt.div {f g : M → G} {s : Set M} {x₀ : M}
+    (hf : ContMdiffWithinAt I' I n f s x₀) (hg : ContMdiffWithinAt I' I n g s x₀) :
+    ContMdiffWithinAt I' I n (fun x => f x / g x) s x₀ := by simp_rw [div_eq_mul_inv];
+  exact hf.mul hg.inv
+#align cont_mdiff_within_at.div ContMdiffWithinAt.div
+#align cont_mdiff_within_at.sub ContMdiffWithinAt.sub
+
+@[to_additive]
+theorem ContMdiffAt.div {f g : M → G} {x₀ : M} (hf : ContMdiffAt I' I n f x₀)
+    (hg : ContMdiffAt I' I n g x₀) : ContMdiffAt I' I n (fun x => f x / g x) x₀ := by
+  simp_rw [div_eq_mul_inv]; exact hf.mul hg.inv
+#align cont_mdiff_at.div ContMdiffAt.div
+#align cont_mdiff_at.sub ContMdiffAt.sub
+
+@[to_additive]
+theorem ContMdiffOn.div {f g : M → G} {s : Set M} (hf : ContMdiffOn I' I n f s)
+    (hg : ContMdiffOn I' I n g s) : ContMdiffOn I' I n (fun x => f x / g x) s := by
+  simp_rw [div_eq_mul_inv]; exact hf.mul hg.inv
+#align cont_mdiff_on.div ContMdiffOn.div
+#align cont_mdiff_on.sub ContMdiffOn.sub
+
+@[to_additive]
+theorem ContMdiff.div {f g : M → G} (hf : ContMdiff I' I n f) (hg : ContMdiff I' I n g) :
+    ContMdiff I' I n fun x => f x / g x := by simp_rw [div_eq_mul_inv]; exact hf.mul hg.inv
+#align cont_mdiff.div ContMdiff.div
+#align cont_mdiff.sub ContMdiff.sub
+
+@[to_additive]
+theorem SmoothWithinAt.div {f g : M → G} {s : Set M} {x₀ : M} (hf : SmoothWithinAt I' I f s x₀)
+    (hg : SmoothWithinAt I' I g s x₀) : SmoothWithinAt I' I (fun x => f x / g x) s x₀ :=
+  hf.div hg
+#align smooth_within_at.div SmoothWithinAt.div
+#align smooth_within_at.sub SmoothWithinAt.sub
+
+@[to_additive]
+theorem SmoothAt.div {f g : M → G} {x₀ : M} (hf : SmoothAt I' I f x₀) (hg : SmoothAt I' I g x₀) :
+    SmoothAt I' I (fun x => f x / g x) x₀ :=
+  hf.div hg
+#align smooth_at.div SmoothAt.div
+#align smooth_at.sub SmoothAt.sub
 
 @[to_additive]
 theorem SmoothOn.div {f g : M → G} {s : Set M} (hf : SmoothOn I' I f s) (hg : SmoothOn I' I g s) :
-    SmoothOn I' I (f / g) s := by rw [div_eq_mul_inv];
-  exact ((smooth_mul I).comp_smoothOn (hf.prod_mk hg.inv) : _)
+    SmoothOn I' I (f / g) s :=
+  hf.div hg
 #align smooth_on.div SmoothOn.div
 #align smooth_on.sub SmoothOn.sub
 
+@[to_additive]
+theorem Smooth.div {f g : M → G} (hf : Smooth I' I f) (hg : Smooth I' I g) : Smooth I' I (f / g) :=
+  hf.div hg
+#align smooth.div Smooth.div
+#align smooth.sub Smooth.sub
+
 end LieGroup
 
 section ProdLieGroup

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

@@ -49,8 +49,8 @@ open scoped Manifold
 /-- A Lie (additive) group is a group and a smooth manifold at the same time in which
 the addition and negation operations are smooth. -/
 class LieAddGroup {𝕜 : Type _} [NontriviallyNormedField 𝕜] {H : Type _} [TopologicalSpace H]
-  {E : Type _} [NormedAddCommGroup E] [NormedSpace 𝕜 E] (I : ModelWithCorners 𝕜 E H) (G : Type _)
-  [AddGroup G] [TopologicalSpace G] [ChartedSpace H G] extends HasSmoothAdd I G : Prop where
+    {E : Type _} [NormedAddCommGroup E] [NormedSpace 𝕜 E] (I : ModelWithCorners 𝕜 E H) (G : Type _)
+    [AddGroup G] [TopologicalSpace G] [ChartedSpace H G] extends HasSmoothAdd I G : Prop where
   smooth_neg : Smooth I I fun a : G => -a
 #align lie_add_group LieAddGroup
 
@@ -59,8 +59,8 @@ class LieAddGroup {𝕜 : Type _} [NontriviallyNormedField 𝕜] {H : Type _} [T
 the multiplication and inverse operations are smooth. -/
 @[to_additive]
 class LieGroup {𝕜 : Type _} [NontriviallyNormedField 𝕜] {H : Type _} [TopologicalSpace H]
-  {E : Type _} [NormedAddCommGroup E] [NormedSpace 𝕜 E] (I : ModelWithCorners 𝕜 E H) (G : Type _)
-  [Group G] [TopologicalSpace G] [ChartedSpace H G] extends HasSmoothMul I G : Prop where
+    {E : Type _} [NormedAddCommGroup E] [NormedSpace 𝕜 E] (I : ModelWithCorners 𝕜 E H) (G : Type _)
+    [Group G] [TopologicalSpace G] [ChartedSpace H G] extends HasSmoothMul I G : Prop where
   smooth_inv : Smooth I I fun a : G => a⁻¹
 #align lie_group LieGroup
 #align lie_add_group LieAddGroup

