geometry.manifold.bump_function ⟷ Mathlib.Geometry.Manifold.BumpFunction

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

@@ -3,8 +3,8 @@ Copyright (c) 2021 Yury Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov
 -/
-import Analysis.Calculus.BumpFunctionFindim
-import Geometry.Manifold.ContMdiff
+import Analysis.Calculus.BumpFunction.FiniteDimension
+import Geometry.Manifold.ContMDiff.Defs
 
 #align_import geometry.manifold.bump_function from "leanprover-community/mathlib"@"30faa0c3618ce1472bf6305ae0e3fa56affa3f95"
 

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

@@ -246,7 +246,7 @@ theorem nonempty_support : (support f).Nonempty :=
 #print SmoothBumpFunction.isCompact_symm_image_closedBall /-
 theorem isCompact_symm_image_closedBall :
     IsCompact ((extChartAt I c).symm '' (closedBall (extChartAt I c c) f.rOut ∩ range I)) :=
-  ((isCompact_closedBall _ _).inter_right I.closed_range).image_of_continuousOn <|
+  ((isCompact_closedBall _ _).inter_right I.isClosed_range).image_of_continuousOn <|
     (continuousOn_extChartAt_symm _ _).mono f.closedBall_subset
 #align smooth_bump_function.is_compact_symm_image_closed_ball SmoothBumpFunction.isCompact_symm_image_closedBall
 -/

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

@@ -163,7 +163,7 @@ theorem image_eq_inter_preimage_of_subset_support {s : Set M} (hs : s ⊆ suppor
     extChartAt I c '' s =
       closedBall (extChartAt I c c) f.rOut ∩ range I ∩ (extChartAt I c).symm ⁻¹' s :=
   by
-  rw [support_eq_inter_preimage, subset_inter_iff, ← extChartAt_source I, ← image_subset_iff] at hs 
+  rw [support_eq_inter_preimage, subset_inter_iff, ← extChartAt_source I, ← image_subset_iff] at hs
   cases' hs with hse hsf
   apply subset.antisymm
   · refine' subset_inter (subset_inter (subset.trans hsf ball_subset_closed_ball) _) _
@@ -294,7 +294,7 @@ theorem exists_r_pos_lt_subset_ball {s : Set M} (hsc : IsClosed s) (hs : s ⊆ s
   by
   set e := extChartAt I c
   have : IsClosed (e '' s) := f.is_closed_image_of_is_closed hsc hs
-  rw [support_eq_inter_preimage, subset_inter_iff, ← image_subset_iff] at hs 
+  rw [support_eq_inter_preimage, subset_inter_iff, ← image_subset_iff] at hs
   rcases exists_pos_lt_subset_ball f.R_pos this hs.2 with ⟨r, hrR, hr⟩
   exact ⟨r, hrR, subset_inter hs.1 (image_subset_iff.1 hr)⟩
 #align smooth_bump_function.exists_r_pos_lt_subset_ball SmoothBumpFunction.exists_r_pos_lt_subset_ball

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

@@ -415,7 +415,7 @@ variable [SmoothManifoldWithCorners I M] {I}
 /-- A smooth bump function is infinitely smooth. -/
 protected theorem smooth : Smooth I 𝓘(ℝ) f :=
   by
-  refine' contMDiff_of_support fun x hx => _
+  refine' contMDiff_of_tsupport fun x hx => _
   have : x ∈ (chart_at H c).source := f.tsupport_subset_chart_at_source hx
   refine'
     ContMDiffAt.congr_of_eventuallyEq _
@@ -442,7 +442,7 @@ on the source of the chart at `c`, then `f • g` is smooth on the whole manifol
 theorem smooth_smul {G} [NormedAddCommGroup G] [NormedSpace ℝ G] {g : M → G}
     (hg : SmoothOn I 𝓘(ℝ, G) g (chartAt H c).source) : Smooth I 𝓘(ℝ, G) fun x => f x • g x :=
   by
-  apply contMDiff_of_support fun x hx => _
+  apply contMDiff_of_tsupport fun x hx => _
   have : x ∈ (chart_at H c).source
   calc
     x ∈ tsupport fun x => f x • g x := hx

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

@@ -278,7 +278,7 @@ theorem isClosed_image_of_isClosed {s : Set M} (hsc : IsClosed s) (hs : s ⊆ su
   by
   rw [f.image_eq_inter_preimage_of_subset_support hs]
   refine'
-    ContinuousOn.preimage_closed_of_closed
+    ContinuousOn.preimage_isClosed_of_isClosed
       ((continuousOn_extChartAt_symm _ _).mono f.closed_ball_subset) _ hsc
   exact IsClosed.inter is_closed_ball I.closed_range
 #align smooth_bump_function.is_closed_image_of_is_closed SmoothBumpFunction.isClosed_image_of_isClosed

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

@@ -3,8 +3,8 @@ Copyright (c) 2021 Yury Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov
 -/
-import Mathbin.Analysis.Calculus.BumpFunctionFindim
-import Mathbin.Geometry.Manifold.ContMdiff
+import Analysis.Calculus.BumpFunctionFindim
+import Geometry.Manifold.ContMdiff
 
 #align_import geometry.manifold.bump_function from "leanprover-community/mathlib"@"30faa0c3618ce1472bf6305ae0e3fa56affa3f95"
 
@@ -369,7 +369,7 @@ theorem tsupport_subset_chartAt_source : tsupport f ⊆ (chartAt H c).source :=
 
 #print SmoothBumpFunction.hasCompactSupport /-
 protected theorem hasCompactSupport : HasCompactSupport f :=
-  isCompact_of_isClosed_subset f.isCompact_symm_image_closedBall isClosed_closure
+  IsCompact.of_isClosed_subset f.isCompact_symm_image_closedBall isClosed_closure
     f.tsupport_subset_symm_image_closedBall
 #align smooth_bump_function.has_compact_support SmoothBumpFunction.hasCompactSupport
 -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/001ffdc42920050657fd45bd2b8bfbec8eaaeb29

@@ -261,7 +261,7 @@ theorem nhdsWithin_range_basis :
   by
   refine'
     ((nhdsWithin_hasBasis nhds_basis_closed_ball _).restrict_subset
-          (extChartAt_target_mem_nhdsWithin _ _)).to_has_basis'
+          (extChartAt_target_mem_nhdsWithin _ _)).to_hasBasis'
       _ _
   · rintro R ⟨hR0, hsub⟩
     exact ⟨⟨⟨R / 2, R, half_pos hR0, half_lt_self hR0⟩, hsub⟩, trivial, subset.rfl⟩
@@ -404,7 +404,7 @@ neighborhood of `c` and each neighborhood of `c` includes `support f` for some `
 smooth_bump_function I c` such that `tsupport f ⊆ s`. -/
 theorem nhds_basis_support {s : Set M} (hs : s ∈ 𝓝 c) :
     (𝓝 c).HasBasis (fun f : SmoothBumpFunction I c => tsupport f ⊆ s) fun f => support f :=
-  ((nhds_basis_tsupport I c).restrict_subset hs).to_has_basis'
+  ((nhds_basis_tsupport I c).restrict_subset hs).to_hasBasis'
     (fun f hf => ⟨f, hf.2, subset_closure⟩) fun f hf => f.support_mem_nhds
 #align smooth_bump_function.nhds_basis_support SmoothBumpFunction.nhds_basis_support
 -/

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

@@ -2,15 +2,12 @@
 Copyright (c) 2021 Yury Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov
-
-! This file was ported from Lean 3 source module geometry.manifold.bump_function
-! 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.Analysis.Calculus.BumpFunctionFindim
 import Mathbin.Geometry.Manifold.ContMdiff
 
+#align_import geometry.manifold.bump_function from "leanprover-community/mathlib"@"30faa0c3618ce1472bf6305ae0e3fa56affa3f95"
+
 /-!
 # Smooth bump functions on a smooth manifold
 

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: Yury Kudryashov
 
 ! This file was ported from Lean 3 source module geometry.manifold.bump_function
-! leanprover-community/mathlib commit b018406ad2f2a73223a3a9e198ccae61e6f05318
+! leanprover-community/mathlib commit 30faa0c3618ce1472bf6305ae0e3fa56affa3f95
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.Geometry.Manifold.ContMdiff
 /-!
 # Smooth bump functions on a smooth manifold
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 In this file we define `smooth_bump_function I c` to be a bundled smooth "bump" function centered at
 `c`. It is a structure that consists of two real numbers `0 < r < R` with small enough `R`. We
 define a coercion to function for this type, and for `f : smooth_bump_function I c`, the function

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

@@ -51,6 +51,7 @@ In this section we define a structure for a bundled smooth bump function and pro
 -/
 
 
+#print SmoothBumpFunction /-
 /-- Given a smooth manifold modelled on a finite dimensional space `E`,
 `f : smooth_bump_function I M` is a smooth function on `M` such that in the extended chart `e` at
 `f.c`:
@@ -66,6 +67,7 @@ namespace. -/
 structure SmoothBumpFunction (c : M) extends ContDiffBump (extChartAt I c c) where
   closedBall_subset : closedBall (extChartAt I c c) R ∩ range I ⊆ (extChartAt I c).target
 #align smooth_bump_function SmoothBumpFunction
+-/
 
 variable {M}
 
@@ -73,52 +75,71 @@ namespace SmoothBumpFunction
 
 variable {c : M} (f : SmoothBumpFunction I c) {x : M} {I}
 
+#print SmoothBumpFunction.toFun /-
 /-- The function defined by `f : smooth_bump_function c`. Use automatic coercion to function
 instead. -/
 def toFun : M → ℝ :=
   indicator (chartAt H c).source (f.toContDiffBump ∘ extChartAt I c)
 #align smooth_bump_function.to_fun SmoothBumpFunction.toFun
+-/
 
 instance : CoeFun (SmoothBumpFunction I c) fun _ => M → ℝ :=
   ⟨toFun⟩
 
+#print SmoothBumpFunction.coe_def /-
 theorem coe_def : ⇑f = indicator (chartAt H c).source (f.toContDiffBump ∘ extChartAt I c) :=
   rfl
 #align smooth_bump_function.coe_def SmoothBumpFunction.coe_def
+-/
 
+#print SmoothBumpFunction.rOut_pos /-
 theorem rOut_pos : 0 < f.rOut :=
   f.toContDiffBump.rOut_pos
 #align smooth_bump_function.R_pos SmoothBumpFunction.rOut_pos
+-/
 
+#print SmoothBumpFunction.ball_subset /-
 theorem ball_subset : ball (extChartAt I c c) f.rOut ∩ range I ⊆ (extChartAt I c).target :=
   Subset.trans (inter_subset_inter_left _ ball_subset_closedBall) f.closedBall_subset
 #align smooth_bump_function.ball_subset SmoothBumpFunction.ball_subset
+-/
 
+#print SmoothBumpFunction.eqOn_source /-
 theorem eqOn_source : EqOn f (f.toContDiffBump ∘ extChartAt I c) (chartAt H c).source :=
   eqOn_indicator
 #align smooth_bump_function.eq_on_source SmoothBumpFunction.eqOn_source
+-/
 
