analysis.calculus.bump_function_findim ⟷ Mathlib.Analysis.Calculus.BumpFunction.FiniteDimension

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

@@ -3,7 +3,7 @@ Copyright (c) 2022 Sébastien Gouëzel. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel
 -/
-import Analysis.Calculus.Series
+import Analysis.NormedSpace.FunctionSeries
 import Analysis.Convolution
 import Analysis.InnerProductSpace.EuclideanDist
 import MeasureTheory.Measure.Haar.NormedSpace

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

@@ -59,7 +59,7 @@ theorem exists_smooth_tsupport_subset {s : Set E} {x : E} (hs : s ∈ 𝓝 x) :
     intro y hy
     have : toEuclidean y ∈ Function.support c := by
       simpa only [f, Function.mem_support, Function.comp_apply, Ne.def] using hy
-    rwa [c.support_eq] at this 
+    rwa [c.support_eq] at this
   have f_tsupp : tsupport f ⊆ Euclidean.closedBall x d :=
     by
     rw [tsupport, ← Euclidean.closure_ball _ d_pos.ne']
@@ -118,8 +118,8 @@ theorem IsOpen.exists_smooth_support_eq {s : Set E} (hs : IsOpen s) :
     by
     apply countable.exists_eq_range T_count
     rcases eq_empty_or_nonempty T with (rfl | hT)
-    · simp only [Union_false, Union_empty] at hT 
-      simp only [← hT, not_nonempty_empty] at h's 
+    · simp only [Union_false, Union_empty] at hT
+      simp only [← hT, not_nonempty_empty] at h's
       exact h's.elim
     · exact hT
   let g : ℕ → E → ℝ := fun n => (g0 n).1
@@ -127,12 +127,12 @@ theorem IsOpen.exists_smooth_support_eq {s : Set E} (hs : IsOpen s) :
   have s_g : ∀ x ∈ s, ∃ n, x ∈ support (g n) :=
     by
     intro x hx
-    rw [← hT] at hx 
+    rw [← hT] at hx
     obtain ⟨i, iT, hi⟩ : ∃ (i : ι) (hi : i ∈ T), x ∈ support (i : E → ℝ) := by
       simpa only [mem_Union] using hx
-    rw [hg, mem_range] at iT 
+    rw [hg, mem_range] at iT
     rcases iT with ⟨n, hn⟩
-    rw [← hn] at hi 
+    rw [← hn] at hi
     exact ⟨n, hi⟩
   have g_smooth : ∀ n, ContDiff ℝ ⊤ (g n) := fun n => (g0 n).2.2.2.1
   have g_comp_supp : ∀ n, HasCompactSupport (g n) := fun n => (g0 n).2.2.1
@@ -183,7 +183,7 @@ theorem IsOpen.exists_smooth_support_eq {s : Set E} (hs : IsOpen s) :
   refine' ⟨fun x => ∑' n, (r n • g n) x, _, _, _⟩
   · apply subset.antisymm
     · intro x hx
-      simp only [Pi.smul_apply, Algebra.id.smul_eq_mul, mem_support, Ne.def] at hx 
+      simp only [Pi.smul_apply, Algebra.id.smul_eq_mul, mem_support, Ne.def] at hx
       contrapose! hx
       have : ∀ n, g n x = 0 := by
         intro n
@@ -252,14 +252,14 @@ theorem u_exists :
     · apply ne_of_gt
       have : 0 < f x := by
         apply lt_of_le_of_ne (B x).1 (Ne.symm _)
-        rwa [← f_support] at hx 
+        rwa [← f_support] at hx
       linarith [(B (-x)).1]
     · have I1 : x ∉ support f := by rwa [f_support]
       have I2 : -x ∉ support f := by
         rw [f_support]
-        simp only at hx 
+        simp only at hx
         simpa using hx
-      simp only [mem_support, Classical.not_not] at I1 I2 
+      simp only [mem_support, Classical.not_not] at I1 I2
       simp only [I1, I2, add_zero, zero_div]
   · intro x; simp only [add_comm, neg_neg]
 #align exists_cont_diff_bump_base.u_exists ExistsContDiffBumpBase.u_exists
@@ -435,7 +435,7 @@ theorem y_eq_one_of_mem_closedBall {D : ℝ} {x : E} (Dpos : 0 < D)
     by
     have C : ball x D ⊆ ball 0 1 := by
       apply ball_subset_ball'
-      simp only [mem_closed_ball] at hx 
+      simp only [mem_closed_ball] at hx
       linarith only [hx]
     intro y hy
     simp only [φ, indicator, mem_closed_ball, ite_eq_left_iff, not_le, zero_ne_one]
@@ -460,7 +460,7 @@ theorem y_eq_zero_of_not_mem_ball {D : ℝ} {x : E} (Dpos : 0 < D) (hx : x ∉ b
     have C : ball y D ⊆ ball 0 (1 + D) :=
       by
       apply ball_subset_ball'
-      rw [← dist_zero_right] at h'y 
+      rw [← dist_zero_right] at h'y
       linarith only [h'y]
     exact hx (C (mem_ball_comm.1 hy))
   have Bx : φ x = 0 := B _ (mem_ball_self Dpos)
@@ -499,7 +499,7 @@ theorem y_le_one {D : ℝ} (x : E) (Dpos : 0 < D) : y D x ≤ 1 :=
 theorem y_pos_of_mem_ball {D : ℝ} {x : E} (Dpos : 0 < D) (D_lt_one : D < 1)
     (hx : x ∈ ball (0 : E) (1 + D)) : 0 < y D x :=
   by
-  simp only [mem_ball_zero_iff] at hx 
+  simp only [mem_ball_zero_iff] at hx
   refine' (integral_pos_iff_support_of_nonneg (W_mul_φ_nonneg D x) _).2 _
   · have F_comp : HasCompactSupport (W D) := W_compact_support E Dpos
     have B : locally_integrable (φ : E → ℝ) μ :=
@@ -537,7 +537,7 @@ theorem y_pos_of_mem_ball {D : ℝ} {x : E} (Dpos : 0 < D) (D_lt_one : D < 1)
         apply closed_ball_subset_closed_ball' _ (ball_subset_closed_ball hy)
         rw [← one_smul ℝ x, dist_eq_norm, hz, ← sub_smul, one_smul, norm_smul, ID]
         simp only [-one_div, -mul_eq_zero, B.ne', div_le_iff B, field_simps]
-        simp only [mem_ball_zero_iff] at hx 
+        simp only [mem_ball_zero_iff] at hx
         nlinarith only [hx, D_lt_one]
     apply lt_of_lt_of_le _ (measure_mono C)
     apply measure_ball_pos
@@ -560,7 +560,7 @@ theorem y_smooth : ContDiffOn ℝ ⊤ (uncurry y) (Ioo (0 : ℝ) 1 ×ˢ (univ :
     contrapose! hx
     have : p⁻¹ • x ∈ support u := mem_support.2 hx
     simp only [u_support, norm_smul, mem_ball_zero_iff, Real.norm_eq_abs, abs_inv,
-      abs_of_nonneg hp.1.le, ← div_eq_inv_mul, div_lt_one hp.1] at this 
+      abs_of_nonneg hp.1.le, ← div_eq_inv_mul, div_lt_one hp.1] at this
     rw [mem_closedBall_zero_iff]
     exact this.le.trans hp.2.le
   · exact (locally_integrable_const _).indicator measurableSet_closedBall

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

@@ -177,7 +177,7 @@ theorem IsOpen.exists_smooth_support_eq {s : Set E} (hs : IsOpen s) :
   have S : ∀ x, Summable fun n => (r n • g n) x :=
     by
     intro x
-    refine' summable_of_nnnorm_bounded _ δc.summable fun n => _
+    refine' Summable.of_nnnorm_bounded _ δc.summable fun n => _
     rw [← NNReal.coe_le_coe, coe_nnnorm]
     simpa only [norm_iteratedFDeriv_zero] using hr n 0 (zero_le n) x
   refine' ⟨fun x => ∑' n, (r n • g n) x, _, _, _⟩

mathlib commit https://github.com/leanprover-community/mathlib/commit/b1abe23ae96fef89ad30d9f4362c307f72a55010

@@ -516,7 +516,8 @@ theorem y_pos_of_mem_ball {D : ℝ} {x : E} (Dpos : 0 < D) (D_lt_one : D < 1)
       intro y hy
       simp only [support_mul, W_support E Dpos]
       simp only [φ, mem_inter_iff, mem_support, Ne.def, indicator_apply_eq_zero,
-        mem_closedBall_zero_iff, one_ne_zero, not_forall, not_false_iff, exists_prop, and_true_iff]
+        mem_closedBall_zero_iff, one_ne_zero, Classical.not_forall, not_false_iff, exists_prop,
+        and_true_iff]
       constructor
       · apply ball_subset_ball' _ hy
         simp only [z, norm_smul, abs_of_nonneg Dpos.le, abs_of_nonneg B.le, dist_zero_right,

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

@@ -3,11 +3,11 @@ Copyright (c) 2022 Sébastien Gouëzel. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel
 -/
-import Mathbin.Analysis.Calculus.Series
-import Mathbin.Analysis.Convolution
-import Mathbin.Analysis.InnerProductSpace.EuclideanDist
-import Mathbin.MeasureTheory.Measure.Haar.NormedSpace
-import Mathbin.Data.Set.Pointwise.Support
+import Analysis.Calculus.Series
+import Analysis.Convolution
+import Analysis.InnerProductSpace.EuclideanDist
+import MeasureTheory.Measure.Haar.NormedSpace
+import Data.Set.Pointwise.Support
 
 #align_import analysis.calculus.bump_function_findim from "leanprover-community/mathlib"@"fdc286cc6967a012f41b87f76dcd2797b53152af"
 

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

@@ -2,11 +2,6 @@
 Copyright (c) 2022 Sébastien Gouëzel. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel
-
-! This file was ported from Lean 3 source module analysis.calculus.bump_function_findim
-! leanprover-community/mathlib commit fdc286cc6967a012f41b87f76dcd2797b53152af
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Analysis.Calculus.Series
 import Mathbin.Analysis.Convolution
@@ -14,6 +9,8 @@ import Mathbin.Analysis.InnerProductSpace.EuclideanDist
 import Mathbin.MeasureTheory.Measure.Haar.NormedSpace
 import Mathbin.Data.Set.Pointwise.Support
 
+#align_import analysis.calculus.bump_function_findim from "leanprover-community/mathlib"@"fdc286cc6967a012f41b87f76dcd2797b53152af"
+
 /-!
 # Bump functions in finite-dimensional vector spaces
 