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

@@ -43,7 +43,7 @@ so the definition does not apply. Hence the definition should be more general, a
 
 noncomputable section
 
-open Manifold
+open scoped Manifold
 
 -- See note [Design choices about smooth algebraic structures]
 /-- A Lie (additive) group is a group and a smooth manifold at the same time in which

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

@@ -112,16 +112,13 @@ theorem SmoothOn.inv {f : M → G} {s : Set M} (hf : SmoothOn I' I f s) :
 
 @[to_additive]
 theorem Smooth.div {f g : M → G} (hf : Smooth I' I f) (hg : Smooth I' I g) : Smooth I' I (f / g) :=
-  by
-  rw [div_eq_mul_inv]
-  exact ((smooth_mul I).comp (hf.prod_mk hg.inv) : _)
+  by rw [div_eq_mul_inv]; exact ((smooth_mul I).comp (hf.prod_mk hg.inv) : _)
 #align smooth.div Smooth.div
 #align smooth.sub Smooth.sub
 
 @[to_additive]
 theorem SmoothOn.div {f g : M → G} {s : Set M} (hf : SmoothOn I' I f s) (hg : SmoothOn I' I g s) :
-    SmoothOn I' I (f / g) s := by
-  rw [div_eq_mul_inv]
+    SmoothOn I' I (f / g) s := by rw [div_eq_mul_inv];
   exact ((smooth_mul I).comp_smoothOn (hf.prod_mk hg.inv) : _)
 #align smooth_on.div SmoothOn.div
 #align smooth_on.sub SmoothOn.sub

mathlib commit https://github.com/leanprover-community/mathlib/commit/c9236f47f5b9df573443aa499c0d3968769628b7

@@ -145,11 +145,11 @@ end ProdLieGroup
 /-! ### Normed spaces are Lie groups -/
 
 
-instance normedSpace_lieAddGroup {𝕜 : Type _} [NontriviallyNormedField 𝕜] {E : Type _}
+instance normedSpaceLieAddGroup {𝕜 : Type _} [NontriviallyNormedField 𝕜] {E : Type _}
     [NormedAddCommGroup E] [NormedSpace 𝕜 E] : LieAddGroup 𝓘(𝕜, E) E :=
   {
     model_space_smooth with
     smooth_add := smooth_iff.2 ⟨continuous_add, fun x y => contDiff_add.ContDiffOn⟩
     smooth_neg := smooth_iff.2 ⟨continuous_neg, fun x y => contDiff_neg.ContDiffOn⟩ }
-#align normed_space_lie_add_group normedSpace_lieAddGroup
+#align normed_space_lie_add_group normedSpaceLieAddGroup
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/21e3562c5e12d846c7def5eff8cdbc520d7d4936

@@ -145,11 +145,11 @@ end ProdLieGroup
 /-! ### Normed spaces are Lie groups -/
 
 
-instance normedSpaceLieAddGroup {𝕜 : Type _} [NontriviallyNormedField 𝕜] {E : Type _}
+instance normedSpace_lieAddGroup {𝕜 : Type _} [NontriviallyNormedField 𝕜] {E : Type _}
     [NormedAddCommGroup E] [NormedSpace 𝕜 E] : LieAddGroup 𝓘(𝕜, E) E :=
   {
     model_space_smooth with
     smooth_add := smooth_iff.2 ⟨continuous_add, fun x y => contDiff_add.ContDiffOn⟩
     smooth_neg := smooth_iff.2 ⟨continuous_neg, fun x y => contDiff_neg.ContDiffOn⟩ }
-#align normed_space_lie_add_group normedSpaceLieAddGroup
+#align normed_space_lie_add_group normedSpace_lieAddGroup
 

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

@@ -31,7 +31,7 @@ groups here are not necessarily finite dimensional.
   is smooth
 * `ContMDiff.inv₀` and variants: if `SmoothInv₀ N`, point-wise inversion of smooth maps `f : M → N`
   is smooth at all points at which `f` doesn't vanish.
-  ``ContMDiff.div₀` and variants: if also `SmoothMul N` (i.e., `N` is a Lie group except possibly
+* `ContMDiff.div₀` and variants: if also `SmoothMul N` (i.e., `N` is a Lie group except possibly
   for smoothness of inversion at `0`), similar results hold for point-wise division.
 * `normedSpaceLieAddGroup` : a normed vector space over a nontrivially normed field
   is an additive Lie group.

• tweak section names; add comments explaining what's in them
• add two lemma docstrings
• revamp the module docstring to mention all results
• in the module docstring, separate main definitions and results

@@ -18,13 +18,25 @@ Note that, since a manifold here is not second-countable and Hausdorff a Lie gro
 guaranteed to be second-countable (even though it can be proved it is Hausdorff). Note also that Lie
 groups here are not necessarily finite dimensional.
 
-## Main definitions and statements
+## Main definitions
 
 * `LieAddGroup I G` : a Lie additive group where `G` is a manifold on the model with corners `I`.
-* `LieGroup I G`     : a Lie multiplicative group where `G` is a manifold on the model with
-                        corners `I`.
+* `LieGroup I G` : a Lie multiplicative group where `G` is a manifold on the model with corners `I`.
+* `SmoothInv₀`: typeclass for smooth manifolds with `0` and `Inv` such that inversion is a smooth
+  map at each non-zero point. This includes complete normed fields and (multiplicative) Lie groups.
+
+
+## Main results
+* `ContMDiff.inv`, `ContMDiff.div` and variants: point-wise inversion and division of maps `M → G`
+  is smooth
+* `ContMDiff.inv₀` and variants: if `SmoothInv₀ N`, point-wise inversion of smooth maps `f : M → N`
+  is smooth at all points at which `f` doesn't vanish.
+  ``ContMDiff.div₀` and variants: if also `SmoothMul N` (i.e., `N` is a Lie group except possibly
+  for smoothness of inversion at `0`), similar results hold for point-wise division.
 * `normedSpaceLieAddGroup` : a normed vector space over a nontrivially normed field
-                                 is an additive Lie group.
+  is an additive Lie group.
+* `Instances/UnitsOfNormedAlgebra` shows that the group of units of a complete normed `𝕜`-algebra
+  is a multiplicative Lie group.
 