+#print SmoothBumpFunction.eventuallyEq_of_mem_source /-
 theorem eventuallyEq_of_mem_source (hx : x ∈ (chartAt H c).source) :
     f =ᶠ[𝓝 x] f.toContDiffBump ∘ extChartAt I c :=
   f.EqOnSource.eventuallyEq_of_mem <| IsOpen.mem_nhds (chartAt H c).open_source hx
 #align smooth_bump_function.eventually_eq_of_mem_source SmoothBumpFunction.eventuallyEq_of_mem_source
+-/
 
+#print SmoothBumpFunction.one_of_dist_le /-
 theorem one_of_dist_le (hs : x ∈ (chartAt H c).source)
     (hd : dist (extChartAt I c x) (extChartAt I c c) ≤ f.R) : f x = 1 := by
   simp only [f.eq_on_source hs, (· ∘ ·), f.to_cont_diff_bump.one_of_mem_closed_ball hd]
 #align smooth_bump_function.one_of_dist_le SmoothBumpFunction.one_of_dist_le
+-/
 
+#print SmoothBumpFunction.support_eq_inter_preimage /-
 theorem support_eq_inter_preimage :
     support f = (chartAt H c).source ∩ extChartAt I c ⁻¹' ball (extChartAt I c c) f.rOut := by
   rw [coe_def, support_indicator, (· ∘ ·), support_comp_eq_preimage, ← extChartAt_source I, ←
     (extChartAt I c).symm_image_target_inter_eq', ← (extChartAt I c).symm_image_target_inter_eq',
     f.to_cont_diff_bump.support_eq]
 #align smooth_bump_function.support_eq_inter_preimage SmoothBumpFunction.support_eq_inter_preimage
+-/
 
+#print SmoothBumpFunction.isOpen_support /-
 theorem isOpen_support : IsOpen (support f) := by rw [support_eq_inter_preimage];
   exact isOpen_extChartAt_preimage I c is_open_ball
 #align smooth_bump_function.is_open_support SmoothBumpFunction.isOpen_support
+-/
 
+#print SmoothBumpFunction.support_eq_symm_image /-
 theorem support_eq_symm_image :
     support f = (extChartAt I c).symm '' (ball (extChartAt I c c) f.rOut ∩ range I) :=
   by
@@ -129,11 +150,15 @@ theorem support_eq_symm_image :
     and_congr_right_iff.2 fun hy =>
       ⟨fun h => extChartAt_target_subset_range _ _ h, fun h => f.ball_subset ⟨hy, h⟩⟩
 #align smooth_bump_function.support_eq_symm_image SmoothBumpFunction.support_eq_symm_image
+-/
 
+#print SmoothBumpFunction.support_subset_source /-
 theorem support_subset_source : support f ⊆ (chartAt H c).source := by
   rw [f.support_eq_inter_preimage, ← extChartAt_source I]; exact inter_subset_left _ _
 #align smooth_bump_function.support_subset_source SmoothBumpFunction.support_subset_source
+-/
 
+#print SmoothBumpFunction.image_eq_inter_preimage_of_subset_support /-
 theorem image_eq_inter_preimage_of_subset_support {s : Set M} (hs : s ⊆ support f) :
     extChartAt I c '' s =
       closedBall (extChartAt I c c) f.rOut ∩ range I ∩ (extChartAt I c).symm ⁻¹' s :=
@@ -148,22 +173,30 @@ theorem image_eq_inter_preimage_of_subset_support {s : Set M} (hs : s ⊆ suppor
   · refine' subset.trans (inter_subset_inter_left _ f.closed_ball_subset) _
     rw [(extChartAt I c).image_eq_target_inter_inv_preimage hse]
 #align smooth_bump_function.image_eq_inter_preimage_of_subset_support SmoothBumpFunction.image_eq_inter_preimage_of_subset_support
+-/
 
+#print SmoothBumpFunction.mem_Icc /-
 theorem mem_Icc : f x ∈ Icc (0 : ℝ) 1 :=
   by
   have : f x = 0 ∨ f x = _ := indicator_eq_zero_or_self _ _ _
   cases this <;> rw [this]
   exacts [left_mem_Icc.2 zero_le_one, ⟨f.to_cont_diff_bump.nonneg, f.to_cont_diff_bump.le_one⟩]
 #align smooth_bump_function.mem_Icc SmoothBumpFunction.mem_Icc
+-/
 
+#print SmoothBumpFunction.nonneg /-
 theorem nonneg : 0 ≤ f x :=
   f.mem_Icc.1
 #align smooth_bump_function.nonneg SmoothBumpFunction.nonneg
+-/
 
+#print SmoothBumpFunction.le_one /-
 theorem le_one : f x ≤ 1 :=
   f.mem_Icc.2
 #align smooth_bump_function.le_one SmoothBumpFunction.le_one
+-/
 
+#print SmoothBumpFunction.eventuallyEq_one_of_dist_lt /-
 theorem eventuallyEq_one_of_dist_lt (hs : x ∈ (chartAt H c).source)
     (hd : dist (extChartAt I c x) (extChartAt I c c) < f.R) : f =ᶠ[𝓝 x] 1 :=
   by
@@ -171,38 +204,54 @@ theorem eventuallyEq_one_of_dist_lt (hs : x ∈ (chartAt H c).source)
   rintro z ⟨hzs, hzd : _ < _⟩
   exact f.one_of_dist_le hzs hzd.le
 #align smooth_bump_function.eventually_eq_one_of_dist_lt SmoothBumpFunction.eventuallyEq_one_of_dist_lt
+-/
 
+#print SmoothBumpFunction.eventuallyEq_one /-
 theorem eventuallyEq_one : f =ᶠ[𝓝 c] 1 :=
   f.eventuallyEq_one_of_dist_lt (mem_chart_source _ _) <| by rw [dist_self]; exact f.r_pos
 #align smooth_bump_function.eventually_eq_one SmoothBumpFunction.eventuallyEq_one
+-/
 
+#print SmoothBumpFunction.eq_one /-
 @[simp]
 theorem eq_one : f c = 1 :=
   f.eventuallyEq_one.eq_of_nhds
 #align smooth_bump_function.eq_one SmoothBumpFunction.eq_one
+-/
 
+#print SmoothBumpFunction.support_mem_nhds /-
 theorem support_mem_nhds : support f ∈ 𝓝 c :=
   f.eventuallyEq_one.mono fun x hx => by rw [hx]; exact one_ne_zero
 #align smooth_bump_function.support_mem_nhds SmoothBumpFunction.support_mem_nhds
+-/
 
+#print SmoothBumpFunction.tsupport_mem_nhds /-
 theorem tsupport_mem_nhds : tsupport f ∈ 𝓝 c :=
   mem_of_superset f.support_mem_nhds subset_closure
 #align smooth_bump_function.tsupport_mem_nhds SmoothBumpFunction.tsupport_mem_nhds
+-/
 
+#print SmoothBumpFunction.c_mem_support /-
 theorem c_mem_support : c ∈ support f :=
   mem_of_mem_nhds f.support_mem_nhds
 #align smooth_bump_function.c_mem_support SmoothBumpFunction.c_mem_support
+-/
 
+#print SmoothBumpFunction.nonempty_support /-
 theorem nonempty_support : (support f).Nonempty :=
   ⟨c, f.c_mem_support⟩
 #align smooth_bump_function.nonempty_support SmoothBumpFunction.nonempty_support
+-/
 
+#print SmoothBumpFunction.isCompact_symm_image_closedBall /-
 theorem isCompact_symm_image_closedBall :
     IsCompact ((extChartAt I c).symm '' (closedBall (extChartAt I c c) f.rOut ∩ range I)) :=
   ((isCompact_closedBall _ _).inter_right I.closed_range).image_of_continuousOn <|
     (continuousOn_extChartAt_symm _ _).mono f.closedBall_subset
 #align smooth_bump_function.is_compact_symm_image_closed_ball SmoothBumpFunction.isCompact_symm_image_closedBall
+-/
 
+#print SmoothBumpFunction.nhdsWithin_range_basis /-
 /-- Given a smooth bump function `f : smooth_bump_function I c`, the closed ball of radius `f.R` is
 known to include the support of `f`. These closed balls (in the model normed space `E`) intersected
 with `set.range I` form a basis of `𝓝[range I] (ext_chart_at I c c)`. -/
@@ -221,7 +270,9 @@ theorem nhdsWithin_range_basis :
       inter_mem (mem_nhdsWithin_of_mem_nhds <| closed_ball_mem_nhds _ f.rOut_pos)
         self_mem_nhdsWithin
 #align smooth_bump_function.nhds_within_range_basis SmoothBumpFunction.nhdsWithin_range_basis
+-/
 
+#print SmoothBumpFunction.isClosed_image_of_isClosed /-
 theorem isClosed_image_of_isClosed {s : Set M} (hsc : IsClosed s) (hs : s ⊆ support f) :
     IsClosed (extChartAt I c '' s) :=
   by
@@ -231,7 +282,9 @@ theorem isClosed_image_of_isClosed {s : Set M} (hsc : IsClosed s) (hs : s ⊆ su
       ((continuousOn_extChartAt_symm _ _).mono f.closed_ball_subset) _ hsc
   exact IsClosed.inter is_closed_ball I.closed_range
 #align smooth_bump_function.is_closed_image_of_is_closed SmoothBumpFunction.isClosed_image_of_isClosed
+-/
 
+#print SmoothBumpFunction.exists_r_pos_lt_subset_ball /-
 /-- If `f` is a smooth bump function and `s` closed subset of the support of `f` (i.e., of the open
 ball of radius `f.R`), then there exists `0 < r < f.R` such that `s` is a subset of the open ball of
 radius `r`. Formally, `s ⊆ e.source ∩ e ⁻¹' (ball (e c) r)`, where `e = ext_chart_at I c`. -/
@@ -245,37 +298,49 @@ theorem exists_r_pos_lt_subset_ball {s : Set M} (hsc : IsClosed s) (hs : s ⊆ s
   rcases exists_pos_lt_subset_ball f.R_pos this hs.2 with ⟨r, hrR, hr⟩
   exact ⟨r, hrR, subset_inter hs.1 (image_subset_iff.1 hr)⟩
 #align smooth_bump_function.exists_r_pos_lt_subset_ball SmoothBumpFunction.exists_r_pos_lt_subset_ball
+-/
 
+#print SmoothBumpFunction.updateRIn /-
 /-- Replace `r` with another value in the interval `(0, f.R)`. -/
-def updateR (r : ℝ) (hr : r ∈ Ioo 0 f.rOut) : SmoothBumpFunction I c :=
+def updateRIn (r : ℝ) (hr : r ∈ Ioo 0 f.rOut) : SmoothBumpFunction I c :=
   ⟨⟨r, f.rOut, hr.1, hr.2⟩, f.closedBall_subset⟩
-#align smooth_bump_function.update_r SmoothBumpFunction.updateR
+#align smooth_bump_function.update_r SmoothBumpFunction.updateRIn
+-/
 