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel
 
 ! This file was ported from Lean 3 source module analysis.calculus.bump_function_findim
-! leanprover-community/mathlib commit fd5edc43dc4f10b85abfe544b88f82cf13c5f844
+! leanprover-community/mathlib commit fdc286cc6967a012f41b87f76dcd2797b53152af
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -17,6 +17,9 @@ import Mathbin.Data.Set.Pointwise.Support
 /-!
 # Bump functions in finite-dimensional vector spaces
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 Let `E` be a finite-dimensional real normed vector space. We show that any open set `s` in `E` is
 exactly the support of a smooth function taking values in `[0, 1]`,
 in `is_open.exists_smooth_support_eq`.

mathlib commit https://github.com/leanprover-community/mathlib/commit/d30d31261cdb4d2f5e612eabc3c4bf45556350d5

@@ -39,6 +39,7 @@ section
 
 variable [NormedSpace ℝ E] [FiniteDimensional ℝ E]
 
+#print exists_smooth_tsupport_subset /-
 /-- If a set `s` is a neighborhood of `x`, then there exists a smooth function `f` taking
 values in `[0, 1]`, supported in `s` and with `f x = 1`. -/
 theorem exists_smooth_tsupport_subset {s : Set E} {x : E} (hs : s ∈ 𝓝 x) :
@@ -77,7 +78,9 @@ theorem exists_smooth_tsupport_subset {s : Set E} {x : E} (hs : s ∈ 𝓝 x) :
     apply mem_closed_ball_self
     exact (half_pos d_pos).le
 #align exists_smooth_tsupport_subset exists_smooth_tsupport_subset
+-/
 
+#print IsOpen.exists_smooth_support_eq /-
 /-- Given an open set `s` in a finite-dimensional real normed vector space, there exists a smooth
 function with values in `[0, 1]` whose support is exactly `s`. -/
 theorem IsOpen.exists_smooth_support_eq {s : Set E} (hs : IsOpen s) :
@@ -207,6 +210,7 @@ theorem IsOpen.exists_smooth_support_eq {s : Set E} (hs : IsOpen s) :
     apply (le_abs_self _).trans
     simpa only [norm_iteratedFDeriv_zero] using hr n 0 (zero_le n) y
 #align is_open.exists_smooth_support_eq IsOpen.exists_smooth_support_eq
+-/
 
 end
 
@@ -214,11 +218,13 @@ section
 
 namespace ExistsContDiffBumpBase
 
+#print ExistsContDiffBumpBase.φ /-
 /-- An auxiliary function to construct partitions of unity on finite-dimensional real vector spaces.
 It is the characteristic function of the closed unit ball. -/
 def φ : E → ℝ :=
   (closedBall (0 : E) 1).indicator fun y => (1 : ℝ)
 #align exists_cont_diff_bump_base.φ ExistsContDiffBumpBase.φ
+-/
 
 variable [NormedSpace ℝ E] [FiniteDimensional ℝ E]
 
@@ -226,6 +232,7 @@ section HelperDefinitions
 
 variable (E)
 
+#print ExistsContDiffBumpBase.u_exists /-
 theorem u_exists :
     ∃ u : E → ℝ,
       ContDiff ℝ ⊤ u ∧ (∀ x, u x ∈ Icc (0 : ℝ) 1) ∧ support u = ball 0 1 ∧ ∀ x, u (-x) = u x :=
@@ -256,48 +263,65 @@ theorem u_exists :
       simp only [I1, I2, add_zero, zero_div]
   · intro x; simp only [add_comm, neg_neg]
 #align exists_cont_diff_bump_base.u_exists ExistsContDiffBumpBase.u_exists
+-/
 
 variable {E}
 
+#print ExistsContDiffBumpBase.u /-
 /-- An auxiliary function to construct partitions of unity on finite-dimensional real vector spaces,
 which is smooth, symmetric, and with support equal to the unit ball. -/
 def u (x : E) : ℝ :=
   Classical.choose (u_exists E) x
 #align exists_cont_diff_bump_base.u ExistsContDiffBumpBase.u
+-/
 
 variable (E)
 
+#print ExistsContDiffBumpBase.u_smooth /-
 theorem u_smooth : ContDiff ℝ ⊤ (u : E → ℝ) :=
   (Classical.choose_spec (u_exists E)).1
 #align exists_cont_diff_bump_base.u_smooth ExistsContDiffBumpBase.u_smooth
+-/
 
+#print ExistsContDiffBumpBase.u_continuous /-
 theorem u_continuous : Continuous (u : E → ℝ) :=
   (u_smooth E).Continuous
 #align exists_cont_diff_bump_base.u_continuous ExistsContDiffBumpBase.u_continuous
+-/
 
+#print ExistsContDiffBumpBase.u_support /-
 theorem u_support : support (u : E → ℝ) = ball 0 1 :=
   (Classical.choose_spec (u_exists E)).2.2.1
 #align exists_cont_diff_bump_base.u_support ExistsContDiffBumpBase.u_support
+-/
 
+#print ExistsContDiffBumpBase.u_compact_support /-
 theorem u_compact_support : HasCompactSupport (u : E → ℝ) :=
   by
   rw [hasCompactSupport_def, u_support, closure_ball (0 : E) one_ne_zero]
   exact is_compact_closed_ball _ _
 #align exists_cont_diff_bump_base.u_compact_support ExistsContDiffBumpBase.u_compact_support
+-/
 
 variable {E}
 
+#print ExistsContDiffBumpBase.u_nonneg /-
 theorem u_nonneg (x : E) : 0 ≤ u x :=
   ((Classical.choose_spec (u_exists E)).2.1 x).1
 #align exists_cont_diff_bump_base.u_nonneg ExistsContDiffBumpBase.u_nonneg
+-/
 
+#print ExistsContDiffBumpBase.u_le_one /-
 theorem u_le_one (x : E) : u x ≤ 1 :=
   ((Classical.choose_spec (u_exists E)).2.1 x).2
 #align exists_cont_diff_bump_base.u_le_one ExistsContDiffBumpBase.u_le_one
+-/
 
+#print ExistsContDiffBumpBase.u_neg /-
 theorem u_neg (x : E) : u (-x) = u x :=
   (Classical.choose_spec (u_exists E)).2.2.2 x
 #align exists_cont_diff_bump_base.u_neg ExistsContDiffBumpBase.u_neg
+-/
 
 variable [MeasurableSpace E] [BorelSpace E]
 
@@ -305,26 +329,33 @@ local notation "μ" => MeasureTheory.Measure.addHaar
 
 variable (E)
 
+#print ExistsContDiffBumpBase.u_int_pos /-
 theorem u_int_pos : 0 < ∫ x : E, u x ∂μ :=
   by
   refine' (integral_pos_iff_support_of_nonneg u_nonneg _).mpr _
   · exact (u_continuous E).integrable_of_hasCompactSupport (u_compact_support E)
   · rw [u_support]; exact measure_ball_pos _ _ zero_lt_one
 #align exists_cont_diff_bump_base.u_int_pos ExistsContDiffBumpBase.u_int_pos
+-/
 
 variable {E}
 
+#print ExistsContDiffBumpBase.w /-
 /-- An auxiliary function to construct partitions of unity on finite-dimensional real vector spaces,
 which is smooth, symmetric, with support equal to the ball of radius `D` and integral `1`. -/
 def w (D : ℝ) (x : E) : ℝ :=
   ((∫ x : E, u x ∂μ) * |D| ^ finrank ℝ E)⁻¹ • u (D⁻¹ • x)
 #align exists_cont_diff_bump_base.W ExistsContDiffBumpBase.w
+-/
 
+#print ExistsContDiffBumpBase.w_def /-
 theorem w_def (D : ℝ) :
     (w D : E → ℝ) = fun x => ((∫ x : E, u x ∂μ) * |D| ^ finrank ℝ E)⁻¹ • u (D⁻¹ • x) := by ext1 x;
   rfl
 #align exists_cont_diff_bump_base.W_def ExistsContDiffBumpBase.w_def
+-/
 
+#print ExistsContDiffBumpBase.w_nonneg /-
 theorem w_nonneg (D : ℝ) (x : E) : 0 ≤ w D x :=
   by
   apply mul_nonneg _ (u_nonneg _)
@@ -332,20 +363,26 @@ theorem w_nonneg (D : ℝ) (x : E) : 0 ≤ w D x :=
   apply mul_nonneg (u_int_pos E).le
   apply pow_nonneg (abs_nonneg D)
 #align exists_cont_diff_bump_base.W_nonneg ExistsContDiffBumpBase.w_nonneg
+-/
 
+#print ExistsContDiffBumpBase.w_mul_φ_nonneg /-
 theorem w_mul_φ_nonneg (D : ℝ) (x y : E) : 0 ≤ w D y * φ (x - y) :=
   mul_nonneg (w_nonneg D y) (indicator_nonneg (by simp only [zero_le_one, imp_true_iff]) _)
 #align exists_cont_diff_bump_base.W_mul_φ_nonneg ExistsContDiffBumpBase.w_mul_φ_nonneg
+-/
 
 variable (E)
 
+#print ExistsContDiffBumpBase.w_integral /-
 theorem w_integral {D : ℝ} (Dpos : 0 < D) : ∫ x : E, w D x ∂μ = 1 :=
   by
   simp_rw [W, integral_smul]
   rw [integral_comp_inv_smul_of_nonneg μ (u : E → ℝ) Dpos.le, abs_of_nonneg Dpos.le, mul_comm]
   field_simp [Dpos.ne', (u_int_pos E).ne']
 #align exists_cont_diff_bump_base.W_integral ExistsContDiffBumpBase.w_integral
+-/
 
+#print ExistsContDiffBumpBase.w_support /-
 theorem w_support {D : ℝ} (Dpos : 0 < D) : support (w D : E → ℝ) = ball 0 D :=
   by
   have B : D • ball (0 : E) 1 = ball 0 D := by
@@ -355,15 +392,19 @@ theorem w_support {D : ℝ} (Dpos : 0 < D) : support (w D : E → ℝ) = ball 0
     support_comp_inv_smul₀ Dpos.ne', u_support, B, support_const (u_int_pos E).ne', support_const C,
     abs_of_nonneg Dpos.le]
 #align exists_cont_diff_bump_base.W_support ExistsContDiffBumpBase.w_support
+-/
 
+#print ExistsContDiffBumpBase.w_compact_support /-
 theorem w_compact_support {D : ℝ} (Dpos : 0 < D) : HasCompactSupport (w D : E → ℝ) :=
   by
   rw [hasCompactSupport_def, W_support E Dpos, closure_ball (0 : E) Dpos.ne']
   exact is_compact_closed_ball _ _
 #align exists_cont_diff_bump_base.W_compact_support ExistsContDiffBumpBase.w_compact_support
+-/
 
 variable {E}
 
+#print ExistsContDiffBumpBase.y /-
 /-- An auxiliary function to construct partitions of unity on finite-dimensional real vector spaces.
 It is the convolution between a smooth function of integral `1` supported in the ball of radius `D`,
 with the indicator function of the closed unit ball. Therefore, it is smooth, equal to `1` on the
@@ -371,7 +412,9 @@ ball of radius `1 - D`, with support equal to the ball of radius `1 + D`. -/
 def y (D : ℝ) : E → ℝ :=
   w D ⋆[lsmul ℝ ℝ, μ] φ
 #align exists_cont_diff_bump_base.Y ExistsContDiffBumpBase.y
+-/
 