 ## Implementation notes
 
@@ -42,7 +54,7 @@ noncomputable section
 open scoped Manifold
 
 -- See note [Design choices about smooth algebraic structures]
-/-- A Lie (additive) group is a group and a smooth manifold at the same time in which
+/-- An additive Lie group is a group and a smooth manifold at the same time in which
 the addition and negation operations are smooth. -/
 class LieAddGroup {𝕜 : Type*} [NontriviallyNormedField 𝕜] {H : Type*} [TopologicalSpace H]
     {E : Type*} [NormedAddCommGroup E] [NormedSpace 𝕜 E] (I : ModelWithCorners 𝕜 E H) (G : Type*)
@@ -52,7 +64,7 @@ class LieAddGroup {𝕜 : Type*} [NontriviallyNormedField 𝕜] {H : Type*} [Top
 #align lie_add_group LieAddGroup
 
 -- See note [Design choices about smooth algebraic structures]
-/-- A Lie group is a group and a smooth manifold at the same time in which
+/-- A (multiplicative) Lie group is a group and a smooth manifold at the same time in which
 the multiplication and inverse operations are smooth. -/
 @[to_additive]
 class LieGroup {𝕜 : Type*} [NontriviallyNormedField 𝕜] {H : Type*} [TopologicalSpace H]
@@ -62,7 +74,13 @@ class LieGroup {𝕜 : Type*} [NontriviallyNormedField 𝕜] {H : Type*} [Topolo
   smooth_inv : Smooth I I fun a : G => a⁻¹
 #align lie_group LieGroup
 
-section LieGroup
+/-!
+  ### Smoothness of inversion, negation, division and subtraction
+
+  Let `f : M → G` be a `C^n` or smooth functions into a Lie group, then `f` is point-wise
+  invertible with smooth inverse `f`. If `f` and `g` are two such functions, the quotient
+  `f / g` (i.e., the point-wise product of `f` and the point-wise inverse of `g`) is also smooth. -/
+section PointwiseDivision
 
 variable {𝕜 : Type*} [NontriviallyNormedField 𝕜] {H : Type*} [TopologicalSpace H] {E : Type*}
   [NormedAddCommGroup E] [NormedSpace 𝕜 E] {I : ModelWithCorners 𝕜 E H} {F : Type*}
@@ -78,7 +96,8 @@ section
 
 variable (I)
 
-@[to_additive]
+/-- In a Lie group, inversion is a smooth map. -/
+@[to_additive "In an additive Lie group, inversion is a smooth map."]
 theorem smooth_inv : Smooth I I fun x : G => x⁻¹ :=
   LieGroup.smooth_inv
 #align smooth_inv smooth_inv
@@ -205,9 +224,10 @@ nonrec theorem Smooth.div {f g : M → G} (hf : Smooth I' I f) (hg : Smooth I' I
 #align smooth.div Smooth.div
 #align smooth.sub Smooth.sub
 
-end LieGroup
+end PointwiseDivision
 
-section ProdLieGroup
+/-! Binary product of Lie groups -/
+section Product
 
 -- Instance of product group
 @[to_additive]
@@ -219,7 +239,7 @@ instance {𝕜 : Type*} [NontriviallyNormedField 𝕜] {H : Type*} [TopologicalS
     [Group G'] [LieGroup I' G'] : LieGroup (I.prod I') (G × G') :=
   { SmoothMul.prod _ _ _ _ with smooth_inv := smooth_fst.inv.prod_mk smooth_snd.inv }
 
-end ProdLieGroup
+end Product
 
 /-! ### Normed spaces are Lie groups -/
 
@@ -228,7 +248,12 @@ instance normedSpaceLieAddGroup {𝕜 : Type*} [NontriviallyNormedField 𝕜] {E
   smooth_neg := contDiff_neg.contMDiff
 #align normed_space_lie_add_group normedSpaceLieAddGroup
 
-section HasSmoothInv
+/-! ## Smooth manifolds with smooth inversion away from zero
+
+Typeclass for smooth manifolds with `0` and `Inv` such that inversion is smooth at all non-zero
+points. (This includes multiplicative Lie groups, but also complete normed semifields.)
+Point-wise inversion is smooth when the function/denominator is non-zero. -/
+section SmoothInv₀
 
 -- See note [Design choices about smooth algebraic structures]
 /-- A smooth manifold with `0` and `Inv` such that `fun x ↦ x⁻¹` is smooth at all nonzero points.
@@ -298,8 +323,13 @@ theorem SmoothOn.inv₀ (hf : SmoothOn I' I f s) (h0 : ∀ x ∈ s, f x ≠ 0) :
     SmoothOn I' I (fun x => (f x)⁻¹) s :=
   ContMDiffOn.inv₀ hf h0
 
-end HasSmoothInv
+end SmoothInv₀
+
+/-! ### Point-wise division of smooth functions
 
+If `[SmoothMul I N]` and `[SmoothInv₀ I N]`, point-wise division of smooth functions `f : M → N`
+is smooth whenever the denominator is non-zero. (This includes `N` being a completely normed field.)
+-/
 section Div
 
 variable {𝕜 : Type*} [NontriviallyNormedField 𝕜] {H : Type*} [TopologicalSpace H] {E : Type*}

After this PR, no file in Geometry uses autoImplicit, and in Analysis it's scoped to six declarations.