+#print SmoothBumpFunction.updateRIn_rOut /-
 @[simp]
-theorem updateR_rOut {r : ℝ} (hr : r ∈ Ioo 0 f.rOut) : (f.updateR r hr).rOut = f.rOut :=
+theorem updateRIn_rOut {r : ℝ} (hr : r ∈ Ioo 0 f.rOut) : (f.updateRIn r hr).rOut = f.rOut :=
   rfl
-#align smooth_bump_function.update_r_R SmoothBumpFunction.updateR_rOut
+#align smooth_bump_function.update_r_R SmoothBumpFunction.updateRIn_rOut
+-/
 
+#print SmoothBumpFunction.updateRIn_rIn /-
 @[simp]
-theorem updateR_rIn {r : ℝ} (hr : r ∈ Ioo 0 f.rOut) : (f.updateR r hr).R = r :=
+theorem updateRIn_rIn {r : ℝ} (hr : r ∈ Ioo 0 f.rOut) : (f.updateRIn r hr).R = r :=
   rfl
-#align smooth_bump_function.update_r_r SmoothBumpFunction.updateR_rIn
+#align smooth_bump_function.update_r_r SmoothBumpFunction.updateRIn_rIn
+-/
 
+#print SmoothBumpFunction.support_updateRIn /-
 @[simp]
-theorem support_updateR {r : ℝ} (hr : r ∈ Ioo 0 f.rOut) : support (f.updateR r hr) = support f := by
-  simp only [support_eq_inter_preimage, update_r_R]
-#align smooth_bump_function.support_update_r SmoothBumpFunction.support_updateR
+theorem support_updateRIn {r : ℝ} (hr : r ∈ Ioo 0 f.rOut) :
+    support (f.updateRIn r hr) = support f := by simp only [support_eq_inter_preimage, update_r_R]
+#align smooth_bump_function.support_update_r SmoothBumpFunction.support_updateRIn
+-/
 
 instance : Inhabited (SmoothBumpFunction I c) :=
   Classical.inhabited_of_nonempty nhdsWithin_range_basis.Nonempty
 
 variable [T2Space M]
 
+#print SmoothBumpFunction.isClosed_symm_image_closedBall /-
 theorem isClosed_symm_image_closedBall :
     IsClosed ((extChartAt I c).symm '' (closedBall (extChartAt I c c) f.rOut ∩ range I)) :=
   f.isCompact_symm_image_closedBall.IsClosed
 #align smooth_bump_function.is_closed_symm_image_closed_ball SmoothBumpFunction.isClosed_symm_image_closedBall
+-/
 
+#print SmoothBumpFunction.tsupport_subset_symm_image_closedBall /-
 theorem tsupport_subset_symm_image_closedBall :
     tsupport f ⊆ (extChartAt I c).symm '' (closedBall (extChartAt I c c) f.rOut ∩ range I) :=
   by
@@ -284,7 +349,9 @@ theorem tsupport_subset_symm_image_closedBall :
     closure_minimal (image_subset _ <| inter_subset_inter_left _ ball_subset_closed_ball)
       f.is_closed_symm_image_closed_ball
 #align smooth_bump_function.tsupport_subset_symm_image_closed_ball SmoothBumpFunction.tsupport_subset_symm_image_closedBall
+-/
 
+#print SmoothBumpFunction.tsupport_subset_extChartAt_source /-
 theorem tsupport_subset_extChartAt_source : tsupport f ⊆ (extChartAt I c).source :=
   calc
     tsupport f ⊆ (extChartAt I c).symm '' (closedBall (extChartAt I c c) f.rOut ∩ range I) :=
@@ -292,18 +359,24 @@ theorem tsupport_subset_extChartAt_source : tsupport f ⊆ (extChartAt I c).sour
     _ ⊆ (extChartAt I c).symm '' (extChartAt I c).target := (image_subset _ f.closedBall_subset)
     _ = (extChartAt I c).source := (extChartAt I c).symm_image_target_eq_source
 #align smooth_bump_function.tsupport_subset_ext_chart_at_source SmoothBumpFunction.tsupport_subset_extChartAt_source
+-/
 
+#print SmoothBumpFunction.tsupport_subset_chartAt_source /-
 theorem tsupport_subset_chartAt_source : tsupport f ⊆ (chartAt H c).source := by
   simpa only [extChartAt_source] using f.tsupport_subset_ext_chart_at_source
 #align smooth_bump_function.tsupport_subset_chart_at_source SmoothBumpFunction.tsupport_subset_chartAt_source
+-/
 
+#print SmoothBumpFunction.hasCompactSupport /-
 protected theorem hasCompactSupport : HasCompactSupport f :=
   isCompact_of_isClosed_subset f.isCompact_symm_image_closedBall isClosed_closure
     f.tsupport_subset_symm_image_closedBall
 #align smooth_bump_function.has_compact_support SmoothBumpFunction.hasCompactSupport
+-/
 
 variable (I c)
 
+#print SmoothBumpFunction.nhds_basis_tsupport /-
 /-- The closures of supports of smooth bump functions centered at `c` form a basis of `𝓝 c`.
 In other words, each of these closures is a neighborhood of `c` and each neighborhood of `c`
 includes `tsupport f` for some `f : smooth_bump_function I c`. -/
@@ -320,9 +393,11 @@ theorem nhds_basis_tsupport :
     this.to_has_basis' (fun f hf => ⟨f, trivial, f.tsupport_subset_symm_image_closedBall⟩)
       fun f _ => f.tsupport_mem_nhds
 #align smooth_bump_function.nhds_basis_tsupport SmoothBumpFunction.nhds_basis_tsupport
+-/
 
 variable {c}
 
+#print SmoothBumpFunction.nhds_basis_support /-
 /-- Given `s ∈ 𝓝 c`, the supports of smooth bump functions `f : smooth_bump_function I c` such that
 `tsupport f ⊆ s` form a basis of `𝓝 c`.  In other words, each of these supports is a
 neighborhood of `c` and each neighborhood of `c` includes `support f` for some `f :
@@ -332,9 +407,11 @@ theorem nhds_basis_support {s : Set M} (hs : s ∈ 𝓝 c) :
   ((nhds_basis_tsupport I c).restrict_subset hs).to_has_basis'
     (fun f hf => ⟨f, hf.2, subset_closure⟩) fun f hf => f.support_mem_nhds
 #align smooth_bump_function.nhds_basis_support SmoothBumpFunction.nhds_basis_support
+-/
 
 variable [SmoothManifoldWithCorners I M] {I}
 
+#print SmoothBumpFunction.smooth /-
 /-- A smooth bump function is infinitely smooth. -/
 protected theorem smooth : Smooth I 𝓘(ℝ) f :=
   by
@@ -345,15 +422,21 @@ protected theorem smooth : Smooth I 𝓘(ℝ) f :=
       (f.eq_on_source.eventually_eq_of_mem <| IsOpen.mem_nhds (chart_at _ _).open_source this)
   exact f.to_cont_diff_bump.cont_diff_at.cont_mdiff_at.comp _ (contMDiffAt_extChartAt' this)
 #align smooth_bump_function.smooth SmoothBumpFunction.smooth
+-/
 
+#print SmoothBumpFunction.smoothAt /-
 protected theorem smoothAt {x} : SmoothAt I 𝓘(ℝ) f x :=
   f.smooth.SmoothAt
 #align smooth_bump_function.smooth_at SmoothBumpFunction.smoothAt
+-/
 
+#print SmoothBumpFunction.continuous /-
 protected theorem continuous : Continuous f :=
   f.smooth.Continuous
 #align smooth_bump_function.continuous SmoothBumpFunction.continuous
+-/
 
+#print SmoothBumpFunction.smooth_smul /-
 /-- If `f : smooth_bump_function I c` is a smooth bump function and `g : M → G` is a function smooth
 on the source of the chart at `c`, then `f • g` is smooth on the whole manifold. -/
 theorem smooth_smul {G} [NormedAddCommGroup G] [NormedSpace ℝ G] {g : M → G}
@@ -368,6 +451,7 @@ theorem smooth_smul {G} [NormedAddCommGroup G] [NormedSpace ℝ G] {g : M → G}
   exact
     f.smooth_at.smul ((hg _ this).ContMDiffAt <| IsOpen.mem_nhds (chart_at _ _).open_source this)
 #align smooth_bump_function.smooth_smul SmoothBumpFunction.smooth_smul
+-/
 
 end SmoothBumpFunction
 

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

@@ -338,12 +338,12 @@ variable [SmoothManifoldWithCorners I M] {I}
 /-- A smooth bump function is infinitely smooth. -/
 protected theorem smooth : Smooth I 𝓘(ℝ) f :=
   by
-  refine' contMdiff_of_support fun x hx => _
+  refine' contMDiff_of_support fun x hx => _
   have : x ∈ (chart_at H c).source := f.tsupport_subset_chart_at_source hx
   refine'
-    ContMdiffAt.congr_of_eventuallyEq _
+    ContMDiffAt.congr_of_eventuallyEq _
       (f.eq_on_source.eventually_eq_of_mem <| IsOpen.mem_nhds (chart_at _ _).open_source this)
-  exact f.to_cont_diff_bump.cont_diff_at.cont_mdiff_at.comp _ (contMdiffAt_ext_chart_at' this)
+  exact f.to_cont_diff_bump.cont_diff_at.cont_mdiff_at.comp _ (contMDiffAt_extChartAt' this)
 #align smooth_bump_function.smooth SmoothBumpFunction.smooth
 
 protected theorem smoothAt {x} : SmoothAt I 𝓘(ℝ) f x :=
@@ -359,14 +359,14 @@ on the source of the chart at `c`, then `f • g` is smooth on the whole manifol
 theorem smooth_smul {G} [NormedAddCommGroup G] [NormedSpace ℝ G] {g : M → G}
     (hg : SmoothOn I 𝓘(ℝ, G) g (chartAt H c).source) : Smooth I 𝓘(ℝ, G) fun x => f x • g x :=
   by
-  apply contMdiff_of_support fun x hx => _
+  apply contMDiff_of_support fun x hx => _
   have : x ∈ (chart_at H c).source
   calc
     x ∈ tsupport fun x => f x • g x := hx
     _ ⊆ tsupport f := (tsupport_smul_subset_left _ _)
     _ ⊆ (chart_at _ c).source := f.tsupport_subset_chart_at_source
   exact
-    f.smooth_at.smul ((hg _ this).ContMdiffAt <| IsOpen.mem_nhds (chart_at _ _).open_source this)
+    f.smooth_at.smul ((hg _ this).ContMDiffAt <| IsOpen.mem_nhds (chart_at _ _).open_source this)
 #align smooth_bump_function.smooth_smul SmoothBumpFunction.smooth_smul
 
 end SmoothBumpFunction

mathlib commit https://github.com/leanprover-community/mathlib/commit/7e5137f579de09a059a5ce98f364a04e221aabf0