+#print ExistsContDiffBumpBase.y_neg /-
 theorem y_neg (D : ℝ) (x : E) : y D (-x) = y D x :=
   by
   apply convolution_neg_of_neg_eq
@@ -381,7 +424,9 @@ theorem y_neg (D : ℝ) (x : E) : y D (-x) = y D x :=
   · apply eventually_of_forall fun x => _
     simp only [φ, indicator, mem_closedBall_zero_iff, norm_neg]
 #align exists_cont_diff_bump_base.Y_neg ExistsContDiffBumpBase.y_neg
+-/
 
+#print ExistsContDiffBumpBase.y_eq_one_of_mem_closedBall /-
 theorem y_eq_one_of_mem_closedBall {D : ℝ} {x : E} (Dpos : 0 < D)
     (hx : x ∈ closedBall (0 : E) (1 - D)) : y D x = 1 :=
   by
@@ -402,7 +447,9 @@ theorem y_eq_one_of_mem_closedBall {D : ℝ} {x : E} (Dpos : 0 < D)
   simp only [lsmul_apply, Algebra.id.smul_eq_mul, integral_mul_right, W_integral E Dpos, Bx,
     one_mul]
 #align exists_cont_diff_bump_base.Y_eq_one_of_mem_closed_ball ExistsContDiffBumpBase.y_eq_one_of_mem_closedBall
+-/
 
+#print ExistsContDiffBumpBase.y_eq_zero_of_not_mem_ball /-
 theorem y_eq_zero_of_not_mem_ball {D : ℝ} {x : E} (Dpos : 0 < D) (hx : x ∉ ball (0 : E) (1 + D)) :
     y D x = 0 := by
   change (W D ⋆[lsmul ℝ ℝ, μ] φ) x = 0
@@ -421,11 +468,15 @@ theorem y_eq_zero_of_not_mem_ball {D : ℝ} {x : E} (Dpos : 0 < D) (hx : x ∉ b
   rw [convolution_eq_right' _ (le_of_eq (W_support E Dpos)) B']
   simp only [lsmul_apply, Algebra.id.smul_eq_mul, Bx, MulZeroClass.mul_zero, integral_const]
 #align exists_cont_diff_bump_base.Y_eq_zero_of_not_mem_ball ExistsContDiffBumpBase.y_eq_zero_of_not_mem_ball
+-/
 
+#print ExistsContDiffBumpBase.y_nonneg /-
 theorem y_nonneg (D : ℝ) (x : E) : 0 ≤ y D x :=
   integral_nonneg (w_mul_φ_nonneg D x)
 #align exists_cont_diff_bump_base.Y_nonneg ExistsContDiffBumpBase.y_nonneg
+-/
 
+#print ExistsContDiffBumpBase.y_le_one /-
 theorem y_le_one {D : ℝ} (x : E) (Dpos : 0 < D) : y D x ≤ 1 :=
   by
   have A : (W D ⋆[lsmul ℝ ℝ, μ] φ) x ≤ (W D ⋆[lsmul ℝ ℝ, μ] 1) x :=
@@ -442,7 +493,9 @@ theorem y_le_one {D : ℝ} (x : E) (Dpos : 0 < D) : y D x ≤ 1 :=
       lsmul_apply, Algebra.id.smul_eq_mul, integral_mul_left, W_integral E Dpos, Pi.smul_apply]
   exact A.trans (le_of_eq B)
 #align exists_cont_diff_bump_base.Y_le_one ExistsContDiffBumpBase.y_le_one
+-/
 
+#print ExistsContDiffBumpBase.y_pos_of_mem_ball /-
 theorem y_pos_of_mem_ball {D : ℝ} {x : E} (Dpos : 0 < D) (D_lt_one : D < 1)
     (hx : x ∈ ball (0 : E) (1 + D)) : 0 < y D x :=
   by
@@ -489,10 +542,12 @@ theorem y_pos_of_mem_ball {D : ℝ} {x : E} (Dpos : 0 < D) (D_lt_one : D < 1)
     apply measure_ball_pos
     exact div_pos (mul_pos Dpos (by linarith only [hx])) B
 #align exists_cont_diff_bump_base.Y_pos_of_mem_ball ExistsContDiffBumpBase.y_pos_of_mem_ball
+-/
 
 variable (E)
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print ExistsContDiffBumpBase.y_smooth /-
 theorem y_smooth : ContDiffOn ℝ ⊤ (uncurry y) (Ioo (0 : ℝ) 1 ×ˢ (univ : Set E)) :=
   by
   have hs : IsOpen (Ioo (0 : ℝ) (1 : ℝ)) := isOpen_Ioo
@@ -520,13 +575,16 @@ theorem y_smooth : ContDiffOn ℝ ⊤ (uncurry y) (Ioo (0 : ℝ) 1 ×ˢ (univ :
     · apply (u_smooth E).comp_contDiffOn
       exact ContDiffOn.smul (cont_diff_on_fst.inv fun x hx => ne_of_gt hx.1.1) contDiffOn_snd
 #align exists_cont_diff_bump_base.Y_smooth ExistsContDiffBumpBase.y_smooth
+-/
 
+#print ExistsContDiffBumpBase.y_support /-
 theorem y_support {D : ℝ} (Dpos : 0 < D) (D_lt_one : D < 1) :
     support (y D : E → ℝ) = ball (0 : E) (1 + D) :=
   support_eq_iff.2
     ⟨fun x hx => (y_pos_of_mem_ball Dpos D_lt_one hx).ne', fun x hx =>
       y_eq_zero_of_not_mem_ball Dpos hx⟩
 #align exists_cont_diff_bump_base.Y_support ExistsContDiffBumpBase.y_support
+-/
 
 variable {E}
 

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

@@ -301,7 +301,6 @@ theorem u_neg (x : E) : u (-x) = u x :=
 
 variable [MeasurableSpace E] [BorelSpace E]
 
--- mathport name: exprμ
 local notation "μ" => MeasureTheory.Measure.addHaar
 
 variable (E)

mathlib commit https://github.com/leanprover-community/mathlib/commit/a3e83f0fa4391c8740f7d773a7a9b74e311ae2a3

@@ -340,7 +340,7 @@ theorem w_mul_φ_nonneg (D : ℝ) (x y : E) : 0 ≤ w D y * φ (x - y) :=
 
 variable (E)
 
-theorem w_integral {D : ℝ} (Dpos : 0 < D) : (∫ x : E, w D x ∂μ) = 1 :=
+theorem w_integral {D : ℝ} (Dpos : 0 < D) : ∫ x : E, w D x ∂μ = 1 :=
   by
   simp_rw [W, integral_smul]
   rw [integral_comp_inv_smul_of_nonneg μ (u : E → ℝ) Dpos.le, abs_of_nonneg Dpos.le, mul_comm]

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

@@ -170,7 +170,6 @@ theorem IsOpen.exists_smooth_support_eq {s : Set E} (hs : IsOpen s) :
         positivity
       _ ≤ M⁻¹ * δ n * M := (mul_le_mul_of_nonneg_left ((hR i x).trans (IR i hi)) (by positivity))
       _ = δ n := by field_simp [M_pos.ne']
-      
   choose r rpos hr using this
   have S : ∀ x, Summable fun n => (r n • g n) x :=
     by
@@ -589,7 +588,6 @@ instance (priority := 100) {E : Type _} [NormedAddCommGroup E] [NormedSpace ℝ
           2 / (R + 1) * ‖x‖ ≤ 2 / (R + 1) * 1 :=
             mul_le_mul_of_nonneg_left hx (div_nonneg zero_le_two A.le)
           _ = 1 - (R - 1) / (R + 1) := by field_simp [A.ne']; ring
-          
       support := fun R hR => by
         have A : 0 < (R + 1) / 2 := by linarith
         have A' : 0 < R + 1 := by linarith

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

@@ -49,9 +49,9 @@ theorem exists_smooth_tsupport_subset {s : Set E} {x : E} (hs : s ∈ 𝓝 x) :
   exact euclidean.nhds_basis_closed_ball.mem_iff.1 hs
   let c : ContDiffBump (toEuclidean x) :=
     { R := d / 2
-      r := d
-      r_pos := half_pos d_pos
-      r_lt_r := half_lt_self d_pos }
+      rOut := d
+      rIn_pos := half_pos d_pos
+      rIn_lt_rOut := half_lt_self d_pos }
   let f : E → ℝ := c ∘ toEuclidean
   have f_supp : f.support ⊆ Euclidean.ball x d :=
     by

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

@@ -28,8 +28,8 @@ the indicator function of `closed_ball 0 1` with a function as above with `s = b
 
 noncomputable section
 
-open
-  Set Metric TopologicalSpace Function Asymptotics MeasureTheory FiniteDimensional ContinuousLinearMap Filter MeasureTheory.Measure
+open Set Metric TopologicalSpace Function Asymptotics MeasureTheory FiniteDimensional
+  ContinuousLinearMap Filter MeasureTheory.Measure
 