@@ -37,9 +37,6 @@ so the definition does not apply. Hence the definition should be more general, a
 `I : ModelWithCorners 𝕜 E H`.
 -/
 
-set_option autoImplicit true
-
-
 noncomputable section
 
 open scoped Manifold
@@ -268,7 +265,7 @@ theorem hasContinuousInv₀_of_hasSmoothInv₀ : HasContinuousInv₀ G :=
 theorem SmoothOn_inv₀ : SmoothOn I I (Inv.inv : G → G) {0}ᶜ := fun _x hx =>
   (smoothAt_inv₀ I hx).smoothWithinAt
 
-variable {I}
+variable {I} {s : Set M} {a : M}
 
 theorem ContMDiffWithinAt.inv₀ (hf : ContMDiffWithinAt I' I n f s a) (ha : f a ≠ 0) :
     ContMDiffWithinAt I' I n (fun x => (f x)⁻¹) s a :=
@@ -310,7 +307,7 @@ variable {𝕜 : Type*} [NontriviallyNormedField 𝕜] {H : Type*} [TopologicalS
   [TopologicalSpace G] [ChartedSpace H G] [GroupWithZero G] [SmoothInv₀ I G] [SmoothMul I G]
   {E' : Type*} [NormedAddCommGroup E'] [NormedSpace 𝕜 E'] {H' : Type*} [TopologicalSpace H']
   {I' : ModelWithCorners 𝕜 E' H'} {M : Type*} [TopologicalSpace M] [ChartedSpace H' M]
-  {f g : M → G}
+  {f g : M → G} {s : Set M} {a : M} {n : ℕ∞}
 
 theorem ContMDiffWithinAt.div₀
     (hf : ContMDiffWithinAt I' I n f s a) (hg : ContMDiffWithinAt I' I n g s a) (h₀ : g a ≠ 0) :

Autoimplicits are highly controversial and also defeat the performance-improving work in #6474.

The intent of this PR is to make autoImplicit opt-in on a per-file basis, by disabling it in the lakefile and enabling it again with set_option autoImplicit true in the few files that rely on it.

That also keeps this PR small, as opposed to attempting to "fix" files to not need it any more.

I claim that many of the uses of autoImplicit in these files are accidental; situations such as:

• Assuming variables are in scope, but pasting the lemma in the wrong section
• Pasting in a lemma from a scratch file without checking to see if the variable names are consistent with the rest of the file
• Making a copy-paste error between lemmas and forgetting to add an explicit arguments.

Having set_option autoImplicit false as the default prevents these types of mistake being made in the 90% of files where autoImplicits are not used at all, and causes them to be caught by CI during review.

I think there were various points during the port where we encouraged porters to delete the universes u v lines; I think having autoparams for universe variables only would cover a lot of the cases we actually use them, while avoiding any real shortcomings.

A Zulip poll (after combining overlapping votes accordingly) was in favor of this change with 5:5:18 as the no:dontcare:yes vote ratio.

While this PR was being reviewed, a handful of files gained some more likely-accidental autoImplicits. In these places, set_option autoImplicit true has been placed locally within a section, rather than at the top of the file.

@@ -37,6 +37,8 @@ so the definition does not apply. Hence the definition should be more general, a
 `I : ModelWithCorners 𝕜 E H`.
 -/
 
+set_option autoImplicit true
+
 
 noncomputable section
 

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

This has nice performance benefits.

@@ -45,8 +45,8 @@ open scoped Manifold
 -- See note [Design choices about smooth algebraic structures]
 /-- A Lie (additive) group is a group and a smooth manifold at the same time in which
 the addition and negation operations are smooth. -/
-class LieAddGroup {𝕜 : Type _} [NontriviallyNormedField 𝕜] {H : Type _} [TopologicalSpace H]
-    {E : Type _} [NormedAddCommGroup E] [NormedSpace 𝕜 E] (I : ModelWithCorners 𝕜 E H) (G : Type _)
+class LieAddGroup {𝕜 : Type*} [NontriviallyNormedField 𝕜] {H : Type*} [TopologicalSpace H]
+    {E : Type*} [NormedAddCommGroup E] [NormedSpace 𝕜 E] (I : ModelWithCorners 𝕜 E H) (G : Type*)
     [AddGroup G] [TopologicalSpace G] [ChartedSpace H G] extends SmoothAdd I G : Prop where
   /-- Negation is smooth in an additive Lie group. -/
   smooth_neg : Smooth I I fun a : G => -a
@@ -56,8 +56,8 @@ class LieAddGroup {𝕜 : Type _} [NontriviallyNormedField 𝕜] {H : Type _} [T
 /-- A Lie group is a group and a smooth manifold at the same time in which
 the multiplication and inverse operations are smooth. -/
 @[to_additive]
-class LieGroup {𝕜 : Type _} [NontriviallyNormedField 𝕜] {H : Type _} [TopologicalSpace H]
-    {E : Type _} [NormedAddCommGroup E] [NormedSpace 𝕜 E] (I : ModelWithCorners 𝕜 E H) (G : Type _)
+class LieGroup {𝕜 : Type*} [NontriviallyNormedField 𝕜] {H : Type*} [TopologicalSpace H]
+    {E : Type*} [NormedAddCommGroup E] [NormedSpace 𝕜 E] (I : ModelWithCorners 𝕜 E H) (G : Type*)
     [Group G] [TopologicalSpace G] [ChartedSpace H G] extends SmoothMul I G : Prop where
   /-- Inversion is smooth in a Lie group. -/
   smooth_inv : Smooth I I fun a : G => a⁻¹
@@ -65,14 +65,14 @@ class LieGroup {𝕜 : Type _} [NontriviallyNormedField 𝕜] {H : Type _} [Topo
 