@@ -291,7 +291,6 @@ theorem tsupport_subset_extChartAt_source : tsupport f ⊆ (extChartAt I c).sour
       f.tsupport_subset_symm_image_closedBall
     _ ⊆ (extChartAt I c).symm '' (extChartAt I c).target := (image_subset _ f.closedBall_subset)
     _ = (extChartAt I c).source := (extChartAt I c).symm_image_target_eq_source
-    
 #align smooth_bump_function.tsupport_subset_ext_chart_at_source SmoothBumpFunction.tsupport_subset_extChartAt_source
 
 theorem tsupport_subset_chartAt_source : tsupport f ⊆ (chartAt H c).source := by
@@ -366,7 +365,6 @@ theorem smooth_smul {G} [NormedAddCommGroup G] [NormedSpace ℝ G] {g : M → G}
     x ∈ tsupport fun x => f x • g x := hx
     _ ⊆ tsupport f := (tsupport_smul_subset_left _ _)
     _ ⊆ (chart_at _ c).source := f.tsupport_subset_chart_at_source
-    
   exact
     f.smooth_at.smul ((hg _ this).ContMdiffAt <| IsOpen.mem_nhds (chart_at _ _).open_source this)
 #align smooth_bump_function.smooth_smul SmoothBumpFunction.smooth_smul

mathlib commit https://github.com/leanprover-community/mathlib/commit/58a272265b5e05f258161260dd2c5d247213cbd3

@@ -86,11 +86,11 @@ theorem coe_def : ⇑f = indicator (chartAt H c).source (f.toContDiffBump ∘ ex
   rfl
 #align smooth_bump_function.coe_def SmoothBumpFunction.coe_def
 
-theorem r_pos : 0 < f.r :=
-  f.toContDiffBump.r_pos
-#align smooth_bump_function.R_pos SmoothBumpFunction.r_pos
+theorem rOut_pos : 0 < f.rOut :=
+  f.toContDiffBump.rOut_pos
+#align smooth_bump_function.R_pos SmoothBumpFunction.rOut_pos
 
-theorem ball_subset : ball (extChartAt I c c) f.r ∩ range I ⊆ (extChartAt I c).target :=
+theorem ball_subset : ball (extChartAt I c c) f.rOut ∩ range I ⊆ (extChartAt I c).target :=
   Subset.trans (inter_subset_inter_left _ ball_subset_closedBall) f.closedBall_subset
 #align smooth_bump_function.ball_subset SmoothBumpFunction.ball_subset
 
@@ -109,7 +109,7 @@ theorem one_of_dist_le (hs : x ∈ (chartAt H c).source)
 #align smooth_bump_function.one_of_dist_le SmoothBumpFunction.one_of_dist_le
 
 theorem support_eq_inter_preimage :
-    support f = (chartAt H c).source ∩ extChartAt I c ⁻¹' ball (extChartAt I c c) f.r := by
+    support f = (chartAt H c).source ∩ extChartAt I c ⁻¹' ball (extChartAt I c c) f.rOut := by
   rw [coe_def, support_indicator, (· ∘ ·), support_comp_eq_preimage, ← extChartAt_source I, ←
     (extChartAt I c).symm_image_target_inter_eq', ← (extChartAt I c).symm_image_target_inter_eq',
     f.to_cont_diff_bump.support_eq]
@@ -120,7 +120,7 @@ theorem isOpen_support : IsOpen (support f) := by rw [support_eq_inter_preimage]
 #align smooth_bump_function.is_open_support SmoothBumpFunction.isOpen_support
 
 theorem support_eq_symm_image :
-    support f = (extChartAt I c).symm '' (ball (extChartAt I c c) f.r ∩ range I) :=
+    support f = (extChartAt I c).symm '' (ball (extChartAt I c c) f.rOut ∩ range I) :=
   by
   rw [f.support_eq_inter_preimage, ← extChartAt_source I, ←
     (extChartAt I c).symm_image_target_inter_eq', inter_comm]
@@ -136,7 +136,7 @@ theorem support_subset_source : support f ⊆ (chartAt H c).source := by
 
 theorem image_eq_inter_preimage_of_subset_support {s : Set M} (hs : s ⊆ support f) :
     extChartAt I c '' s =
-      closedBall (extChartAt I c c) f.r ∩ range I ∩ (extChartAt I c).symm ⁻¹' s :=
+      closedBall (extChartAt I c c) f.rOut ∩ range I ∩ (extChartAt I c).symm ⁻¹' s :=
   by
   rw [support_eq_inter_preimage, subset_inter_iff, ← extChartAt_source I, ← image_subset_iff] at hs 
   cases' hs with hse hsf
@@ -198,7 +198,7 @@ theorem nonempty_support : (support f).Nonempty :=
 #align smooth_bump_function.nonempty_support SmoothBumpFunction.nonempty_support
 
 theorem isCompact_symm_image_closedBall :
-    IsCompact ((extChartAt I c).symm '' (closedBall (extChartAt I c c) f.r ∩ range I)) :=
+    IsCompact ((extChartAt I c).symm '' (closedBall (extChartAt I c c) f.rOut ∩ range I)) :=
   ((isCompact_closedBall _ _).inter_right I.closed_range).image_of_continuousOn <|
     (continuousOn_extChartAt_symm _ _).mono f.closedBall_subset
 #align smooth_bump_function.is_compact_symm_image_closed_ball SmoothBumpFunction.isCompact_symm_image_closedBall
@@ -208,7 +208,7 @@ known to include the support of `f`. These closed balls (in the model normed spa
 with `set.range I` form a basis of `𝓝[range I] (ext_chart_at I c c)`. -/
 theorem nhdsWithin_range_basis :
     (𝓝[range I] extChartAt I c c).HasBasis (fun f : SmoothBumpFunction I c => True) fun f =>
-      closedBall (extChartAt I c c) f.r ∩ range I :=
+      closedBall (extChartAt I c c) f.rOut ∩ range I :=
   by
   refine'
     ((nhdsWithin_hasBasis nhds_basis_closed_ball _).restrict_subset
@@ -218,7 +218,8 @@ theorem nhdsWithin_range_basis :
     exact ⟨⟨⟨R / 2, R, half_pos hR0, half_lt_self hR0⟩, hsub⟩, trivial, subset.rfl⟩
   ·
     exact fun f _ =>
-      inter_mem (mem_nhdsWithin_of_mem_nhds <| closed_ball_mem_nhds _ f.r_pos) self_mem_nhdsWithin
+      inter_mem (mem_nhdsWithin_of_mem_nhds <| closed_ball_mem_nhds _ f.rOut_pos)
+        self_mem_nhdsWithin
 #align smooth_bump_function.nhds_within_range_basis SmoothBumpFunction.nhdsWithin_range_basis
 
 theorem isClosed_image_of_isClosed {s : Set M} (hsc : IsClosed s) (hs : s ⊆ support f) :
@@ -235,7 +236,7 @@ theorem isClosed_image_of_isClosed {s : Set M} (hsc : IsClosed s) (hs : s ⊆ su
 ball of radius `f.R`), then there exists `0 < r < f.R` such that `s` is a subset of the open ball of
 radius `r`. Formally, `s ⊆ e.source ∩ e ⁻¹' (ball (e c) r)`, where `e = ext_chart_at I c`. -/
 theorem exists_r_pos_lt_subset_ball {s : Set M} (hsc : IsClosed s) (hs : s ⊆ support f) :
-    ∃ (r : _) (hr : r ∈ Ioo 0 f.r),
+    ∃ (r : _) (hr : r ∈ Ioo 0 f.rOut),
       s ⊆ (chartAt H c).source ∩ extChartAt I c ⁻¹' ball (extChartAt I c c) r :=
   by
   set e := extChartAt I c
@@ -246,24 +247,22 @@ theorem exists_r_pos_lt_subset_ball {s : Set M} (hsc : IsClosed s) (hs : s ⊆ s
 #align smooth_bump_function.exists_r_pos_lt_subset_ball SmoothBumpFunction.exists_r_pos_lt_subset_ball
 
 /-- Replace `r` with another value in the interval `(0, f.R)`. -/
-def updateR (r : ℝ) (hr : r ∈ Ioo 0 f.r) : SmoothBumpFunction I c :=
-  ⟨⟨r, f.r, hr.1, hr.2⟩, f.closedBall_subset⟩
+def updateR (r : ℝ) (hr : r ∈ Ioo 0 f.rOut) : SmoothBumpFunction I c :=
+  ⟨⟨r, f.rOut, hr.1, hr.2⟩, f.closedBall_subset⟩
 #align smooth_bump_function.update_r SmoothBumpFunction.updateR
 
 @[simp]
-theorem updateR_r {r : ℝ} (hr : r ∈ Ioo 0 f.r) : (f.updateR r hr).r = f.r :=
+theorem updateR_rOut {r : ℝ} (hr : r ∈ Ioo 0 f.rOut) : (f.updateR r hr).rOut = f.rOut :=
   rfl
-#align smooth_bump_function.update_r_R SmoothBumpFunction.updateR_r
+#align smooth_bump_function.update_r_R SmoothBumpFunction.updateR_rOut
 
-/- warning: smooth_bump_function.update_r_r clashes with smooth_bump_function.update_r_R -> SmoothBumpFunction.updateR_r
-Case conversion may be inaccurate. Consider using '#align smooth_bump_function.update_r_r SmoothBumpFunction.updateR_rₓ'. -/
 @[simp]
-theorem updateR_r {r : ℝ} (hr : r ∈ Ioo 0 f.r) : (f.updateR r hr).R = r :=
+theorem updateR_rIn {r : ℝ} (hr : r ∈ Ioo 0 f.rOut) : (f.updateR r hr).R = r :=
   rfl
-#align smooth_bump_function.update_r_r SmoothBumpFunction.updateR_r
+#align smooth_bump_function.update_r_r SmoothBumpFunction.updateR_rIn
 
 @[simp]
-theorem support_updateR {r : ℝ} (hr : r ∈ Ioo 0 f.r) : support (f.updateR r hr) = support f := by
+theorem support_updateR {r : ℝ} (hr : r ∈ Ioo 0 f.rOut) : support (f.updateR r hr) = support f := by
   simp only [support_eq_inter_preimage, update_r_R]
 #align smooth_bump_function.support_update_r SmoothBumpFunction.support_updateR
 
@@ -273,12 +272,12 @@ instance : Inhabited (SmoothBumpFunction I c) :=
 variable [T2Space M]
 
 theorem isClosed_symm_image_closedBall :
-    IsClosed ((extChartAt I c).symm '' (closedBall (extChartAt I c c) f.r ∩ range I)) :=
+    IsClosed ((extChartAt I c).symm '' (closedBall (extChartAt I c c) f.rOut ∩ range I)) :=
   f.isCompact_symm_image_closedBall.IsClosed
 #align smooth_bump_function.is_closed_symm_image_closed_ball SmoothBumpFunction.isClosed_symm_image_closedBall
 
 theorem tsupport_subset_symm_image_closedBall :
-    tsupport f ⊆ (extChartAt I c).symm '' (closedBall (extChartAt I c c) f.r ∩ range I) :=
+    tsupport f ⊆ (extChartAt I c).symm '' (closedBall (extChartAt I c c) f.rOut ∩ range I) :=
   by
   rw [tsupport, support_eq_symm_image]
   exact
@@ -288,7 +287,7 @@ theorem tsupport_subset_symm_image_closedBall :
 
 theorem tsupport_subset_extChartAt_source : tsupport f ⊆ (extChartAt I c).source :=
   calc
-    tsupport f ⊆ (extChartAt I c).symm '' (closedBall (extChartAt I c c) f.r ∩ range I) :=
+    tsupport f ⊆ (extChartAt I c).symm '' (closedBall (extChartAt I c c) f.rOut ∩ range I) :=
       f.tsupport_subset_symm_image_closedBall
     _ ⊆ (extChartAt I c).symm '' (extChartAt I c).target := (image_subset _ f.closedBall_subset)
     _ = (extChartAt I c).source := (extChartAt I c).symm_image_target_eq_source
@@ -314,7 +313,7 @@ theorem nhds_basis_tsupport :
   by
   have :
     (𝓝 c).HasBasis (fun f : SmoothBumpFunction I c => True) fun f =>
-      (extChartAt I c).symm '' (closed_ball (extChartAt I c c) f.r ∩ range I) :=
+      (extChartAt I c).symm '' (closed_ball (extChartAt I c c) f.rOut ∩ range I) :=
     by
     rw [← map_extChartAt_symm_nhdsWithin_range I c]
     exact nhds_within_range_basis.map _