 open scoped Pointwise Topology NNReal BigOperators convolution
 
@@ -45,7 +45,7 @@ theorem exists_smooth_tsupport_subset {s : Set E} {x : E} (hs : s ∈ 𝓝 x) :
     ∃ f : E → ℝ,
       tsupport f ⊆ s ∧ HasCompactSupport f ∧ ContDiff ℝ ⊤ f ∧ range f ⊆ Icc 0 1 ∧ f x = 1 :=
   by
-  obtain ⟨d, d_pos, hd⟩ : ∃ (d : ℝ)(hr : 0 < d), Euclidean.closedBall x d ⊆ s
+  obtain ⟨d, d_pos, hd⟩ : ∃ (d : ℝ) (hr : 0 < d), Euclidean.closedBall x d ⊆ s
   exact euclidean.nhds_basis_closed_ball.mem_iff.1 hs
   let c : ContDiffBump (toEuclidean x) :=
     { R := d / 2
@@ -58,7 +58,7 @@ theorem exists_smooth_tsupport_subset {s : Set E} {x : E} (hs : s ∈ 𝓝 x) :
     intro y hy
     have : toEuclidean y ∈ Function.support c := by
       simpa only [f, Function.mem_support, Function.comp_apply, Ne.def] using hy
-    rwa [c.support_eq] at this
+    rwa [c.support_eq] at this 
   have f_tsupp : tsupport f ⊆ Euclidean.closedBall x d :=
     by
     rw [tsupport, ← Euclidean.closure_ball _ d_pos.ne']
@@ -115,8 +115,8 @@ theorem IsOpen.exists_smooth_support_eq {s : Set E} (hs : IsOpen s) :
     by
     apply countable.exists_eq_range T_count
     rcases eq_empty_or_nonempty T with (rfl | hT)
-    · simp only [Union_false, Union_empty] at hT
-      simp only [← hT, not_nonempty_empty] at h's
+    · simp only [Union_false, Union_empty] at hT 
+      simp only [← hT, not_nonempty_empty] at h's 
       exact h's.elim
     · exact hT
   let g : ℕ → E → ℝ := fun n => (g0 n).1
@@ -124,12 +124,12 @@ theorem IsOpen.exists_smooth_support_eq {s : Set E} (hs : IsOpen s) :
   have s_g : ∀ x ∈ s, ∃ n, x ∈ support (g n) :=
     by
     intro x hx
-    rw [← hT] at hx
-    obtain ⟨i, iT, hi⟩ : ∃ (i : ι)(hi : i ∈ T), x ∈ support (i : E → ℝ) := by
+    rw [← hT] at hx 
+    obtain ⟨i, iT, hi⟩ : ∃ (i : ι) (hi : i ∈ T), x ∈ support (i : E → ℝ) := by
       simpa only [mem_Union] using hx
-    rw [hg, mem_range] at iT
+    rw [hg, mem_range] at iT 
     rcases iT with ⟨n, hn⟩
-    rw [← hn] at hi
+    rw [← hn] at hi 
     exact ⟨n, hi⟩
   have g_smooth : ∀ n, ContDiff ℝ ⊤ (g n) := fun n => (g0 n).2.2.2.1
   have g_comp_supp : ∀ n, HasCompactSupport (g n) := fun n => (g0 n).2.2.1
@@ -181,7 +181,7 @@ theorem IsOpen.exists_smooth_support_eq {s : Set E} (hs : IsOpen s) :
   refine' ⟨fun x => ∑' n, (r n • g n) x, _, _, _⟩
   · apply subset.antisymm
     · intro x hx
-      simp only [Pi.smul_apply, Algebra.id.smul_eq_mul, mem_support, Ne.def] at hx
+      simp only [Pi.smul_apply, Algebra.id.smul_eq_mul, mem_support, Ne.def] at hx 
       contrapose! hx
       have : ∀ n, g n x = 0 := by
         intro n
@@ -246,14 +246,14 @@ theorem u_exists :
     · apply ne_of_gt
       have : 0 < f x := by
         apply lt_of_le_of_ne (B x).1 (Ne.symm _)
-        rwa [← f_support] at hx
+        rwa [← f_support] at hx 
       linarith [(B (-x)).1]
     · have I1 : x ∉ support f := by rwa [f_support]
       have I2 : -x ∉ support f := by
         rw [f_support]
-        simp only at hx
+        simp only at hx 
         simpa using hx
-      simp only [mem_support, Classical.not_not] at I1 I2
+      simp only [mem_support, Classical.not_not] at I1 I2 
       simp only [I1, I2, add_zero, zero_div]
   · intro x; simp only [add_comm, neg_neg]
 #align exists_cont_diff_bump_base.u_exists ExistsContDiffBumpBase.u_exists
@@ -392,7 +392,7 @@ theorem y_eq_one_of_mem_closedBall {D : ℝ} {x : E} (Dpos : 0 < D)
     by
     have C : ball x D ⊆ ball 0 1 := by
       apply ball_subset_ball'
-      simp only [mem_closed_ball] at hx
+      simp only [mem_closed_ball] at hx 
       linarith only [hx]
     intro y hy
     simp only [φ, indicator, mem_closed_ball, ite_eq_left_iff, not_le, zero_ne_one]
@@ -415,7 +415,7 @@ theorem y_eq_zero_of_not_mem_ball {D : ℝ} {x : E} (Dpos : 0 < D) (hx : x ∉ b
     have C : ball y D ⊆ ball 0 (1 + D) :=
       by
       apply ball_subset_ball'
-      rw [← dist_zero_right] at h'y
+      rw [← dist_zero_right] at h'y 
       linarith only [h'y]
     exact hx (C (mem_ball_comm.1 hy))
   have Bx : φ x = 0 := B _ (mem_ball_self Dpos)
@@ -448,7 +448,7 @@ theorem y_le_one {D : ℝ} (x : E) (Dpos : 0 < D) : y D x ≤ 1 :=
 theorem y_pos_of_mem_ball {D : ℝ} {x : E} (Dpos : 0 < D) (D_lt_one : D < 1)
     (hx : x ∈ ball (0 : E) (1 + D)) : 0 < y D x :=
   by
-  simp only [mem_ball_zero_iff] at hx
+  simp only [mem_ball_zero_iff] at hx 
   refine' (integral_pos_iff_support_of_nonneg (W_mul_φ_nonneg D x) _).2 _
   · have F_comp : HasCompactSupport (W D) := W_compact_support E Dpos
     have B : locally_integrable (φ : E → ℝ) μ :=
@@ -485,7 +485,7 @@ theorem y_pos_of_mem_ball {D : ℝ} {x : E} (Dpos : 0 < D) (D_lt_one : D < 1)
         apply closed_ball_subset_closed_ball' _ (ball_subset_closed_ball hy)
         rw [← one_smul ℝ x, dist_eq_norm, hz, ← sub_smul, one_smul, norm_smul, ID]
         simp only [-one_div, -mul_eq_zero, B.ne', div_le_iff B, field_simps]
-        simp only [mem_ball_zero_iff] at hx
+        simp only [mem_ball_zero_iff] at hx 
         nlinarith only [hx, D_lt_one]
     apply lt_of_lt_of_le _ (measure_mono C)
     apply measure_ball_pos
@@ -506,7 +506,7 @@ theorem y_smooth : ContDiffOn ℝ ⊤ (uncurry y) (Ioo (0 : ℝ) 1 ×ˢ (univ :
     contrapose! hx
     have : p⁻¹ • x ∈ support u := mem_support.2 hx
     simp only [u_support, norm_smul, mem_ball_zero_iff, Real.norm_eq_abs, abs_inv,
-      abs_of_nonneg hp.1.le, ← div_eq_inv_mul, div_lt_one hp.1] at this
+      abs_of_nonneg hp.1.le, ← div_eq_inv_mul, div_lt_one hp.1] at this 
     rw [mem_closedBall_zero_iff]
     exact this.le.trans hp.2.le
   · exact (locally_integrable_const _).indicator measurableSet_closedBall
@@ -588,7 +588,7 @@ instance (priority := 100) {E : Type _} [NormedAddCommGroup E] [NormedSpace ℝ
         calc
           2 / (R + 1) * ‖x‖ ≤ 2 / (R + 1) * 1 :=
             mul_le_mul_of_nonneg_left hx (div_nonneg zero_le_two A.le)
-          _ = 1 - (R - 1) / (R + 1) := by field_simp [A.ne'] ; ring
+          _ = 1 - (R - 1) / (R + 1) := by field_simp [A.ne']; ring
           
       support := fun R hR => by
         have A : 0 < (R + 1) / 2 := by linarith

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

@@ -137,18 +137,18 @@ theorem IsOpen.exists_smooth_support_eq {s : Set E} (hs : IsOpen s) :
   obtain ⟨δ, δpos, c, δc, c_lt⟩ :
     ∃ δ : ℕ → ℝ≥0, (∀ i : ℕ, 0 < δ i) ∧ ∃ c : NNReal, HasSum δ c ∧ c < 1
   exact NNReal.exists_pos_sum_of_countable one_ne_zero ℕ
-  have : ∀ n : ℕ, ∃ r : ℝ, 0 < r ∧ ∀ i ≤ n, ∀ x, ‖iteratedFderiv ℝ i (r • g n) x‖ ≤ δ n :=
+  have : ∀ n : ℕ, ∃ r : ℝ, 0 < r ∧ ∀ i ≤ n, ∀ x, ‖iteratedFDeriv ℝ i (r • g n) x‖ ≤ δ n :=
     by
     intro n
-    have : ∀ i, ∃ R, ∀ x, ‖iteratedFderiv ℝ i (fun x => g n x) x‖ ≤ R :=
+    have : ∀ i, ∃ R, ∀ x, ‖iteratedFDeriv ℝ i (fun x => g n x) x‖ ≤ R :=
       by
       intro i
-      have : BddAbove (range fun x => ‖iteratedFderiv ℝ i (fun x : E => g n x) x‖) :=
+      have : BddAbove (range fun x => ‖iteratedFDeriv ℝ i (fun x : E => g n x) x‖) :=
         by
         apply
-          ((g_smooth n).continuous_iteratedFderiv le_top).norm.bddAbove_range_of_hasCompactSupport
+          ((g_smooth n).continuous_iteratedFDeriv le_top).norm.bddAbove_range_of_hasCompactSupport
         apply HasCompactSupport.comp_left _ norm_zero
-        apply (g_comp_supp n).iteratedFderiv
+        apply (g_comp_supp n).iteratedFDeriv
       rcases this with ⟨R, hR⟩
       exact ⟨R, fun x => hR (mem_range_self _)⟩
     choose R hR using this
@@ -164,9 +164,9 @@ theorem IsOpen.exists_smooth_support_eq {s : Set E} (hs : IsOpen s) :
       linarith
     refine' ⟨M⁻¹ * δ n, by positivity, fun i hi x => _⟩
     calc
-      ‖iteratedFderiv ℝ i ((M⁻¹ * δ n) • g n) x‖ = ‖(M⁻¹ * δ n) • iteratedFderiv ℝ i (g n) x‖ := by
-        rw [iteratedFderiv_const_smul_apply]; exact (g_smooth n).of_le le_top
-      _ = M⁻¹ * δ n * ‖iteratedFderiv ℝ i (g n) x‖ := by rw [norm_smul, Real.norm_of_nonneg];
+      ‖iteratedFDeriv ℝ i ((M⁻¹ * δ n) • g n) x‖ = ‖(M⁻¹ * δ n) • iteratedFDeriv ℝ i (g n) x‖ := by
+        rw [iteratedFDeriv_const_smul_apply]; exact (g_smooth n).of_le le_top
+      _ = M⁻¹ * δ n * ‖iteratedFDeriv ℝ i (g n) x‖ := by rw [norm_smul, Real.norm_of_nonneg];
         positivity
       _ ≤ M⁻¹ * δ n * M := (mul_le_mul_of_nonneg_left ((hR i x).trans (IR i hi)) (by positivity))
       _ = δ n := by field_simp [M_pos.ne']
@@ -177,7 +177,7 @@ theorem IsOpen.exists_smooth_support_eq {s : Set E} (hs : IsOpen s) :
     intro x
     refine' summable_of_nnnorm_bounded _ δc.summable fun n => _
     rw [← NNReal.coe_le_coe, coe_nnnorm]
-    simpa only [norm_iteratedFderiv_zero] using hr n 0 (zero_le n) x
+    simpa only [norm_iteratedFDeriv_zero] using hr n 0 (zero_le n) x
   refine' ⟨fun x => ∑' n, (r n • g n) x, _, _, _⟩
   · apply subset.antisymm
     · intro x hx
@@ -206,7 +206,7 @@ theorem IsOpen.exists_smooth_support_eq {s : Set E} (hs : IsOpen s) :
     apply tsum_le_tsum _ (S y) A.summable
     intro n
     apply (le_abs_self _).trans
-    simpa only [norm_iteratedFderiv_zero] using hr n 0 (zero_le n) y
+    simpa only [norm_iteratedFDeriv_zero] using hr n 0 (zero_le n) y
 #align is_open.exists_smooth_support_eq IsOpen.exists_smooth_support_eq
 
 end

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

@@ -31,7 +31,7 @@ noncomputable section
 open
   Set Metric TopologicalSpace Function Asymptotics MeasureTheory FiniteDimensional ContinuousLinearMap Filter MeasureTheory.Measure
 