 section LieGroup
 
-variable {𝕜 : Type _} [NontriviallyNormedField 𝕜] {H : Type _} [TopologicalSpace H] {E : Type _}
-  [NormedAddCommGroup E] [NormedSpace 𝕜 E] {I : ModelWithCorners 𝕜 E H} {F : Type _}
-  [NormedAddCommGroup F] [NormedSpace 𝕜 F] {J : ModelWithCorners 𝕜 F F} {G : Type _}
-  [TopologicalSpace G] [ChartedSpace H G] [Group G] [LieGroup I G] {E' : Type _}
-  [NormedAddCommGroup E'] [NormedSpace 𝕜 E'] {H' : Type _} [TopologicalSpace H']
-  {I' : ModelWithCorners 𝕜 E' H'} {M : Type _} [TopologicalSpace M] [ChartedSpace H' M]
-  {E'' : Type _} [NormedAddCommGroup E''] [NormedSpace 𝕜 E''] {H'' : Type _} [TopologicalSpace H'']
-  {I'' : ModelWithCorners 𝕜 E'' H''} {M' : Type _} [TopologicalSpace M'] [ChartedSpace H'' M']
+variable {𝕜 : Type*} [NontriviallyNormedField 𝕜] {H : Type*} [TopologicalSpace H] {E : Type*}
+  [NormedAddCommGroup E] [NormedSpace 𝕜 E] {I : ModelWithCorners 𝕜 E H} {F : Type*}
+  [NormedAddCommGroup F] [NormedSpace 𝕜 F] {J : ModelWithCorners 𝕜 F F} {G : Type*}
+  [TopologicalSpace G] [ChartedSpace H G] [Group G] [LieGroup I G] {E' : Type*}
+  [NormedAddCommGroup E'] [NormedSpace 𝕜 E'] {H' : Type*} [TopologicalSpace H']
+  {I' : ModelWithCorners 𝕜 E' H'} {M : Type*} [TopologicalSpace M] [ChartedSpace H' M]
+  {E'' : Type*} [NormedAddCommGroup E''] [NormedSpace 𝕜 E''] {H'' : Type*} [TopologicalSpace H'']
+  {I'' : ModelWithCorners 𝕜 E'' H''} {M' : Type*} [TopologicalSpace M'] [ChartedSpace H'' M']
   {n : ℕ∞}
 
 section
@@ -212,11 +212,11 @@ section ProdLieGroup
 
 -- Instance of product group
 @[to_additive]
-instance {𝕜 : Type _} [NontriviallyNormedField 𝕜] {H : Type _} [TopologicalSpace H] {E : Type _}
-    [NormedAddCommGroup E] [NormedSpace 𝕜 E] {I : ModelWithCorners 𝕜 E H} {G : Type _}
-    [TopologicalSpace G] [ChartedSpace H G] [Group G] [LieGroup I G] {E' : Type _}
-    [NormedAddCommGroup E'] [NormedSpace 𝕜 E'] {H' : Type _} [TopologicalSpace H']
-    {I' : ModelWithCorners 𝕜 E' H'} {G' : Type _} [TopologicalSpace G'] [ChartedSpace H' G']
+instance {𝕜 : Type*} [NontriviallyNormedField 𝕜] {H : Type*} [TopologicalSpace H] {E : Type*}
+    [NormedAddCommGroup E] [NormedSpace 𝕜 E] {I : ModelWithCorners 𝕜 E H} {G : Type*}
+    [TopologicalSpace G] [ChartedSpace H G] [Group G] [LieGroup I G] {E' : Type*}
+    [NormedAddCommGroup E'] [NormedSpace 𝕜 E'] {H' : Type*} [TopologicalSpace H']
+    {I' : ModelWithCorners 𝕜 E' H'} {G' : Type*} [TopologicalSpace G'] [ChartedSpace H' G']
     [Group G'] [LieGroup I' G'] : LieGroup (I.prod I') (G × G') :=
   { SmoothMul.prod _ _ _ _ with smooth_inv := smooth_fst.inv.prod_mk smooth_snd.inv }
 
@@ -224,7 +224,7 @@ end ProdLieGroup
 
 /-! ### Normed spaces are Lie groups -/
 
-instance normedSpaceLieAddGroup {𝕜 : Type _} [NontriviallyNormedField 𝕜] {E : Type _}
+instance normedSpaceLieAddGroup {𝕜 : Type*} [NontriviallyNormedField 𝕜] {E : Type*}
     [NormedAddCommGroup E] [NormedSpace 𝕜 E] : LieAddGroup 𝓘(𝕜, E) E where
   smooth_neg := contDiff_neg.contMDiff
 #align normed_space_lie_add_group normedSpaceLieAddGroup
@@ -234,24 +234,24 @@ section HasSmoothInv
 -- See note [Design choices about smooth algebraic structures]
 /-- A smooth manifold with `0` and `Inv` such that `fun x ↦ x⁻¹` is smooth at all nonzero points.
 Any complete normed (semi)field has this property. -/
-class SmoothInv₀ {𝕜 : Type _} [NontriviallyNormedField 𝕜] {H : Type _} [TopologicalSpace H]
-    {E : Type _} [NormedAddCommGroup E] [NormedSpace 𝕜 E] (I : ModelWithCorners 𝕜 E H) (G : Type _)
+class SmoothInv₀ {𝕜 : Type*} [NontriviallyNormedField 𝕜] {H : Type*} [TopologicalSpace H]
+    {E : Type*} [NormedAddCommGroup E] [NormedSpace 𝕜 E] (I : ModelWithCorners 𝕜 E H) (G : Type*)
     [Inv G] [Zero G] [TopologicalSpace G] [ChartedSpace H G] : Prop where
   /-- Inversion is smooth away from `0`. -/
   smoothAt_inv₀ : ∀ ⦃x : G⦄, x ≠ 0 → SmoothAt I I (fun y ↦ y⁻¹) x
 