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

@@ -138,7 +138,7 @@ theorem image_eq_inter_preimage_of_subset_support {s : Set M} (hs : s ⊆ suppor
     extChartAt I c '' s =
       closedBall (extChartAt I c c) f.r ∩ range I ∩ (extChartAt I c).symm ⁻¹' s :=
   by
-  rw [support_eq_inter_preimage, subset_inter_iff, ← extChartAt_source I, ← image_subset_iff] at hs
+  rw [support_eq_inter_preimage, subset_inter_iff, ← extChartAt_source I, ← image_subset_iff] at hs 
   cases' hs with hse hsf
   apply subset.antisymm
   · refine' subset_inter (subset_inter (subset.trans hsf ball_subset_closed_ball) _) _
@@ -153,7 +153,7 @@ theorem mem_Icc : f x ∈ Icc (0 : ℝ) 1 :=
   by
   have : f x = 0 ∨ f x = _ := indicator_eq_zero_or_self _ _ _
   cases this <;> rw [this]
-  exacts[left_mem_Icc.2 zero_le_one, ⟨f.to_cont_diff_bump.nonneg, f.to_cont_diff_bump.le_one⟩]
+  exacts [left_mem_Icc.2 zero_le_one, ⟨f.to_cont_diff_bump.nonneg, f.to_cont_diff_bump.le_one⟩]
 #align smooth_bump_function.mem_Icc SmoothBumpFunction.mem_Icc
 
 theorem nonneg : 0 ≤ f x :=
@@ -235,12 +235,12 @@ theorem isClosed_image_of_isClosed {s : Set M} (hsc : IsClosed s) (hs : s ⊆ su
 ball of radius `f.R`), then there exists `0 < r < f.R` such that `s` is a subset of the open ball of
 radius `r`. Formally, `s ⊆ e.source ∩ e ⁻¹' (ball (e c) r)`, where `e = ext_chart_at I c`. -/
 theorem exists_r_pos_lt_subset_ball {s : Set M} (hsc : IsClosed s) (hs : s ⊆ support f) :
-    ∃ (r : _)(hr : r ∈ Ioo 0 f.r),
+    ∃ (r : _) (hr : r ∈ Ioo 0 f.r),
       s ⊆ (chartAt H c).source ∩ extChartAt I c ⁻¹' ball (extChartAt I c c) r :=
   by
   set e := extChartAt I c
   have : IsClosed (e '' s) := f.is_closed_image_of_is_closed hsc hs
-  rw [support_eq_inter_preimage, subset_inter_iff, ← image_subset_iff] at hs
+  rw [support_eq_inter_preimage, subset_inter_iff, ← image_subset_iff] at hs 
   rcases exists_pos_lt_subset_ball f.R_pos this hs.2 with ⟨r, hrR, hr⟩
   exact ⟨r, hrR, subset_inter hs.1 (image_subset_iff.1 hr)⟩
 #align smooth_bump_function.exists_r_pos_lt_subset_ball SmoothBumpFunction.exists_r_pos_lt_subset_ball

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

@@ -40,7 +40,7 @@ variable {E : Type uE} [NormedAddCommGroup E] [NormedSpace ℝ E] [FiniteDimensi
 
 open Function Filter FiniteDimensional Set Metric
 
-open Topology Manifold Classical Filter BigOperators
+open scoped Topology Manifold Classical Filter BigOperators
 
 noncomputable section
 

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

@@ -256,8 +256,6 @@ theorem updateR_r {r : ℝ} (hr : r ∈ Ioo 0 f.r) : (f.updateR r hr).r = f.r :=
 #align smooth_bump_function.update_r_R SmoothBumpFunction.updateR_r
 
 /- warning: smooth_bump_function.update_r_r clashes with smooth_bump_function.update_r_R -> SmoothBumpFunction.updateR_r
-warning: smooth_bump_function.update_r_r -> SmoothBumpFunction.updateR_r is a dubious translation:
-<too large>
 Case conversion may be inaccurate. Consider using '#align smooth_bump_function.update_r_r SmoothBumpFunction.updateR_rₓ'. -/
 @[simp]
 theorem updateR_r {r : ℝ} (hr : r ∈ Ioo 0 f.r) : (f.updateR r hr).R = r :=

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

@@ -115,9 +115,7 @@ theorem support_eq_inter_preimage :
     f.to_cont_diff_bump.support_eq]
 #align smooth_bump_function.support_eq_inter_preimage SmoothBumpFunction.support_eq_inter_preimage
 
-theorem isOpen_support : IsOpen (support f) :=
-  by
-  rw [support_eq_inter_preimage]
+theorem isOpen_support : IsOpen (support f) := by rw [support_eq_inter_preimage];
   exact isOpen_extChartAt_preimage I c is_open_ball
 #align smooth_bump_function.is_open_support SmoothBumpFunction.isOpen_support
 
@@ -132,10 +130,8 @@ theorem support_eq_symm_image :
       ⟨fun h => extChartAt_target_subset_range _ _ h, fun h => f.ball_subset ⟨hy, h⟩⟩
 #align smooth_bump_function.support_eq_symm_image SmoothBumpFunction.support_eq_symm_image
 
-theorem support_subset_source : support f ⊆ (chartAt H c).source :=
-  by
-  rw [f.support_eq_inter_preimage, ← extChartAt_source I]
-  exact inter_subset_left _ _
+theorem support_subset_source : support f ⊆ (chartAt H c).source := by
+  rw [f.support_eq_inter_preimage, ← extChartAt_source I]; exact inter_subset_left _ _
 #align smooth_bump_function.support_subset_source SmoothBumpFunction.support_subset_source
 
 theorem image_eq_inter_preimage_of_subset_support {s : Set M} (hs : s ⊆ support f) :
@@ -146,8 +142,7 @@ theorem image_eq_inter_preimage_of_subset_support {s : Set M} (hs : s ⊆ suppor
   cases' hs with hse hsf
   apply subset.antisymm
   · refine' subset_inter (subset_inter (subset.trans hsf ball_subset_closed_ball) _) _
-    · rintro _ ⟨x, -, rfl⟩
-      exact mem_range_self _
+    · rintro _ ⟨x, -, rfl⟩; exact mem_range_self _
     · rw [(extChartAt I c).image_eq_target_inter_inv_preimage hse]
       exact inter_subset_right _ _
   · refine' subset.trans (inter_subset_inter_left _ f.closed_ball_subset) _
@@ -178,10 +173,7 @@ theorem eventuallyEq_one_of_dist_lt (hs : x ∈ (chartAt H c).source)
 #align smooth_bump_function.eventually_eq_one_of_dist_lt SmoothBumpFunction.eventuallyEq_one_of_dist_lt
 
 theorem eventuallyEq_one : f =ᶠ[𝓝 c] 1 :=
-  f.eventuallyEq_one_of_dist_lt (mem_chart_source _ _) <|
-    by
-    rw [dist_self]
-    exact f.r_pos
+  f.eventuallyEq_one_of_dist_lt (mem_chart_source _ _) <| by rw [dist_self]; exact f.r_pos
 #align smooth_bump_function.eventually_eq_one SmoothBumpFunction.eventuallyEq_one
 
 @[simp]
@@ -190,9 +182,7 @@ theorem eq_one : f c = 1 :=
 #align smooth_bump_function.eq_one SmoothBumpFunction.eq_one
 
 theorem support_mem_nhds : support f ∈ 𝓝 c :=
-  f.eventuallyEq_one.mono fun x hx => by
-    rw [hx]
-    exact one_ne_zero
+  f.eventuallyEq_one.mono fun x hx => by rw [hx]; exact one_ne_zero
 #align smooth_bump_function.support_mem_nhds SmoothBumpFunction.support_mem_nhds
 
 theorem tsupport_mem_nhds : tsupport f ∈ 𝓝 c :=

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

@@ -267,10 +267,7 @@ theorem updateR_r {r : ℝ} (hr : r ∈ Ioo 0 f.r) : (f.updateR r hr).r = f.r :=
 
 /- warning: smooth_bump_function.update_r_r clashes with smooth_bump_function.update_r_R -> SmoothBumpFunction.updateR_r
 warning: smooth_bump_function.update_r_r -> SmoothBumpFunction.updateR_r is a dubious translation:
-lean 3 declaration is
-  forall {E : Type.{u1}} [_inst_1 : NormedAddCommGroup.{u1} E] [_inst_2 : NormedSpace.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)] [_inst_3 : FiniteDimensional.{0, u1} Real E Real.divisionRing (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2)] {H : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} H] {I : ModelWithCorners.{0, u1, u2} Real (DenselyNormedField.toNontriviallyNormedField.{0} Real Real.denselyNormedField) E _inst_1 _inst_2 H _inst_4} {M : Type.{u3}} [_inst_5 : TopologicalSpace.{u3} M] [_inst_6 : ChartedSpace.{u2, u3} H _inst_4 M _inst_5] [_inst_7 : SmoothManifoldWithCorners.{0, u1, u2, u3} Real (DenselyNormedField.toNontriviallyNormedField.{0} Real Real.denselyNormedField) E _inst_1 _inst_2 H _inst_4 I M _inst_5 _inst_6] {c : M} (f : SmoothBumpFunction.{u1, u2, u3} E _inst_1 _inst_2 _inst_3 H _inst_4 I M _inst_5 _inst_6 _inst_7 c) {r : Real} (hr : Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) r (Set.Ioo.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (ContDiffBump.r.{u1} E (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (LocalEquiv.{u3, u1} M E) (fun (_x : LocalEquiv.{u3, u1} M E) => M -> E) (LocalEquiv.hasCoeToFun.{u3, u1} M E) (extChartAt.{0, u1, u3, u2} Real E M H (DenselyNormedField.toNontriviallyNormedField.{0} Real Real.denselyNormedField) _inst_1 _inst_2 _inst_4 _inst_5 I _inst_6 c) c) (SmoothBumpFunction.toContDiffBump.{u1, u2, u3} E _inst_1 _inst_2 _inst_3 H _inst_4 I M _inst_5 _inst_6 _inst_7 c f)))), Eq.{1} Real (ContDiffBump.r.{u1} E (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (LocalEquiv.{u3, u1} M E) (fun (_x : LocalEquiv.{u3, u1} M E) => M -> E) (LocalEquiv.hasCoeToFun.{u3, u1} M E) (extChartAt.{0, u1, u3, u2} Real E M H (DenselyNormedField.toNontriviallyNormedField.{0} Real Real.denselyNormedField) _inst_1 _inst_2 _inst_4 _inst_5 I _inst_6 c) c) (SmoothBumpFunction.toContDiffBump.{u1, u2, u3} E _inst_1 _inst_2 _inst_3 H _inst_4 I M _inst_5 _inst_6 _inst_7 c (SmoothBumpFunction.updateR.{u1, u2, u3} E _inst_1 _inst_2 _inst_3 H _inst_4 I M _inst_5 _inst_6 _inst_7 c f r hr))) r
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+<too large>
 Case conversion may be inaccurate. Consider using '#align smooth_bump_function.update_r_r SmoothBumpFunction.updateR_rₓ'. -/
 @[simp]
 theorem updateR_r {r : ℝ} (hr : r ∈ Ioo 0 f.r) : (f.updateR r hr).R = r :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/2af0836443b4cfb5feda0df0051acdb398304931