-open Pointwise Topology NNReal BigOperators convolution
+open scoped Pointwise Topology NNReal BigOperators convolution
 
 variable {E : Type _} [NormedAddCommGroup E]
 

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

@@ -164,13 +164,9 @@ theorem IsOpen.exists_smooth_support_eq {s : Set E} (hs : IsOpen s) :
       linarith
     refine' ⟨M⁻¹ * δ n, by positivity, fun i hi x => _⟩
     calc
-      ‖iteratedFderiv ℝ i ((M⁻¹ * δ n) • g n) x‖ = ‖(M⁻¹ * δ n) • iteratedFderiv ℝ i (g n) x‖ :=
-        by
-        rw [iteratedFderiv_const_smul_apply]
-        exact (g_smooth n).of_le le_top
-      _ = M⁻¹ * δ n * ‖iteratedFderiv ℝ i (g n) x‖ :=
-        by
-        rw [norm_smul, Real.norm_of_nonneg]
+      ‖iteratedFderiv ℝ i ((M⁻¹ * δ n) • g n) x‖ = ‖(M⁻¹ * δ n) • iteratedFderiv ℝ i (g n) x‖ := by
+        rw [iteratedFderiv_const_smul_apply]; exact (g_smooth n).of_le le_top
+      _ = M⁻¹ * δ n * ‖iteratedFderiv ℝ i (g n) x‖ := by rw [norm_smul, Real.norm_of_nonneg];
         positivity
       _ ≤ M⁻¹ * δ n * M := (mul_le_mul_of_nonneg_left ((hR i x).trans (IR i hi)) (by positivity))
       _ = δ n := by field_simp [M_pos.ne']
@@ -193,8 +189,7 @@ theorem IsOpen.exists_smooth_support_eq {s : Set E} (hs : IsOpen s) :
         exact g_s n hx
       simp only [this, MulZeroClass.mul_zero, tsum_zero]
     · intro x hx
-      obtain ⟨n, hn⟩ : ∃ n, x ∈ support (g n)
-      exact s_g x hx
+      obtain ⟨n, hn⟩ : ∃ n, x ∈ support (g n); exact s_g x hx
       have I : 0 < r n * g n x := mul_pos (rpos n) (lt_of_le_of_ne (g_nonneg n x) (Ne.symm hn))
       exact ne_of_gt (tsum_pos (S x) (fun i => mul_nonneg (rpos i).le (g_nonneg i x)) n I)
   · refine'
@@ -260,8 +255,7 @@ theorem u_exists :
         simpa using hx
       simp only [mem_support, Classical.not_not] at I1 I2
       simp only [I1, I2, add_zero, zero_div]
-  · intro x
-    simp only [add_comm, neg_neg]
+  · intro x; simp only [add_comm, neg_neg]
 #align exists_cont_diff_bump_base.u_exists ExistsContDiffBumpBase.u_exists
 
 variable {E}
@@ -317,8 +311,7 @@ theorem u_int_pos : 0 < ∫ x : E, u x ∂μ :=
   by
   refine' (integral_pos_iff_support_of_nonneg u_nonneg _).mpr _
   · exact (u_continuous E).integrable_of_hasCompactSupport (u_compact_support E)
-  · rw [u_support]
-    exact measure_ball_pos _ _ zero_lt_one
+  · rw [u_support]; exact measure_ball_pos _ _ zero_lt_one
 #align exists_cont_diff_bump_base.u_int_pos ExistsContDiffBumpBase.u_int_pos
 
 variable {E}
@@ -330,9 +323,7 @@ def w (D : ℝ) (x : E) : ℝ :=
 #align exists_cont_diff_bump_base.W ExistsContDiffBumpBase.w
 
 theorem w_def (D : ℝ) :
-    (w D : E → ℝ) = fun x => ((∫ x : E, u x ∂μ) * |D| ^ finrank ℝ E)⁻¹ • u (D⁻¹ • x) :=
-  by
-  ext1 x
+    (w D : E → ℝ) = fun x => ((∫ x : E, u x ∂μ) * |D| ^ finrank ℝ E)⁻¹ • u (D⁻¹ • x) := by ext1 x;
   rfl
 #align exists_cont_diff_bump_base.W_def ExistsContDiffBumpBase.w_def
 
@@ -408,9 +399,7 @@ theorem y_eq_one_of_mem_closedBall {D : ℝ} {x : E} (Dpos : 0 < D)
     intro h'y
     linarith only [mem_ball.1 (C hy), h'y]
   have Bx : φ x = 1 := B _ (mem_ball_self Dpos)
-  have B' : ∀ y, y ∈ ball x D → φ y = φ x := by
-    rw [Bx]
-    exact B
+  have B' : ∀ y, y ∈ ball x D → φ y = φ x := by rw [Bx]; exact B
   rw [convolution_eq_right' _ (le_of_eq (W_support E Dpos)) B']
   simp only [lsmul_apply, Algebra.id.smul_eq_mul, integral_mul_right, W_integral E Dpos, Bx,
     one_mul]
@@ -430,9 +419,7 @@ theorem y_eq_zero_of_not_mem_ball {D : ℝ} {x : E} (Dpos : 0 < D) (hx : x ∉ b
       linarith only [h'y]
     exact hx (C (mem_ball_comm.1 hy))
   have Bx : φ x = 0 := B _ (mem_ball_self Dpos)
-  have B' : ∀ y, y ∈ ball x D → φ y = φ x := by
-    rw [Bx]
-    exact B
+  have B' : ∀ y, y ∈ ball x D → φ y = φ x := by rw [Bx]; exact B
   rw [convolution_eq_right' _ (le_of_eq (W_support E Dpos)) B']
   simp only [lsmul_apply, Algebra.id.smul_eq_mul, Bx, MulZeroClass.mul_zero, integral_const]
 #align exists_cont_diff_bump_base.Y_eq_zero_of_not_mem_ball ExistsContDiffBumpBase.y_eq_zero_of_not_mem_ball
@@ -531,8 +518,7 @@ theorem y_smooth : ContDiffOn ℝ ⊤ (uncurry y) (Ioo (0 : ℝ) 1 ×ˢ (univ :
       simp_rw [← Real.norm_eq_abs]
       apply @ContDiffOn.norm ℝ
       · exact contDiffOn_fst
-      · intro x hx
-        exact ne_of_gt hx.1.1
+      · intro x hx; exact ne_of_gt hx.1.1
     · apply (u_smooth E).comp_contDiffOn
       exact ContDiffOn.smul (cont_diff_on_fst.inv fun x hx => ne_of_gt hx.1.1) contDiffOn_snd
 #align exists_cont_diff_bump_base.Y_smooth ExistsContDiffBumpBase.y_smooth
@@ -554,10 +540,7 @@ instance (priority := 100) {E : Type _} [NormedAddCommGroup E] [NormedSpace ℝ
   by
   refine' ⟨⟨_⟩⟩
   borelize E
-  have IR : ∀ R : ℝ, 1 < R → 0 < (R - 1) / (R + 1) :=
-    by
-    intro R hR
-    apply div_pos <;> linarith
+  have IR : ∀ R : ℝ, 1 < R → 0 < (R - 1) / (R + 1) := by intro R hR; apply div_pos <;> linarith
   exact
     { toFun := fun R x => if 1 < R then Y ((R - 1) / (R + 1)) (((R + 1) / 2)⁻¹ • x) else 0
       mem_Icc := fun R x => by
@@ -605,9 +588,7 @@ instance (priority := 100) {E : Type _} [NormedAddCommGroup E] [NormedSpace ℝ
         calc
           2 / (R + 1) * ‖x‖ ≤ 2 / (R + 1) * 1 :=
             mul_le_mul_of_nonneg_left hx (div_nonneg zero_le_two A.le)
-          _ = 1 - (R - 1) / (R + 1) := by
-            field_simp [A.ne']
-            ring
+          _ = 1 - (R - 1) / (R + 1) := by field_simp [A.ne'] ; ring
           
       support := fun R hR => by
         have A : 0 < (R + 1) / 2 := by linarith

mathlib commit https://github.com/leanprover-community/mathlib/commit/f51de8769c34652d82d1c8e5f8f18f8374782bed

@@ -4,14 +4,14 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel
 
 ! This file was ported from Lean 3 source module analysis.calculus.bump_function_findim
-! leanprover-community/mathlib commit f0c8bf9245297a541f468be517f1bde6195105e9
+! leanprover-community/mathlib commit fd5edc43dc4f10b85abfe544b88f82cf13c5f844
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
 import Mathbin.Analysis.Calculus.Series
 import Mathbin.Analysis.Convolution
 import Mathbin.Analysis.InnerProductSpace.EuclideanDist
-import Mathbin.MeasureTheory.Measure.HaarLebesgue
+import Mathbin.MeasureTheory.Measure.Haar.NormedSpace
 import Mathbin.Data.Set.Pointwise.Support
 
 /-!

mathlib commit https://github.com/leanprover-community/mathlib/commit/738054fa93d43512da144ec45ce799d18fd44248

@@ -4,13 +4,14 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel
 
 ! This file was ported from Lean 3 source module analysis.calculus.bump_function_findim
-! leanprover-community/mathlib commit 2c1d8ca2812b64f88992a5294ea3dba144755cd1
+! leanprover-community/mathlib commit f0c8bf9245297a541f468be517f1bde6195105e9
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
 import Mathbin.Analysis.Calculus.Series
 import Mathbin.Analysis.Convolution
 import Mathbin.Analysis.InnerProductSpace.EuclideanDist
+import Mathbin.MeasureTheory.Measure.HaarLebesgue
 import Mathbin.Data.Set.Pointwise.Support
 
 /-!

mathlib commit https://github.com/leanprover-community/mathlib/commit/92c69b77c5a7dc0f7eeddb552508633305157caa

@@ -308,14 +308,14 @@ theorem u_neg (x : E) : u (-x) = u x :=
 variable [MeasurableSpace E] [BorelSpace E]
 