-instance {𝕜 : Type _} [NontriviallyNormedField 𝕜] [CompleteSpace 𝕜] : SmoothInv₀ 𝓘(𝕜) 𝕜 :=
+instance {𝕜 : Type*} [NontriviallyNormedField 𝕜] [CompleteSpace 𝕜] : SmoothInv₀ 𝓘(𝕜) 𝕜 :=
   { smoothAt_inv₀ := by
       intro x hx
       change ContMDiffAt 𝓘(𝕜) 𝓘(𝕜) ⊤ Inv.inv x
       rw [contMDiffAt_iff_contDiffAt]
       exact contDiffAt_inv 𝕜 hx }
 
-variable {𝕜 : Type _} [NontriviallyNormedField 𝕜] {H : Type _} [TopologicalSpace H] {E : Type _}
-  [NormedAddCommGroup E] [NormedSpace 𝕜 E] (I : ModelWithCorners 𝕜 E H) {G : Type _}
-  [TopologicalSpace G] [ChartedSpace H G] [Inv G] [Zero G] [SmoothInv₀ I G] {E' : Type _}
-  [NormedAddCommGroup E'] [NormedSpace 𝕜 E'] {H' : Type _} [TopologicalSpace H']
-  {I' : ModelWithCorners 𝕜 E' H'} {M : Type _} [TopologicalSpace M] [ChartedSpace H' M]
+variable {𝕜 : Type*} [NontriviallyNormedField 𝕜] {H : Type*} [TopologicalSpace H] {E : Type*}
+  [NormedAddCommGroup E] [NormedSpace 𝕜 E] (I : ModelWithCorners 𝕜 E H) {G : Type*}
+  [TopologicalSpace G] [ChartedSpace H G] [Inv G] [Zero G] [SmoothInv₀ I G] {E' : Type*}
+  [NormedAddCommGroup E'] [NormedSpace 𝕜 E'] {H' : Type*} [TopologicalSpace H']
+  {I' : ModelWithCorners 𝕜 E' H'} {M : Type*} [TopologicalSpace M] [ChartedSpace H' M]
   {n : ℕ∞} {f g : M → G}
 
 theorem smoothAt_inv₀ {x : G} (hx : x ≠ 0) : SmoothAt I I (fun y ↦ y⁻¹) x :=
@@ -303,11 +303,11 @@ end HasSmoothInv
 
 section Div
 
-variable {𝕜 : Type _} [NontriviallyNormedField 𝕜] {H : Type _} [TopologicalSpace H] {E : Type _}
-  [NormedAddCommGroup E] [NormedSpace 𝕜 E] {I : ModelWithCorners 𝕜 E H} {G : Type _}
+variable {𝕜 : Type*} [NontriviallyNormedField 𝕜] {H : Type*} [TopologicalSpace H] {E : Type*}
+  [NormedAddCommGroup E] [NormedSpace 𝕜 E] {I : ModelWithCorners 𝕜 E H} {G : Type*}
   [TopologicalSpace G] [ChartedSpace H G] [GroupWithZero G] [SmoothInv₀ I G] [SmoothMul I G]
-  {E' : Type _} [NormedAddCommGroup E'] [NormedSpace 𝕜 E'] {H' : Type _} [TopologicalSpace H']
-  {I' : ModelWithCorners 𝕜 E' H'} {M : Type _} [TopologicalSpace M] [ChartedSpace H' M]
+  {E' : Type*} [NormedAddCommGroup E'] [NormedSpace 𝕜 E'] {H' : Type*} [TopologicalSpace H']
+  {I' : ModelWithCorners 𝕜 E' H'} {M : Type*} [TopologicalSpace M] [ChartedSpace H' M]
   {f g : M → G}
 
 theorem ContMDiffWithinAt.div₀

We have currently (additive or multiplicative) Lie groups but no typeclass to express that division is smooth away from zero in fields. This PR adds such a typeclass, modelled on the one we already have in topological spaces.

@@ -48,6 +48,7 @@ the addition and negation operations are smooth. -/
 class LieAddGroup {𝕜 : Type _} [NontriviallyNormedField 𝕜] {H : Type _} [TopologicalSpace H]
     {E : Type _} [NormedAddCommGroup E] [NormedSpace 𝕜 E] (I : ModelWithCorners 𝕜 E H) (G : Type _)
     [AddGroup G] [TopologicalSpace G] [ChartedSpace H G] extends SmoothAdd I G : Prop where
+  /-- Negation is smooth in an additive Lie group. -/
   smooth_neg : Smooth I I fun a : G => -a
 #align lie_add_group LieAddGroup
 
@@ -58,6 +59,7 @@ the multiplication and inverse operations are smooth. -/
 class LieGroup {𝕜 : Type _} [NontriviallyNormedField 𝕜] {H : Type _} [TopologicalSpace H]
     {E : Type _} [NormedAddCommGroup E] [NormedSpace 𝕜 E] (I : ModelWithCorners 𝕜 E H) (G : Type _)
     [Group G] [TopologicalSpace G] [ChartedSpace H G] extends SmoothMul I G : Prop where
+  /-- Inversion is smooth in a Lie group. -/
   smooth_inv : Smooth I I fun a : G => a⁻¹
 #align lie_group LieGroup
 