@@ -266,13 +266,16 @@ theorem updateR_r {r : ℝ} (hr : r ∈ Ioo 0 f.r) : (f.updateR r hr).r = f.r :=
 #align smooth_bump_function.update_r_R SmoothBumpFunction.updateR_r
 
 /- warning: smooth_bump_function.update_r_r clashes with smooth_bump_function.update_r_R -> SmoothBumpFunction.updateR_r
+warning: smooth_bump_function.update_r_r -> SmoothBumpFunction.updateR_r is a dubious translation:
+lean 3 declaration is
+  forall {E : Type.{u1}} [_inst_1 : NormedAddCommGroup.{u1} E] [_inst_2 : NormedSpace.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)] [_inst_3 : FiniteDimensional.{0, u1} Real E Real.divisionRing (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2)] {H : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} H] {I : ModelWithCorners.{0, u1, u2} Real (DenselyNormedField.toNontriviallyNormedField.{0} Real Real.denselyNormedField) E _inst_1 _inst_2 H _inst_4} {M : Type.{u3}} [_inst_5 : TopologicalSpace.{u3} M] [_inst_6 : ChartedSpace.{u2, u3} H _inst_4 M _inst_5] [_inst_7 : SmoothManifoldWithCorners.{0, u1, u2, u3} Real (DenselyNormedField.toNontriviallyNormedField.{0} Real Real.denselyNormedField) E _inst_1 _inst_2 H _inst_4 I M _inst_5 _inst_6] {c : M} (f : SmoothBumpFunction.{u1, u2, u3} E _inst_1 _inst_2 _inst_3 H _inst_4 I M _inst_5 _inst_6 _inst_7 c) {r : Real} (hr : Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) r (Set.Ioo.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (ContDiffBump.r.{u1} E (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (LocalEquiv.{u3, u1} M E) (fun (_x : LocalEquiv.{u3, u1} M E) => M -> E) (LocalEquiv.hasCoeToFun.{u3, u1} M E) (extChartAt.{0, u1, u3, u2} Real E M H (DenselyNormedField.toNontriviallyNormedField.{0} Real Real.denselyNormedField) _inst_1 _inst_2 _inst_4 _inst_5 I _inst_6 c) c) (SmoothBumpFunction.toContDiffBump.{u1, u2, u3} E _inst_1 _inst_2 _inst_3 H _inst_4 I M _inst_5 _inst_6 _inst_7 c f)))), Eq.{1} Real (ContDiffBump.r.{u1} E (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (LocalEquiv.{u3, u1} M E) (fun (_x : LocalEquiv.{u3, u1} M E) => M -> E) (LocalEquiv.hasCoeToFun.{u3, u1} M E) (extChartAt.{0, u1, u3, u2} Real E M H (DenselyNormedField.toNontriviallyNormedField.{0} Real Real.denselyNormedField) _inst_1 _inst_2 _inst_4 _inst_5 I _inst_6 c) c) (SmoothBumpFunction.toContDiffBump.{u1, u2, u3} E _inst_1 _inst_2 _inst_3 H _inst_4 I M _inst_5 _inst_6 _inst_7 c (SmoothBumpFunction.updateR.{u1, u2, u3} E _inst_1 _inst_2 _inst_3 H _inst_4 I M _inst_5 _inst_6 _inst_7 c f r hr))) r
+but is expected to have type
+  forall {E : Type.{u1}} [_inst_1 : NormedAddCommGroup.{u1} E] [_inst_2 : NormedSpace.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1)] [_inst_3 : FiniteDimensional.{0, u1} Real E Real.divisionRing (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_1) (NormedSpace.toModule.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_1) _inst_2)] {H : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} H] {I : ModelWithCorners.{0, u1, u2} Real (DenselyNormedField.toNontriviallyNormedField.{0} Real Real.denselyNormedField) E _inst_1 _inst_2 H _inst_4} {M : Type.{u3}} [_inst_5 : TopologicalSpace.{u3} M] [_inst_6 : ChartedSpace.{u2, u3} H _inst_4 M _inst_5] [_inst_7 : SmoothManifoldWithCorners.{0, u1, u2, u3} Real (DenselyNormedField.toNontriviallyNormedField.{0} Real Real.denselyNormedField) E _inst_1 _inst_2 H _inst_4 I M _inst_5 _inst_6] {c : M} (f : SmoothBumpFunction.{u1, u2, u3} E _inst_1 _inst_2 _inst_3 H _inst_4 I M _inst_5 _inst_6 _inst_7 c) {r : Real} (hr : Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) r (Set.Ioo.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (ContDiffBump.r.{u1} E (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (LocalEquiv.{u3, u1} M E) (fun (_x : LocalEquiv.{u3, u1} M E) => M -> E) (LocalEquiv.hasCoeToFun.{u3, u1} M E) (extChartAt.{0, u1, u3, u2} Real E M H (DenselyNormedField.toNontriviallyNormedField.{0} Real Real.denselyNormedField) _inst_1 _inst_2 _inst_4 _inst_5 I _inst_6 c) c) (SmoothBumpFunction.toContDiffBump.{u1, u2, u3} E _inst_1 _inst_2 _inst_3 H _inst_4 I M _inst_5 _inst_6 _inst_7 c f)))), Eq.{1} Real (ContDiffBump.r.{u1} E (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (LocalEquiv.{u3, u1} M E) (fun (_x : LocalEquiv.{u3, u1} M E) => M -> E) (LocalEquiv.hasCoeToFun.{u3, u1} M E) (extChartAt.{0, u1, u3, u2} Real E M H (DenselyNormedField.toNontriviallyNormedField.{0} Real Real.denselyNormedField) _inst_1 _inst_2 _inst_4 _inst_5 I _inst_6 c) c) (SmoothBumpFunction.toContDiffBump.{u1, u2, u3} E _inst_1 _inst_2 _inst_3 H _inst_4 I M _inst_5 _inst_6 _inst_7 c (SmoothBumpFunction.updateR.{u1, u2, u3} E _inst_1 _inst_2 _inst_3 H _inst_4 I M _inst_5 _inst_6 _inst_7 c f r hr))) (ContDiffBump.r.{u1} E (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (LocalEquiv.{u3, u1} M E) (fun (_x : LocalEquiv.{u3, u1} M E) => M -> E) (LocalEquiv.hasCoeToFun.{u3, u1} M E) (extChartAt.{0, u1, u3, u2} Real E M H (DenselyNormedField.toNontriviallyNormedField.{0} Real Real.denselyNormedField) _inst_1 _inst_2 _inst_4 _inst_5 I _inst_6 c) c) (SmoothBumpFunction.toContDiffBump.{u1, u2, u3} E _inst_1 _inst_2 _inst_3 H _inst_4 I M _inst_5 _inst_6 _inst_7 c f))
 Case conversion may be inaccurate. Consider using '#align smooth_bump_function.update_r_r SmoothBumpFunction.updateR_rₓ'. -/
-#print SmoothBumpFunction.updateR_r /-
 @[simp]
 theorem updateR_r {r : ℝ} (hr : r ∈ Ioo 0 f.r) : (f.updateR r hr).R = r :=
   rfl
 #align smooth_bump_function.update_r_r SmoothBumpFunction.updateR_r
--/
 
 @[simp]
 theorem support_updateR {r : ℝ} (hr : r ∈ Ioo 0 f.r) : support (f.updateR r hr) = support f := by

mathlib commit https://github.com/leanprover-community/mathlib/commit/4c586d291f189eecb9d00581aeb3dd998ac34442

@@ -302,7 +302,7 @@ theorem tsupport_subset_extChartAt_source : tsupport f ⊆ (extChartAt I c).sour
   calc
     tsupport f ⊆ (extChartAt I c).symm '' (closedBall (extChartAt I c c) f.r ∩ range I) :=
       f.tsupport_subset_symm_image_closedBall
-    _ ⊆ (extChartAt I c).symm '' (extChartAt I c).target := image_subset _ f.closedBall_subset
+    _ ⊆ (extChartAt I c).symm '' (extChartAt I c).target := (image_subset _ f.closedBall_subset)
     _ = (extChartAt I c).source := (extChartAt I c).symm_image_target_eq_source
     
 #align smooth_bump_function.tsupport_subset_ext_chart_at_source SmoothBumpFunction.tsupport_subset_extChartAt_source
@@ -377,7 +377,7 @@ theorem smooth_smul {G} [NormedAddCommGroup G] [NormedSpace ℝ G] {g : M → G}
   have : x ∈ (chart_at H c).source
   calc
     x ∈ tsupport fun x => f x • g x := hx
-    _ ⊆ tsupport f := tsupport_smul_subset_left _ _
+    _ ⊆ tsupport f := (tsupport_smul_subset_left _ _)
     _ ⊆ (chart_at _ c).source := f.tsupport_subset_chart_at_source
     
   exact

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

Co-authored-by: Moritz Firsching <firsching@google.com>

@@ -269,7 +269,7 @@ theorem tsupport_subset_extChartAt_source : tsupport f ⊆ (extChartAt I c).sour
   calc
     tsupport f ⊆ (extChartAt I c).symm '' (closedBall (extChartAt I c c) f.rOut ∩ range I) :=
       f.tsupport_subset_symm_image_closedBall
-    _ ⊆ (extChartAt I c).symm '' (extChartAt I c).target := (image_subset _ f.closedBall_subset)
+    _ ⊆ (extChartAt I c).symm '' (extChartAt I c).target := image_subset _ f.closedBall_subset
     _ = (extChartAt I c).source := (extChartAt I c).symm_image_target_eq_source
 #align smooth_bump_function.tsupport_subset_ext_chart_at_source SmoothBumpFunction.tsupport_subset_extChartAt_source
 
@@ -338,7 +338,7 @@ theorem smooth_smul {G} [NormedAddCommGroup G] [NormedSpace ℝ G] {g : M → G}
   -- Porting note: was a more readable `calc`
   -- calc
   --   x ∈ tsupport fun x => f x • g x := hx
-  --   _ ⊆ tsupport f := (tsupport_smul_subset_left _ _)
+  --   _ ⊆ tsupport f := tsupport_smul_subset_left _ _
   --   _ ⊆ (chart_at _ c).source := f.tsupport_subset_chartAt_source
     f.tsupport_subset_chartAt_source <| tsupport_smul_subset_left _ _ hx
   exact f.smoothAt.smul ((hg _ this).contMDiffAt <| (chartAt _ _).open_source.mem_nhds this)

All these lemmas refer to the range of some function being open/range (i.e. isOpen or isClosed).