 -- mathport name: exprμ
-local notation "μ" => MeasureTheory.Measure.add_haar
+local notation "μ" => MeasureTheory.Measure.addHaar
 
 variable (E)
 
 theorem u_int_pos : 0 < ∫ x : E, u x ∂μ :=
   by
   refine' (integral_pos_iff_support_of_nonneg u_nonneg _).mpr _
-  · exact (u_continuous E).integrableOfHasCompactSupport (u_compact_support E)
+  · exact (u_continuous E).integrable_of_hasCompactSupport (u_compact_support E)
   · rw [u_support]
     exact measure_ball_pos _ _ zero_lt_one
 #align exists_cont_diff_bump_base.u_int_pos ExistsContDiffBumpBase.u_int_pos

mathlib commit https://github.com/leanprover-community/mathlib/commit/36b8aa61ea7c05727161f96a0532897bd72aedab

@@ -4,15 +4,14 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel
 
 ! This file was ported from Lean 3 source module analysis.calculus.bump_function_findim
-! leanprover-community/mathlib commit 8c8c544bf24ced19b1e76c34bb3262bdae620f82
+! leanprover-community/mathlib commit 2c1d8ca2812b64f88992a5294ea3dba144755cd1
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
-import Mathbin.Analysis.Calculus.BumpFunctionInner
 import Mathbin.Analysis.Calculus.Series
 import Mathbin.Analysis.Convolution
+import Mathbin.Analysis.InnerProductSpace.EuclideanDist
 import Mathbin.Data.Set.Pointwise.Support
-import Mathbin.MeasureTheory.Measure.HaarLebesgue
 
 /-!
 # Bump functions in finite-dimensional vector spaces

mathlib commit https://github.com/leanprover-community/mathlib/commit/17ad94b4953419f3e3ce3e77da3239c62d1d09f0

@@ -360,7 +360,7 @@ theorem w_integral {D : ℝ} (Dpos : 0 < D) : (∫ x : E, w D x ∂μ) = 1 :=
 theorem w_support {D : ℝ} (Dpos : 0 < D) : support (w D : E → ℝ) = ball 0 D :=
   by
   have B : D • ball (0 : E) 1 = ball 0 D := by
-    rw [smul_unit_ball Dpos.ne', Real.norm_of_nonneg Dpos.le]
+    rw [smul_unitBall Dpos.ne', Real.norm_of_nonneg Dpos.le]
   have C : D ^ finrank ℝ E ≠ 0 := pow_ne_zero _ Dpos.ne'
   simp only [W_def, Algebra.id.smul_eq_mul, support_mul, support_inv, univ_inter,
     support_comp_inv_smul₀ Dpos.ne', u_support, B, support_const (u_int_pos E).ne', support_const C,

mathlib commit https://github.com/leanprover-community/mathlib/commit/3180fab693e2cee3bff62675571264cb8778b212

@@ -191,7 +191,7 @@ theorem IsOpen.exists_smooth_support_eq {s : Set E} (hs : IsOpen s) :
         intro n
         contrapose! hx
         exact g_s n hx
-      simp only [this, mul_zero, tsum_zero]
+      simp only [this, MulZeroClass.mul_zero, tsum_zero]
     · intro x hx
       obtain ⟨n, hn⟩ : ∃ n, x ∈ support (g n)
       exact s_g x hx
@@ -434,7 +434,7 @@ theorem y_eq_zero_of_not_mem_ball {D : ℝ} {x : E} (Dpos : 0 < D) (hx : x ∉ b
     rw [Bx]
     exact B
   rw [convolution_eq_right' _ (le_of_eq (W_support E Dpos)) B']
-  simp only [lsmul_apply, Algebra.id.smul_eq_mul, Bx, mul_zero, integral_const]
+  simp only [lsmul_apply, Algebra.id.smul_eq_mul, Bx, MulZeroClass.mul_zero, integral_const]
 #align exists_cont_diff_bump_base.Y_eq_zero_of_not_mem_ball ExistsContDiffBumpBase.y_eq_zero_of_not_mem_ball
 
 theorem y_nonneg (D : ℝ) (x : E) : 0 ≤ y D x :=

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

@@ -172,7 +172,7 @@ theorem IsOpen.exists_smooth_support_eq {s : Set E} (hs : IsOpen s) :
         by
         rw [norm_smul, Real.norm_of_nonneg]
         positivity
-      _ ≤ M⁻¹ * δ n * M := mul_le_mul_of_nonneg_left ((hR i x).trans (IR i hi)) (by positivity)
+      _ ≤ M⁻¹ * δ n * M := (mul_le_mul_of_nonneg_left ((hR i x).trans (IR i hi)) (by positivity))
       _ = δ n := by field_simp [M_pos.ne']
       
   choose r rpos hr using this

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

Now that I am defining NNRat.cast, I want a definitive answer to this naming issue. Plenty of lemmas in mathlib already use natCast/intCast/ratCast over nat_cast/int_cast/rat_cast, and this matches with the general expectation that underscore-separated name parts correspond to a single declaration.

@@ -357,7 +357,7 @@ def y (D : ℝ) : E → ℝ :=
 theorem y_neg (D : ℝ) (x : E) : y D (-x) = y D x := by
   apply convolution_neg_of_neg_eq
   · filter_upwards with x
-    simp only [w_def, Real.rpow_nat_cast, mul_inv_rev, smul_neg, u_neg, smul_eq_mul, forall_const]
+    simp only [w_def, Real.rpow_natCast, mul_inv_rev, smul_neg, u_neg, smul_eq_mul, forall_const]
   · filter_upwards with x
     simp only [φ, indicator, mem_closedBall, dist_zero_right, norm_neg, forall_const]
 #align exists_cont_diff_bump_base.Y_neg ExistsContDiffBumpBase.y_neg

@@ -54,7 +54,7 @@ theorem exists_smooth_tsupport_subset {s : Set E} {x : E} (hs : s ∈ 𝓝 x) :
   have f_supp : f.support ⊆ Euclidean.ball x d := by
     intro y hy
     have : toEuclidean y ∈ Function.support c := by
-      simpa only [Function.mem_support, Function.comp_apply, Ne.def] using hy
+      simpa only [Function.mem_support, Function.comp_apply, Ne] using hy
     rwa [c.support_eq] at this
   have f_tsupp : tsupport f ⊆ Euclidean.closedBall x d := by
     rw [tsupport, ← Euclidean.closure_ball _ d_pos.ne']
@@ -96,7 +96,7 @@ theorem IsOpen.exists_smooth_support_eq {s : Set E} (hs : IsOpen s) :
       rcases exists_smooth_tsupport_subset (hs.mem_nhds hx) with ⟨f, hf⟩
       let g : ι := ⟨f, (subset_tsupport f).trans hf.1, hf.2.1, hf.2.2.1, hf.2.2.2.1⟩
       have : x ∈ support (g : E → ℝ) := by
-        simp only [hf.2.2.2.2, Subtype.coe_mk, mem_support, Ne.def, one_ne_zero, not_false_iff]
+        simp only [hf.2.2.2.2, Subtype.coe_mk, mem_support, Ne, one_ne_zero, not_false_iff]
       exact mem_iUnion_of_mem _ this
     simp_rw [← this]
     apply isOpen_iUnion_countable
@@ -164,7 +164,7 @@ theorem IsOpen.exists_smooth_support_eq {s : Set E} (hs : IsOpen s) :
   refine' ⟨fun x => ∑' n, (r n • g n) x, _, _, _⟩
   · apply Subset.antisymm
     · intro x hx
-      simp only [Pi.smul_apply, Algebra.id.smul_eq_mul, mem_support, Ne.def] at hx
+      simp only [Pi.smul_apply, Algebra.id.smul_eq_mul, mem_support, Ne] at hx
       contrapose! hx
       have : ∀ n, g n x = 0 := by
         intro n
@@ -435,7 +435,7 @@ theorem y_pos_of_mem_ball {D : ℝ} {x : E} (Dpos : 0 < D) (D_lt_one : D < 1)
     have C : ball z (D * (1 + D - ‖x‖) / (1 + D)) ⊆ support fun y : E => w D y * φ (x - y) := by
       intro y hy
       simp only [support_mul, w_support E Dpos]
-      simp only [φ, mem_inter_iff, mem_support, Ne.def, indicator_apply_eq_zero,
+      simp only [φ, mem_inter_iff, mem_support, Ne, indicator_apply_eq_zero,
         mem_closedBall_zero_iff, one_ne_zero, not_forall, not_false_iff, exists_prop, and_true_iff]
       constructor
       · apply ball_subset_ball' _ hy
@@ -446,9 +446,9 @@ theorem y_pos_of_mem_ball {D : ℝ} {x : E} (Dpos : 0 < D) (D_lt_one : D < 1)
         rfl
       · have ID : ‖D / (1 + D) - 1‖ = 1 / (1 + D) := by
           rw [Real.norm_of_nonpos]
-          · simp only [B.ne', Ne.def, not_false_iff, mul_one, neg_sub, add_tsub_cancel_right,
+          · simp only [B.ne', Ne, not_false_iff, mul_one, neg_sub, add_tsub_cancel_right,
               field_simps]
-          · simp only [B.ne', Ne.def, not_false_iff, mul_one, field_simps]
+          · simp only [B.ne', Ne, not_false_iff, mul_one, field_simps]
             apply div_nonpos_of_nonpos_of_nonneg _ B.le
             linarith only
         rw [← mem_closedBall_iff_norm']

This is presumably not exhaustive, but covers about a hundred instances.

Style opinions (e.g., why a particular change is great/not a good idea) are very welcome; I'm still forming my own.

@@ -356,9 +356,9 @@ def y (D : ℝ) : E → ℝ :=
 
 theorem y_neg (D : ℝ) (x : E) : y D (-x) = y D x := by
   apply convolution_neg_of_neg_eq
-  · apply eventually_of_forall fun x => _
+  · filter_upwards with x
     simp only [w_def, Real.rpow_nat_cast, mul_inv_rev, smul_neg, u_neg, smul_eq_mul, forall_const]
-  · apply eventually_of_forall fun x => _
+  · filter_upwards with x
     simp only [φ, indicator, mem_closedBall, dist_zero_right, norm_neg, forall_const]
 #align exists_cont_diff_bump_base.Y_neg ExistsContDiffBumpBase.y_neg
 

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".

@@ -294,7 +294,7 @@ theorem u_int_pos : 0 < ∫ x : E, u x ∂μ := by
 #align exists_cont_diff_bump_base.u_int_pos ExistsContDiffBumpBase.u_int_pos
 
 variable {E}
--- porting note: `W` upper case
+-- Porting note: `W` upper case
 set_option linter.uppercaseLean3 false
 
 /-- An auxiliary function to construct partitions of unity on finite-dimensional real vector spaces,

This covers many instances, but is not exhaustive.

Independently of whether that syntax should be avoided (similar to #10534), I think all these changes are small improvements.