@@ -226,3 +228,118 @@ instance normedSpaceLieAddGroup {𝕜 : Type _} [NontriviallyNormedField 𝕜] {
     [NormedAddCommGroup E] [NormedSpace 𝕜 E] : LieAddGroup 𝓘(𝕜, E) E where
   smooth_neg := contDiff_neg.contMDiff
 #align normed_space_lie_add_group normedSpaceLieAddGroup
+
+section HasSmoothInv
+
+-- See note [Design choices about smooth algebraic structures]
+/-- A smooth manifold with `0` and `Inv` such that `fun x ↦ x⁻¹` is smooth at all nonzero points.
+Any complete normed (semi)field has this property. -/
+class SmoothInv₀ {𝕜 : Type _} [NontriviallyNormedField 𝕜] {H : Type _} [TopologicalSpace H]
+    {E : Type _} [NormedAddCommGroup E] [NormedSpace 𝕜 E] (I : ModelWithCorners 𝕜 E H) (G : Type _)
+    [Inv G] [Zero G] [TopologicalSpace G] [ChartedSpace H G] : Prop where
+  /-- Inversion is smooth away from `0`. -/
+  smoothAt_inv₀ : ∀ ⦃x : G⦄, x ≠ 0 → SmoothAt I I (fun y ↦ y⁻¹) x
+
+instance {𝕜 : Type _} [NontriviallyNormedField 𝕜] [CompleteSpace 𝕜] : SmoothInv₀ 𝓘(𝕜) 𝕜 :=
+  { smoothAt_inv₀ := by
+      intro x hx
+      change ContMDiffAt 𝓘(𝕜) 𝓘(𝕜) ⊤ Inv.inv x
+      rw [contMDiffAt_iff_contDiffAt]
+      exact contDiffAt_inv 𝕜 hx }
+
+variable {𝕜 : Type _} [NontriviallyNormedField 𝕜] {H : Type _} [TopologicalSpace H] {E : Type _}
+  [NormedAddCommGroup E] [NormedSpace 𝕜 E] (I : ModelWithCorners 𝕜 E H) {G : Type _}
+  [TopologicalSpace G] [ChartedSpace H G] [Inv G] [Zero G] [SmoothInv₀ I G] {E' : Type _}
+  [NormedAddCommGroup E'] [NormedSpace 𝕜 E'] {H' : Type _} [TopologicalSpace H']
+  {I' : ModelWithCorners 𝕜 E' H'} {M : Type _} [TopologicalSpace M] [ChartedSpace H' M]
+  {n : ℕ∞} {f g : M → G}
+
+theorem smoothAt_inv₀ {x : G} (hx : x ≠ 0) : SmoothAt I I (fun y ↦ y⁻¹) x :=
+  SmoothInv₀.smoothAt_inv₀ hx
+
+/-- In a manifold with smooth inverse away from `0`, the inverse is continuous away from `0`.
+This is not an instance for technical reasons, see
+note [Design choices about smooth algebraic structures]. -/
+theorem hasContinuousInv₀_of_hasSmoothInv₀ : HasContinuousInv₀ G :=
+  { continuousAt_inv₀ := fun _ hx ↦ (smoothAt_inv₀ I hx).continuousAt }
+
+theorem SmoothOn_inv₀ : SmoothOn I I (Inv.inv : G → G) {0}ᶜ := fun _x hx =>
+  (smoothAt_inv₀ I hx).smoothWithinAt
+
+variable {I}
+
+theorem ContMDiffWithinAt.inv₀ (hf : ContMDiffWithinAt I' I n f s a) (ha : f a ≠ 0) :
+    ContMDiffWithinAt I' I n (fun x => (f x)⁻¹) s a :=
+  (smoothAt_inv₀ I ha).contMDiffAt.comp_contMDiffWithinAt a hf
+
+theorem ContMDiffAt.inv₀ (hf : ContMDiffAt I' I n f a) (ha : f a ≠ 0) :
+    ContMDiffAt I' I n (fun x ↦ (f x)⁻¹) a :=
+  (smoothAt_inv₀ I ha).contMDiffAt.comp a hf
+
+theorem ContMDiff.inv₀ (hf : ContMDiff I' I n f) (h0 : ∀ x, f x ≠ 0) :
+    ContMDiff I' I n (fun x ↦ (f x)⁻¹) :=
+  fun x ↦ ContMDiffAt.inv₀ (hf x) (h0 x)
+
+theorem ContMDiffOn.inv₀ (hf : ContMDiffOn I' I n f s) (h0 : ∀ x ∈ s, f x ≠ 0) :
+    ContMDiffOn I' I n (fun x => (f x)⁻¹) s :=
+  fun x hx ↦ ContMDiffWithinAt.inv₀ (hf x hx) (h0 x hx)
+
+theorem SmoothWithinAt.inv₀ (hf : SmoothWithinAt I' I f s a) (ha : f a ≠ 0) :
+    SmoothWithinAt I' I (fun x => (f x)⁻¹) s a :=
+  ContMDiffWithinAt.inv₀ hf ha
+
+theorem SmoothAt.inv₀ (hf : SmoothAt I' I f a) (ha : f a ≠ 0) :
+    SmoothAt I' I (fun x => (f x)⁻¹) a :=
+  ContMDiffAt.inv₀ hf ha
+
+theorem Smooth.inv₀ (hf : Smooth I' I f) (h0 : ∀ x, f x ≠ 0) : Smooth I' I fun x => (f x)⁻¹ :=
+  ContMDiff.inv₀ hf h0
+
+theorem SmoothOn.inv₀ (hf : SmoothOn I' I f s) (h0 : ∀ x ∈ s, f x ≠ 0) :
+    SmoothOn I' I (fun x => (f x)⁻¹) s :=
+  ContMDiffOn.inv₀ hf h0
+
+end HasSmoothInv
+
+section Div
+
+variable {𝕜 : Type _} [NontriviallyNormedField 𝕜] {H : Type _} [TopologicalSpace H] {E : Type _}
+  [NormedAddCommGroup E] [NormedSpace 𝕜 E] {I : ModelWithCorners 𝕜 E H} {G : Type _}
+  [TopologicalSpace G] [ChartedSpace H G] [GroupWithZero G] [SmoothInv₀ I G] [SmoothMul I G]
+  {E' : Type _} [NormedAddCommGroup E'] [NormedSpace 𝕜 E'] {H' : Type _} [TopologicalSpace H']
+  {I' : ModelWithCorners 𝕜 E' H'} {M : Type _} [TopologicalSpace M] [ChartedSpace H' M]
+  {f g : M → G}
+
+theorem ContMDiffWithinAt.div₀
+    (hf : ContMDiffWithinAt I' I n f s a) (hg : ContMDiffWithinAt I' I n g s a) (h₀ : g a ≠ 0) :
+    ContMDiffWithinAt I' I n (f / g) s a := by
+  simpa [div_eq_mul_inv] using hf.mul (hg.inv₀ h₀)
+
+theorem ContMDiffOn.div₀ (hf : ContMDiffOn I' I n f s) (hg : ContMDiffOn I' I n g s)
+    (h₀ : ∀ x ∈ s, g x ≠ 0) : ContMDiffOn I' I n (f / g) s := by
+  simpa [div_eq_mul_inv] using hf.mul (hg.inv₀ h₀)
+
+theorem ContMDiffAt.div₀ (hf : ContMDiffAt I' I n f a) (hg : ContMDiffAt I' I n g a)
+    (h₀ : g a ≠ 0) : ContMDiffAt I' I n (f / g) a := by
+  simpa [div_eq_mul_inv] using hf.mul (hg.inv₀ h₀)
+
+theorem ContMDiff.div₀ (hf : ContMDiff I' I n f) (hg : ContMDiff I' I n g) (h₀ : ∀ x, g x ≠ 0) :
+    ContMDiff I' I n (f / g) := by simpa only [div_eq_mul_inv] using hf.mul (hg.inv₀ h₀)
+
+theorem SmoothWithinAt.div₀ (hf : SmoothWithinAt I' I f s a)
+    (hg : SmoothWithinAt I' I g s a) (h₀ : g a ≠ 0) : SmoothWithinAt I' I (f / g) s a :=
+  ContMDiffWithinAt.div₀ hf hg h₀
+
+theorem SmoothOn.div₀ (hf : SmoothOn I' I f s) (hg : SmoothOn I' I g s) (h₀ : ∀ x ∈ s, g x ≠ 0) :
+    SmoothOn I' I (f / g) s :=
+  ContMDiffOn.div₀ hf hg h₀
+
+theorem SmoothAt.div₀ (hf : SmoothAt I' I f a) (hg : SmoothAt I' I g a) (h₀ : g a ≠ 0) :
+    SmoothAt I' I (f / g) a :=
+  ContMDiffAt.div₀ hf hg h₀
+
+theorem Smooth.div₀ (hf : Smooth I' I f) (hg : Smooth I' I g) (h₀ : ∀ x, g x ≠ 0) :
+    Smooth I' I (f / g) :=
+  ContMDiff.div₀ hf hg h₀
+
+end Div