@@ -194,7 +194,7 @@ theorem nonempty_support : (support f).Nonempty :=
 
 theorem isCompact_symm_image_closedBall :
     IsCompact ((extChartAt I c).symm '' (closedBall (extChartAt I c c) f.rOut ∩ range I)) :=
-  ((isCompact_closedBall _ _).inter_right I.closed_range).image_of_continuousOn <|
+  ((isCompact_closedBall _ _).inter_right I.isClosed_range).image_of_continuousOn <|
     (continuousOn_extChartAt_symm _ _).mono f.closedBall_subset
 #align smooth_bump_function.is_compact_symm_image_closed_ball SmoothBumpFunction.isCompact_symm_image_closedBall
 
@@ -217,7 +217,7 @@ theorem isClosed_image_of_isClosed {s : Set M} (hsc : IsClosed s) (hs : s ⊆ su
   rw [f.image_eq_inter_preimage_of_subset_support hs]
   refine' ContinuousOn.preimage_isClosed_of_isClosed
     ((continuousOn_extChartAt_symm _ _).mono f.closedBall_subset) _ hsc
-  exact IsClosed.inter isClosed_ball I.closed_range
+  exact IsClosed.inter isClosed_ball I.isClosed_range
 #align smooth_bump_function.is_closed_image_of_is_closed SmoothBumpFunction.isClosed_image_of_isClosed
 
 /-- If `f` is a smooth bump function and `s` closed subset of the support of `f` (i.e., of the open

Homogenises porting notes via capitalisation and addition of whitespace.

It makes the following changes:

• converts "--porting note" into "-- Porting note";
• converts "porting note" into "Porting note".

@@ -248,7 +248,7 @@ theorem support_updateRIn {r : ℝ} (hr : r ∈ Ioo 0 f.rOut) :
   simp only [support_eq_inter_preimage, updateRIn_rOut]
 #align smooth_bump_function.support_update_r SmoothBumpFunction.support_updateRIn
 
--- porting note: was an `Inhabited` instance
+-- Porting note: was an `Inhabited` instance
 instance : Nonempty (SmoothBumpFunction I c) := nhdsWithin_range_basis.nonempty
 
 variable [T2Space M]
@@ -335,7 +335,7 @@ theorem smooth_smul {G} [NormedAddCommGroup G] [NormedSpace ℝ G] {g : M → G}
     (hg : SmoothOn I 𝓘(ℝ, G) g (chartAt H c).source) : Smooth I 𝓘(ℝ, G) fun x => f x • g x := by
   refine contMDiff_of_tsupport fun x hx => ?_
   have : x ∈ (chartAt H c).source :=
-  -- porting note: was a more readable `calc`
+  -- Porting note: was a more readable `calc`
   -- calc
   --   x ∈ tsupport fun x => f x • g x := hx
   --   _ ⊆ tsupport f := (tsupport_smul_subset_left _ _)

No changes to tactic file, it's just boring fixes throughout the library.

This follows on from #6964.

Co-authored-by: sgouezel <sebastien.gouezel@univ-rennes1.fr> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

@@ -334,13 +334,13 @@ on the source of the chart at `c`, then `f • g` is smooth on the whole manifol
 theorem smooth_smul {G} [NormedAddCommGroup G] [NormedSpace ℝ G] {g : M → G}
     (hg : SmoothOn I 𝓘(ℝ, G) g (chartAt H c).source) : Smooth I 𝓘(ℝ, G) fun x => f x • g x := by
   refine contMDiff_of_tsupport fun x hx => ?_
-  have : x ∈ (chartAt H c).source
+  have : x ∈ (chartAt H c).source :=
   -- porting note: was a more readable `calc`
   -- calc
   --   x ∈ tsupport fun x => f x • g x := hx
   --   _ ⊆ tsupport f := (tsupport_smul_subset_left _ _)
   --   _ ⊆ (chart_at _ c).source := f.tsupport_subset_chartAt_source
-  · exact f.tsupport_subset_chartAt_source <| tsupport_smul_subset_left _ _ hx
+    f.tsupport_subset_chartAt_source <| tsupport_smul_subset_left _ _ hx
   exact f.smoothAt.smul ((hg _ this).contMDiffAt <| (chartAt _ _).open_source.mem_nhds this)
 #align smooth_bump_function.smooth_smul SmoothBumpFunction.smooth_smul
 

• multiplicativise contMDiff_of_support, contMDiffWithinAt_of_not_mem and contMDiffAt_of_not_mem and use to_additive
• golf extend_one with the multiplicative version
• generalise these lemmas to manifolds with zero/one
• slight clean-up: remove unused variables and opens
• slight drive-by golfing of one proof
• deprecate eventuallyEq_zero_nhds in favor of not_mem_tsupport_iff_eventuallyEq

Addresses the post-merge review comments in #9669.

Co-authored-by: ADedecker <anatolededecker@gmail.com> Co-authored-by: grunweg <grunweg@posteo.de>

@@ -314,7 +314,7 @@ variable [SmoothManifoldWithCorners I M] {I}
 
 /-- A smooth bump function is infinitely smooth. -/
 protected theorem smooth : Smooth I 𝓘(ℝ) f := by
-  refine' contMDiff_of_support fun x hx => _
+  refine contMDiff_of_tsupport fun x hx => ?_
   have : x ∈ (chartAt H c).source := f.tsupport_subset_chartAt_source hx
   refine ContMDiffAt.congr_of_eventuallyEq ?_ <| f.eqOn_source.eventuallyEq_of_mem <|
     (chartAt H c).open_source.mem_nhds this
@@ -333,7 +333,7 @@ protected theorem continuous : Continuous f :=
 on the source of the chart at `c`, then `f • g` is smooth on the whole manifold. -/
 theorem smooth_smul {G} [NormedAddCommGroup G] [NormedSpace ℝ G] {g : M → G}
     (hg : SmoothOn I 𝓘(ℝ, G) g (chartAt H c).source) : Smooth I 𝓘(ℝ, G) fun x => f x • g x := by
-  refine contMDiff_of_support fun x hx => ?_
+  refine contMDiff_of_tsupport fun x hx => ?_
   have : x ∈ (chartAt H c).source
   -- porting note: was a more readable `calc`
   -- calc

While at it, switch from refine' to refine (easy cases only) in the lines I'm touching anyway.

@@ -101,7 +101,7 @@ theorem eqOn_source : EqOn f (f.toContDiffBump ∘ extChartAt I c) (chartAt H c)
 
 theorem eventuallyEq_of_mem_source (hx : x ∈ (chartAt H c).source) :
     f =ᶠ[𝓝 x] f.toContDiffBump ∘ extChartAt I c :=
-  f.eqOn_source.eventuallyEq_of_mem <| IsOpen.mem_nhds (chartAt H c).open_source hx
+  f.eqOn_source.eventuallyEq_of_mem <| (chartAt H c).open_source.mem_nhds hx
 #align smooth_bump_function.eventually_eq_of_mem_source SmoothBumpFunction.eventuallyEq_of_mem_source
 
 theorem one_of_dist_le (hs : x ∈ (chartAt H c).source)
@@ -316,8 +316,8 @@ variable [SmoothManifoldWithCorners I M] {I}
 protected theorem smooth : Smooth I 𝓘(ℝ) f := by
   refine' contMDiff_of_support fun x hx => _
   have : x ∈ (chartAt H c).source := f.tsupport_subset_chartAt_source hx
-  refine' ContMDiffAt.congr_of_eventuallyEq _ <| f.eqOn_source.eventuallyEq_of_mem <|
-    IsOpen.mem_nhds (chartAt H c).open_source this
+  refine ContMDiffAt.congr_of_eventuallyEq ?_ <| f.eqOn_source.eventuallyEq_of_mem <|
+    (chartAt H c).open_source.mem_nhds this
   exact f.contDiffAt.contMDiffAt.comp _ (contMDiffAt_extChartAt' this)
 #align smooth_bump_function.smooth SmoothBumpFunction.smooth
 
@@ -341,7 +341,7 @@ theorem smooth_smul {G} [NormedAddCommGroup G] [NormedSpace ℝ G] {g : M → G}
   --   _ ⊆ tsupport f := (tsupport_smul_subset_left _ _)
   --   _ ⊆ (chart_at _ c).source := f.tsupport_subset_chartAt_source
   · exact f.tsupport_subset_chartAt_source <| tsupport_smul_subset_left _ _ hx
-  exact f.smoothAt.smul ((hg _ this).contMDiffAt <| IsOpen.mem_nhds (chartAt _ _).open_source this)
+  exact f.smoothAt.smul ((hg _ this).contMDiffAt <| (chartAt _ _).open_source.mem_nhds this)
 #align smooth_bump_function.smooth_smul SmoothBumpFunction.smooth_smul
 
 end SmoothBumpFunction

At about 2200 lines, this is currently the longest file in the Geometry/Manifolds.

(It also moves the slowly compiling proof of ContMDiffWithinAt.cle_arrowCongr out of a common recompilation path.)

@@ -4,7 +4,8 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov
 -/
 import Mathlib.Analysis.Calculus.BumpFunction.FiniteDimension
-import Mathlib.Geometry.Manifold.ContMDiff
+import Mathlib.Geometry.Manifold.ContMDiff.Atlas
+import Mathlib.Geometry.Manifold.ContMDiff.NormedSpace
 
 #align_import geometry.manifold.bump_function from "leanprover-community/mathlib"@"b018406ad2f2a73223a3a9e198ccae61e6f05318"
 

This PR renames the field Clopens.clopen' -> Clopens.isClopen', and the lemmas

• preimage_closed_of_closed -> ContinuousOn.preimage_isClosed_of_isClosed

as well as: ClopenUpperSet.clopen -> ClopenUpperSet.isClopen connectedComponent_eq_iInter_clopen -> connectedComponent_eq_iInter_isClopen connectedComponent_subset_iInter_clopen -> connectedComponent_subset_iInter_isClopen continuous_boolIndicator_iff_clopen -> continuous_boolIndicator_iff_isClopen continuousOn_boolIndicator_iff_clopen -> continuousOn_boolIndicator_iff_isClopen DiscreteQuotient.ofClopen -> DiscreteQuotient.ofIsClopen disjoint_or_subset_of_clopen -> disjoint_or_subset_of_isClopen exists_clopen_{lower,upper}of_not_le -> exists_isClopen{lower,upper}_of_not_le exists_clopen_of_cofiltered -> exists_isClopen_of_cofiltered exists_clopen_of_totally_separated -> exists_isClopen_of_totally_separated exists_clopen_upper_or_lower_of_ne -> exists_isClopen_upper_or_lower_of_ne IsPreconnected.subset_clopen -> IsPreconnected.subset_isClopen isTotallyDisconnected_of_clopen_set -> isTotallyDisconnected_of_isClopen_set LocallyConstant.ofClopen_fiber_one -> LocallyConstant.ofIsClopen_fiber_one LocallyConstant.ofClopen_fiber_zero -> LocallyConstant.ofIsClopen_fiber_zero LocallyConstant.ofClopen -> LocallyConstant.ofIsClopen preimage_clopen_of_clopen -> preimage_isClopen_of_isClopen TopologicalSpace.Clopens.clopen -> TopologicalSpace.Clopens.isClopen

@@ -214,7 +214,7 @@ theorem nhdsWithin_range_basis :
 theorem isClosed_image_of_isClosed {s : Set M} (hsc : IsClosed s) (hs : s ⊆ support f) :
     IsClosed (extChartAt I c '' s) := by
   rw [f.image_eq_inter_preimage_of_subset_support hs]
-  refine' ContinuousOn.preimage_closed_of_closed
+  refine' ContinuousOn.preimage_isClosed_of_isClosed
     ((continuousOn_extChartAt_symm _ _).mono f.closedBall_subset) _ hsc
   exact IsClosed.inter isClosed_ball I.closed_range
 #align smooth_bump_function.is_closed_image_of_is_closed SmoothBumpFunction.isClosed_image_of_isClosed

As discussed on Zulip.