@@ -123,8 +123,8 @@ theorem IsOpen.exists_smooth_support_eq {s : Set E} (hs : IsOpen s) :
   have g_comp_supp : ∀ n, HasCompactSupport (g n) := fun n => (g0 n).2.2.1
   have g_nonneg : ∀ n x, 0 ≤ g n x := fun n x => ((g0 n).2.2.2.2 (mem_range_self x)).1
   obtain ⟨δ, δpos, c, δc, c_lt⟩ :
-    ∃ δ : ℕ → ℝ≥0, (∀ i : ℕ, 0 < δ i) ∧ ∃ c : NNReal, HasSum δ c ∧ c < 1
-  exact NNReal.exists_pos_sum_of_countable one_ne_zero ℕ
+      ∃ δ : ℕ → ℝ≥0, (∀ i : ℕ, 0 < δ i) ∧ ∃ c : NNReal, HasSum δ c ∧ c < 1 :=
+    NNReal.exists_pos_sum_of_countable one_ne_zero ℕ
   have : ∀ n : ℕ, ∃ r : ℝ, 0 < r ∧ ∀ i ≤ n, ∀ x, ‖iteratedFDeriv ℝ i (r • g n) x‖ ≤ δ n := by
     intro n
     have : ∀ i, ∃ R, ∀ x, ‖iteratedFDeriv ℝ i (fun x => g n x) x‖ ≤ R := by
@@ -172,7 +172,7 @@ theorem IsOpen.exists_smooth_support_eq {s : Set E} (hs : IsOpen s) :
         exact g_s n hx
       simp only [this, mul_zero, tsum_zero]
     · intro x hx
-      obtain ⟨n, hn⟩ : ∃ n, x ∈ support (g n); exact s_g x hx
+      obtain ⟨n, hn⟩ : ∃ n, x ∈ support (g n) := s_g x hx
       have I : 0 < r n * g n x := mul_pos (rpos n) (lt_of_le_of_ne (g_nonneg n x) (Ne.symm hn))
       exact ne_of_gt (tsum_pos (S x) (fun i => mul_nonneg (rpos i).le (g_nonneg i x)) n I)
   · refine'
@@ -215,8 +215,8 @@ theorem u_exists :
       ContDiff ℝ ⊤ u ∧ (∀ x, u x ∈ Icc (0 : ℝ) 1) ∧ support u = ball 0 1 ∧ ∀ x, u (-x) = u x := by
   have A : IsOpen (ball (0 : E) 1) := isOpen_ball
   obtain ⟨f, f_support, f_smooth, f_range⟩ :
-    ∃ f : E → ℝ, f.support = ball (0 : E) 1 ∧ ContDiff ℝ ⊤ f ∧ Set.range f ⊆ Set.Icc 0 1
-  exact A.exists_smooth_support_eq
+      ∃ f : E → ℝ, f.support = ball (0 : E) 1 ∧ ContDiff ℝ ⊤ f ∧ Set.range f ⊆ Set.Icc 0 1 :=
+    A.exists_smooth_support_eq
   have B : ∀ x, f x ∈ Icc (0 : ℝ) 1 := fun x => f_range (mem_range_self x)
   refine' ⟨fun x => (f x + f (-x)) / 2, _, _, _, _⟩
   · exact (f_smooth.add (f_smooth.comp contDiff_neg)).div_const _

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

@@ -105,7 +105,7 @@ theorem IsOpen.exists_smooth_support_eq {s : Set E} (hs : IsOpen s) :
   obtain ⟨g0, hg⟩ : ∃ g0 : ℕ → ι, T = range g0 := by
     apply Countable.exists_eq_range T_count
     rcases eq_empty_or_nonempty T with (rfl | hT)
-    · simp only [iUnion_false, iUnion_empty] at hT
+    · simp only [ι, iUnion_false, iUnion_empty] at hT
       simp only [← hT, mem_empty_iff_false, iUnion_of_empty, iUnion_empty, Set.not_nonempty_empty]
           at h's
     · exact hT

Currently, the same file contains the facts that series of functions are continuous (resp. smooth) under suitable assumption. I will need the result on continuity in a file of more topological nature. To avoid importing all calculus in this file, this PR splits the file Analysis.Calculus.Series into Analysis.Calculus.SmoothSeries and Analysis.NormedSpace.FunctionSeries.

It's purely a splitting PR, no result added or removed.

@@ -3,7 +3,7 @@ Copyright (c) 2022 Sébastien Gouëzel. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel
 -/
-import Mathlib.Analysis.Calculus.Series
+import Mathlib.Analysis.Calculus.SmoothSeries
 import Mathlib.Analysis.Calculus.BumpFunction.InnerProduct
 import Mathlib.Analysis.Convolution
 import Mathlib.Analysis.InnerProductSpace.EuclideanDist

Slightly generalize the definition of the operator norm on ContinuousMultilinearMap so that it works when the spaces have seminorms (and not just norms). There are two new lemmas MultilinearMap.zero_of_continuous_of_one_entry_norm_zero and MultilinearMap.bound_of_shell_of_continuous that do the work of the old lemma MultilinearMap.bound_of_shell; I kept that last lemma (with the same hypotheses as before) in case it is useful somewhere else. Also, ContinuousMultilinearMap only gets a SeminormedAddCommGroup instance in general, which is upgraded to a NormedAddCommGroup instance if the target space is normed. Other lemmas and their proofs are unchanged, they are just rearranged to separate the ones that work for general seminormed spaces and the ones that only work for normed spaces.

Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Yury G. Kudryashov <urkud@urkud.name> Co-authored-by: smorel394 <67864981+smorel394@users.noreply.github.com>

@@ -153,7 +153,7 @@ theorem IsOpen.exists_smooth_support_eq {s : Set E} (hs : IsOpen s) :
       ‖iteratedFDeriv ℝ i ((M⁻¹ * δ n) • g n) x‖ = ‖(M⁻¹ * δ n) • iteratedFDeriv ℝ i (g n) x‖ := by
         rw [iteratedFDeriv_const_smul_apply]; exact (g_smooth n).of_le le_top
       _ = M⁻¹ * δ n * ‖iteratedFDeriv ℝ i (g n) x‖ := by
-        rw [norm_smul, Real.norm_of_nonneg]; positivity
+        rw [norm_smul _ (iteratedFDeriv ℝ i (g n) x), Real.norm_of_nonneg]; positivity
       _ ≤ M⁻¹ * δ n * M := (mul_le_mul_of_nonneg_left ((hR i x).trans (IR i hi)) (by positivity))
       _ = δ n := by field_simp
   choose r rpos hr using this

This uses the improved shake script from #9772 to reduce imports across mathlib. The corresponding noshake.json file has been added to #9772.

Co-authored-by: Mario Carneiro <di.gama@gmail.com>

@@ -4,11 +4,12 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel
 -/
 import Mathlib.Analysis.Calculus.Series
-import Mathlib.Analysis.Calculus.BumpFunction.Convolution
 import Mathlib.Analysis.Calculus.BumpFunction.InnerProduct
+import Mathlib.Analysis.Convolution
 import Mathlib.Analysis.InnerProductSpace.EuclideanDist
-import Mathlib.MeasureTheory.Measure.Haar.NormedSpace
 import Mathlib.Data.Set.Pointwise.Support
+import Mathlib.MeasureTheory.Measure.Haar.NormedSpace
+import Mathlib.MeasureTheory.Measure.Haar.Unique
 
 #align_import analysis.calculus.bump_function_findim from "leanprover-community/mathlib"@"fd5edc43dc4f10b85abfe544b88f82cf13c5f844"
 

@@ -551,8 +551,7 @@ instance (priority := 100) {E : Type*} [NormedAddCommGroup E] [NormedSpace ℝ E
         simp only [norm_smul, inv_div, mem_closedBall_zero_iff, Real.norm_eq_abs, abs_div, abs_two,
           abs_of_nonneg A.le]
         calc
-          2 / (R + 1) * ‖x‖ ≤ 2 / (R + 1) * 1 :=
-            mul_le_mul_of_nonneg_left hx (div_nonneg zero_le_two A.le)
+          2 / (R + 1) * ‖x‖ ≤ 2 / (R + 1) := mul_le_of_le_one_right (by positivity) hx
           _ = 1 - (R - 1) / (R + 1) := by field_simp; ring
       support := fun R hR => by
         have A : 0 < (R + 1) / 2 := by linarith

Follow-up #9184

@@ -110,11 +110,10 @@ theorem IsOpen.exists_smooth_support_eq {s : Set E} (hs : IsOpen s) :
     · exact hT
   let g : ℕ → E → ℝ := fun n => (g0 n).1
   have g_s : ∀ n, support (g n) ⊆ s := fun n => (g0 n).2.1
-  have s_g : ∀ x ∈ s, ∃ n, x ∈ support (g n) := by
-    intro x hx
+  have s_g : ∀ x ∈ s, ∃ n, x ∈ support (g n) := fun x hx ↦ by
     rw [← hT] at hx
-    obtain ⟨i, iT, hi⟩ : ∃ (i : ι) (_ : i ∈ T), x ∈ support (i : E → ℝ) := by
-      simpa only [mem_iUnion] using hx
+    obtain ⟨i, iT, hi⟩ : ∃ i ∈ T, x ∈ support (i : E → ℝ) := by
+      simpa only [mem_iUnion, exists_prop] using hx
     rw [hg, mem_range] at iT
     rcases iT with ⟨n, hn⟩
     rw [← hn] at hi

Using Lean4's named arguments, we manage to remove a few hard-to-read explicit function calls [@foo](https://github.com/foo) _ _ _ _ _ ... which used to be necessary in Lean3.

Occasionally, this results in slightly longer code. The benefit of named arguments is readability, as well as to reduce the brittleness of the code when the argument order is changed.

Co-authored-by: Michael Rothgang <rothgami@math.hu-berlin.de>

@@ -484,7 +484,7 @@ theorem y_smooth : ContDiffOn ℝ ⊤ (uncurry y) (Ioo (0 : ℝ) 1 ×ˢ (univ :
           ne_of_gt (mul_pos (u_int_pos E) (pow_pos (abs_pos_of_pos hx.1.1) (finrank ℝ E)))
       apply ContDiffOn.pow
       simp_rw [← Real.norm_eq_abs]
-      apply @ContDiffOn.norm ℝ
+      apply ContDiffOn.norm ℝ
       · exact contDiffOn_fst
       · intro x hx; exact ne_of_gt hx.1.1
     · apply (u_smooth E).comp_contDiffOn

Rename

• summable_of_norm_bounded -> Summable.of_norm_bounded;
• summable_of_norm_bounded_eventually -> Summable.of_norm_bounded_eventually;
• summable_of_nnnorm_bounded -> Summable.of_nnnorm_bounded;
• summable_of_summable_norm -> Summable.of_norm;
• summable_of_summable_nnnorm -> Summable.of_nnnorm;

New lemmas

• Summable.of_norm_bounded_eventually_nat
• Summable.norm

Misc changes

• Golf a few proofs.