• depends on: #5966

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

@@ -2,14 +2,11 @@
 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.lie_group
-! leanprover-community/mathlib commit f9ec187127cc5b381dfcf5f4a22dacca4c20b63d
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Geometry.Manifold.Algebra.Monoid
 
+#align_import geometry.manifold.algebra.lie_group from "leanprover-community/mathlib"@"f9ec187127cc5b381dfcf5f4a22dacca4c20b63d"
+
 /-!
 # Lie groups
 

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Jeremy Tan Jie Rui <reddeloostw@gmail.com>

@@ -50,7 +50,7 @@ open scoped Manifold
 the addition and negation operations are smooth. -/
 class LieAddGroup {𝕜 : Type _} [NontriviallyNormedField 𝕜] {H : Type _} [TopologicalSpace H]
     {E : Type _} [NormedAddCommGroup E] [NormedSpace 𝕜 E] (I : ModelWithCorners 𝕜 E H) (G : Type _)
-    [AddGroup G] [TopologicalSpace G] [ChartedSpace H G] extends HasSmoothAdd I G : Prop where
+    [AddGroup G] [TopologicalSpace G] [ChartedSpace H G] extends SmoothAdd I G : Prop where
   smooth_neg : Smooth I I fun a : G => -a
 #align lie_add_group LieAddGroup
 
@@ -60,7 +60,7 @@ the multiplication and inverse operations are smooth. -/
 @[to_additive]
 class LieGroup {𝕜 : Type _} [NontriviallyNormedField 𝕜] {H : Type _} [TopologicalSpace H]
     {E : Type _} [NormedAddCommGroup E] [NormedSpace 𝕜 E] (I : ModelWithCorners 𝕜 E H) (G : Type _)
-    [Group G] [TopologicalSpace G] [ChartedSpace H G] extends HasSmoothMul I G : Prop where
+    [Group G] [TopologicalSpace G] [ChartedSpace H G] extends SmoothMul I G : Prop where
   smooth_inv : Smooth I I fun a : G => a⁻¹
 #align lie_group LieGroup
 
@@ -219,7 +219,7 @@ instance {𝕜 : Type _} [NontriviallyNormedField 𝕜] {H : Type _} [Topologica
     [NormedAddCommGroup E'] [NormedSpace 𝕜 E'] {H' : Type _} [TopologicalSpace H']
     {I' : ModelWithCorners 𝕜 E' H'} {G' : Type _} [TopologicalSpace G'] [ChartedSpace H' G']
     [Group G'] [LieGroup I' G'] : LieGroup (I.prod I') (G × G') :=
-  { HasSmoothMul.prod _ _ _ _ with smooth_inv := smooth_fst.inv.prod_mk smooth_snd.inv }
+  { SmoothMul.prod _ _ _ _ with smooth_inv := smooth_fst.inv.prod_mk smooth_snd.inv }
 
 end ProdLieGroup