Co-authored-by: grunweg <grunweg@posteo.de>

@@ -277,7 +277,7 @@ theorem tsupport_subset_chartAt_source : tsupport f ⊆ (chartAt H c).source :=
 #align smooth_bump_function.tsupport_subset_chart_at_source SmoothBumpFunction.tsupport_subset_chartAt_source
 
 protected theorem hasCompactSupport : HasCompactSupport f :=
-  isCompact_of_isClosed_subset f.isCompact_symm_image_closedBall isClosed_closure
+  f.isCompact_symm_image_closedBall.of_isClosed_subset isClosed_closure
     f.tsupport_subset_symm_image_closedBall
 #align smooth_bump_function.has_compact_support SmoothBumpFunction.hasCompactSupport
 

@@ -204,7 +204,7 @@ theorem nhdsWithin_range_basis :
     (𝓝[range I] extChartAt I c c).HasBasis (fun _ : SmoothBumpFunction I c => True) fun f =>
       closedBall (extChartAt I c c) f.rOut ∩ range I := by
   refine' ((nhdsWithin_hasBasis nhds_basis_closedBall _).restrict_subset
-    (extChartAt_target_mem_nhdsWithin _ _)).to_has_basis' _ _
+    (extChartAt_target_mem_nhdsWithin _ _)).to_hasBasis' _ _
   · rintro R ⟨hR0, hsub⟩
     exact ⟨⟨⟨R / 2, R, half_pos hR0, half_lt_self hR0⟩, hsub⟩, trivial, Subset.rfl⟩
   · exact fun f _ => inter_mem (mem_nhdsWithin_of_mem_nhds <| closedBall_mem_nhds _ f.rOut_pos)
@@ -293,7 +293,7 @@ theorem nhds_basis_tsupport :
       (extChartAt I c).symm '' (closedBall (extChartAt I c c) f.rOut ∩ range I) := by
     rw [← map_extChartAt_symm_nhdsWithin_range I c]
     exact nhdsWithin_range_basis.map _
-  refine' this.to_has_basis' (fun f _ => ⟨f, trivial, f.tsupport_subset_symm_image_closedBall⟩)
+  refine' this.to_hasBasis' (fun f _ => ⟨f, trivial, f.tsupport_subset_symm_image_closedBall⟩)
     fun f _ => f.tsupport_mem_nhds
 #align smooth_bump_function.nhds_basis_tsupport SmoothBumpFunction.nhds_basis_tsupport
 
@@ -305,7 +305,7 @@ neighborhood of `c` and each neighborhood of `c` includes `support f` for some
 `f : SmoothBumpFunction I c` such that `tsupport f ⊆ s`. -/
 theorem nhds_basis_support {s : Set M} (hs : s ∈ 𝓝 c) :
     (𝓝 c).HasBasis (fun f : SmoothBumpFunction I c => tsupport f ⊆ s) fun f => support f :=
-  ((nhds_basis_tsupport I c).restrict_subset hs).to_has_basis'
+  ((nhds_basis_tsupport I c).restrict_subset hs).to_hasBasis'
     (fun f hf => ⟨f, hf.2, subset_closure⟩) fun f _ => f.support_mem_nhds
 #align smooth_bump_function.nhds_basis_support SmoothBumpFunction.nhds_basis_support
 

• 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 (c) 2021 Yury Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov
-
-! This file was ported from Lean 3 source module geometry.manifold.bump_function
-! leanprover-community/mathlib commit b018406ad2f2a73223a3a9e198ccae61e6f05318
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Analysis.Calculus.BumpFunction.FiniteDimension
 import Mathlib.Geometry.Manifold.ContMDiff
 
+#align_import geometry.manifold.bump_function from "leanprover-community/mathlib"@"b018406ad2f2a73223a3a9e198ccae61e6f05318"
+
 /-!
 # Smooth bump functions on a smooth manifold
 

Fixes #4755

@@ -8,7 +8,7 @@ Authors: Yury Kudryashov
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
-import Mathlib.Analysis.Calculus.BumpFunctionFindim
+import Mathlib.Analysis.Calculus.BumpFunction.FiniteDimension
 import Mathlib.Geometry.Manifold.ContMDiff
 
 /-!

@@ -15,12 +15,12 @@ import Mathlib.Geometry.Manifold.ContMDiff
 # Smooth bump functions on a smooth manifold
 
 In this file we define `SmoothBumpFunction I c` to be a bundled smooth "bump" function centered at
-`c`. It is a structure that consists of two real numbers `0 < r < R` with small enough `R`. We
-define a coercion to function for this type, and for `f : SmoothBumpFunction I c`, the function
+`c`. It is a structure that consists of two real numbers `0 < rIn < rOut` with small enough `rOut`.
+We define a coercion to function for this type, and for `f : SmoothBumpFunction I c`, the function
 `⇑f` written in the extended chart at `c` has the following properties:
 
-* `f x = 1` in the closed ball of radius `f.r` centered at `c`;
-* `f x = 0` outside of the ball of radius `f.R` centered at `c`;
+* `f x = 1` in the closed ball of radius `f.rIn` centered at `c`;
+* `f x = 0` outside of the ball of radius `f.rOut` centered at `c`;
 * `0 ≤ f x ≤ 1` for all `x`.
 
 The actual statements involve (pre)images under `extChartAt I f` and are given as lemmas in the
@@ -53,8 +53,8 @@ In this section we define a structure for a bundled smooth bump function and pro
 `f : SmoothBumpFunction I M` is a smooth function on `M` such that in the extended chart `e` at
 `f.c`:
 
-* `f x = 1` in the closed ball of radius `f.r` centered at `f.c`;
-* `f x = 0` outside of the ball of radius `f.R` centered at `f.c`;
+* `f x = 1` in the closed ball of radius `f.rIn` centered at `f.c`;
+* `f x = 0` outside of the ball of radius `f.rOut` centered at `f.c`;
 * `0 ≤ f x ≤ 1` for all `x`.
 
 The structure contains data required to construct a function with these properties. The function is
@@ -137,7 +137,7 @@ theorem support_subset_source : support f ⊆ (chartAt H c).source := by
 theorem image_eq_inter_preimage_of_subset_support {s : Set M} (hs : s ⊆ support f) :
     extChartAt I c '' s =
       closedBall (extChartAt I c c) f.rOut ∩ range I ∩ (extChartAt I c).symm ⁻¹' s := by
-  rw [support_eq_inter_preimage, subset_inter_iff, ← extChartAt_source I, ← image_subset_iff] at hs 
+  rw [support_eq_inter_preimage, subset_inter_iff, ← extChartAt_source I, ← image_subset_iff] at hs
   cases' hs with hse hsf
   apply Subset.antisymm
   · refine' subset_inter (subset_inter (hsf.trans ball_subset_closedBall) _) _
@@ -223,14 +223,14 @@ theorem isClosed_image_of_isClosed {s : Set M} (hsc : IsClosed s) (hs : s ⊆ su
 #align smooth_bump_function.is_closed_image_of_is_closed SmoothBumpFunction.isClosed_image_of_isClosed
 
 /-- If `f` is a smooth bump function and `s` closed subset of the support of `f` (i.e., of the open
-ball of radius `f.R`), then there exists `0 < r < f.R` such that `s` is a subset of the open ball of
-radius `r`. Formally, `s ⊆ e.source ∩ e ⁻¹' (ball (e c) r)`, where `e = extChartAt I c`. -/
+ball of radius `f.rOut`), then there exists `0 < r < f.rOut` such that `s` is a subset of the open
+ball of radius `r`. Formally, `s ⊆ e.source ∩ e ⁻¹' (ball (e c) r)`, where `e = extChartAt I c`. -/
 theorem exists_r_pos_lt_subset_ball {s : Set M} (hsc : IsClosed s) (hs : s ⊆ support f) :
     ∃ r ∈ Ioo 0 f.rOut,
       s ⊆ (chartAt H c).source ∩ extChartAt I c ⁻¹' ball (extChartAt I c c) r := by
   set e := extChartAt I c
   have : IsClosed (e '' s) := f.isClosed_image_of_isClosed hsc hs
-  rw [support_eq_inter_preimage, subset_inter_iff, ← image_subset_iff] at hs 
+  rw [support_eq_inter_preimage, subset_inter_iff, ← image_subset_iff] at hs
   rcases exists_pos_lt_subset_ball f.rOut_pos this hs.2 with ⟨r, hrR, hr⟩
   exact ⟨r, hrR, subset_inter hs.1 (image_subset_iff.1 hr)⟩
 #align smooth_bump_function.exists_r_pos_lt_subset_ball SmoothBumpFunction.exists_r_pos_lt_subset_ball
@@ -304,8 +304,8 @@ variable {c}
 
 /-- Given `s ∈ 𝓝 c`, the supports of smooth bump functions `f : SmoothBumpFunction I c` such that
 `tsupport f ⊆ s` form a basis of `𝓝 c`.  In other words, each of these supports is a
-neighborhood of `c` and each neighborhood of `c` includes `support f` for some `f :
-SmoothBumpFunction I c` such that `tsupport f ⊆ s`. -/
+neighborhood of `c` and each neighborhood of `c` includes `support f` for some
+`f : SmoothBumpFunction I c` such that `tsupport f ⊆ s`. -/
 theorem nhds_basis_support {s : Set M} (hs : s ∈ 𝓝 c) :
     (𝓝 c).HasBasis (fun f : SmoothBumpFunction I c => tsupport f ⊆ s) fun f => support f :=
   ((nhds_basis_tsupport I c).restrict_subset hs).to_has_basis'
@@ -347,4 +347,3 @@ theorem smooth_smul {G} [NormedAddCommGroup G] [NormedSpace ℝ G] {g : M → G}
 #align smooth_bump_function.smooth_smul SmoothBumpFunction.smooth_smul
 
 end SmoothBumpFunction
-