@@ -157,9 +157,8 @@ theorem IsOpen.exists_smooth_support_eq {s : Set E} (hs : IsOpen s) :
       _ ≤ M⁻¹ * δ n * M := (mul_le_mul_of_nonneg_left ((hR i x).trans (IR i hi)) (by positivity))
       _ = δ n := by field_simp
   choose r rpos hr using this
-  have S : ∀ x, Summable fun n => (r n • g n) x := by
-    intro x
-    refine' summable_of_nnnorm_bounded _ δc.summable fun n => _
+  have S : ∀ x, Summable fun n => (r n • g n) x := fun x ↦ by
+    refine' .of_nnnorm_bounded _ δc.summable fun n => _
     rw [← NNReal.coe_le_coe, coe_nnnorm]
     simpa only [norm_iteratedFDeriv_zero] using hr n 0 (zero_le n) x
   refine' ⟨fun x => ∑' n, (r n • g n) x, _, _, _⟩

Use Bornology.IsBounded instead.

@@ -27,7 +27,7 @@ the indicator function of `closedBall 0 1` with a function as above with `s = ba
 noncomputable section
 
 open Set Metric TopologicalSpace Function Asymptotics MeasureTheory FiniteDimensional
-  ContinuousLinearMap Filter MeasureTheory.Measure
+  ContinuousLinearMap Filter MeasureTheory.Measure Bornology
 
 open scoped Pointwise Topology NNReal BigOperators Convolution
 
@@ -59,10 +59,9 @@ theorem exists_smooth_tsupport_subset {s : Set E} {x : E} (hs : s ∈ 𝓝 x) :
     rw [tsupport, ← Euclidean.closure_ball _ d_pos.ne']
     exact closure_mono f_supp
   refine' ⟨f, f_tsupp.trans hd, _, _, _, _⟩
-  · refine' isCompact_of_isClosed_bounded isClosed_closure _
-    have : Bounded (Euclidean.closedBall x d) := Euclidean.isCompact_closedBall.bounded
-    apply this.mono _
-    refine' (IsClosed.closure_subset_iff Euclidean.isClosed_closedBall).2 _
+  · refine' isCompact_of_isClosed_isBounded isClosed_closure _
+    have : IsBounded (Euclidean.closedBall x d) := Euclidean.isCompact_closedBall.isBounded
+    refine this.subset (Euclidean.isClosed_closedBall.closure_subset_iff.2 ?_)
     exact f_supp.trans Euclidean.ball_subset_closedBall
   · apply c.contDiff.comp
     exact ContinuousLinearEquiv.contDiff _

The main reasons is that having h : 0 < denom in the context should suffice for field_simp to do its job, without the need to manually pass h.ne or similar.

Quite a few have := … ≠ 0 could be dropped, and some field_simp calls no longer need explicit arguments; this is promising.

This does break some proofs where field_simp was not used as a closing tactic, and it now shuffles terms around a bit different. These were fixed. Using field_simp in the middle of a proof seems rather fragile anyways.

As a drive-by contribution, positivity now knows about π > 0.

fixes: #4835

Co-authored-by: Matthew Ballard <matt@mrb.email>

@@ -139,7 +139,6 @@ theorem IsOpen.exists_smooth_support_eq {s : Set E} (hs : IsOpen s) :
       exact ⟨R, fun x => hR (mem_range_self _)⟩
     choose R hR using this
     let M := max (((Finset.range (n + 1)).image R).max' (by simp)) 1
-    have M_pos : 0 < M := zero_lt_one.trans_le (le_max_right _ _)
     have δnpos : 0 < δ n := δpos n
     have IR : ∀ i ≤ n, R i ≤ M := by
       intro i hi
@@ -157,7 +156,7 @@ theorem IsOpen.exists_smooth_support_eq {s : Set E} (hs : IsOpen s) :
       _ = M⁻¹ * δ n * ‖iteratedFDeriv ℝ i (g n) x‖ := by
         rw [norm_smul, Real.norm_of_nonneg]; positivity
       _ ≤ M⁻¹ * δ n * M := (mul_le_mul_of_nonneg_left ((hR i x).trans (IR i hi)) (by positivity))
-      _ = δ n := by field_simp [M_pos.ne']
+      _ = δ n := by field_simp
   choose r rpos hr using this
   have S : ∀ x, Summable fun n => (r n • g n) x := by
     intro x
@@ -328,7 +327,7 @@ variable (E)
 theorem w_integral {D : ℝ} (Dpos : 0 < D) : ∫ x : E, w D x ∂μ = 1 := by
   simp_rw [w, integral_smul]
   rw [integral_comp_inv_smul_of_nonneg μ (u : E → ℝ) Dpos.le, abs_of_nonneg Dpos.le, mul_comm]
-  field_simp [Dpos.ne', (u_int_pos E).ne']
+  field_simp [(u_int_pos E).ne']
 #align exists_cont_diff_bump_base.W_integral ExistsContDiffBumpBase.w_integral
 
 theorem w_support {D : ℝ} (Dpos : 0 < D) : support (w D : E → ℝ) = ball 0 D := by
@@ -557,7 +556,7 @@ instance (priority := 100) {E : Type*} [NormedAddCommGroup E] [NormedSpace ℝ E
         calc
           2 / (R + 1) * ‖x‖ ≤ 2 / (R + 1) * 1 :=
             mul_le_mul_of_nonneg_left hx (div_nonneg zero_le_two A.le)
-          _ = 1 - (R - 1) / (R + 1) := by field_simp [A.ne']; ring
+          _ = 1 - (R - 1) / (R + 1) := by field_simp; ring
       support := fun R hR => by
         have A : 0 < (R + 1) / 2 := by linarith
         have A' : 0 < R + 1 := by linarith
@@ -565,8 +564,7 @@ instance (priority := 100) {E : Type*} [NormedAddCommGroup E] [NormedSpace ℝ E
         simp only [hR, if_true, support_comp_inv_smul₀ A.ne', y_support _ (IR R hR) C,
           _root_.smul_ball A.ne', Real.norm_of_nonneg A.le, smul_zero]
         refine' congr (congr_arg ball (Eq.refl 0)) _
-        field_simp [A'.ne']
-        ring }
+        field_simp; ring }
 
 end ExistsContDiffBumpBase
 

Search&replace MulZeroClass.mul_zero -> mul_zero, MulZeroClass.zero_mul -> zero_mul.

These were introduced by Mathport, as the full name of mul_zero is actually MulZeroClass.mul_zero (it's exported with the short name).

@@ -173,7 +173,7 @@ theorem IsOpen.exists_smooth_support_eq {s : Set E} (hs : IsOpen s) :
         intro n
         contrapose! hx
         exact g_s n hx
-      simp only [this, MulZeroClass.mul_zero, tsum_zero]
+      simp only [this, mul_zero, tsum_zero]
     · intro x hx
       obtain ⟨n, hn⟩ : ∃ n, x ∈ support (g n); exact s_g x hx
       have I : 0 < r n * g n x := mul_pos (rpos n) (lt_of_le_of_ne (g_nonneg n x) (Ne.symm hn))
@@ -399,7 +399,7 @@ theorem y_eq_zero_of_not_mem_ball {D : ℝ} {x : E} (Dpos : 0 < D) (hx : x ∉ b
   have Bx : φ x = 0 := B _ (mem_ball_self Dpos)
   have B' : ∀ y, y ∈ ball x D → φ y = φ x := by rw [Bx]; exact B
   rw [convolution_eq_right' _ (le_of_eq (w_support E Dpos)) B']
-  simp only [lsmul_apply, Algebra.id.smul_eq_mul, Bx, MulZeroClass.mul_zero, integral_const]
+  simp only [lsmul_apply, Algebra.id.smul_eq_mul, Bx, mul_zero, integral_const]
 #align exists_cont_diff_bump_base.Y_eq_zero_of_not_mem_ball ExistsContDiffBumpBase.y_eq_zero_of_not_mem_ball
 
 theorem y_nonneg (D : ℝ) (x : E) : 0 ≤ y D x :=

Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

@@ -237,7 +237,6 @@ theorem u_exists :
     · have I1 : x ∉ support f := by rwa [f_support]
       have I2 : -x ∉ support f := by
         rw [f_support]
-        simp only at hx
         simpa using hx
       simp only [mem_support, Classical.not_not] at I1 I2
       simp only [I1, I2, add_zero, zero_div]
@@ -459,7 +458,6 @@ theorem y_pos_of_mem_ball {D : ℝ} {x : E} (Dpos : 0 < D) (D_lt_one : D < 1)
         apply closedBall_subset_closedBall' _ (ball_subset_closedBall hy)
         rw [← one_smul ℝ x, dist_eq_norm, hz, ← sub_smul, one_smul, norm_smul, ID]
         simp only [B.ne', div_le_iff B, field_simps]
-        simp only [mem_ball_zero_iff] at hx
         nlinarith only [hx, D_lt_one]
     apply lt_of_lt_of_le _ (measure_mono C)
     apply measure_ball_pos

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

This has nice performance benefits.

@@ -31,7 +31,7 @@ open Set Metric TopologicalSpace Function Asymptotics MeasureTheory FiniteDimens
 
 open scoped Pointwise Topology NNReal BigOperators Convolution
 
-variable {E : Type _} [NormedAddCommGroup E]
+variable {E : Type*} [NormedAddCommGroup E]
 
 section
 
@@ -507,7 +507,7 @@ variable {E}
 
 end HelperDefinitions
 
-instance (priority := 100) {E : Type _} [NormedAddCommGroup E] [NormedSpace ℝ E]
+instance (priority := 100) {E : Type*} [NormedAddCommGroup E] [NormedSpace ℝ E]
     [FiniteDimensional ℝ E] : HasContDiffBump E := by
   refine' ⟨⟨_⟩⟩
   borelize E

• depends on: #5966

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

@@ -2,11 +2,6 @@
 Copyright (c) 2022 Sébastien Gouëzel. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel
-
-! This file was ported from Lean 3 source module analysis.calculus.bump_function_findim
-! leanprover-community/mathlib commit fd5edc43dc4f10b85abfe544b88f82cf13c5f844
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Analysis.Calculus.Series
 import Mathlib.Analysis.Calculus.BumpFunction.Convolution
@@ -15,6 +10,8 @@ import Mathlib.Analysis.InnerProductSpace.EuclideanDist
 import Mathlib.MeasureTheory.Measure.Haar.NormedSpace
 import Mathlib.Data.Set.Pointwise.Support
 
+#align_import analysis.calculus.bump_function_findim from "leanprover-community/mathlib"@"fd5edc43dc4f10b85abfe544b88f82cf13c5f844"
+
 /-!
 # Bump functions in finite-dimensional vector spaces
 

Fixes #4755

@@ -9,7 +9,8 @@ Authors: Sébastien Gouëzel
 ! if you have ported upstream changes.
 -/
 import Mathlib.Analysis.Calculus.Series
-import Mathlib.Analysis.Convolution
+import Mathlib.Analysis.Calculus.BumpFunction.Convolution
+import Mathlib.Analysis.Calculus.BumpFunction.InnerProduct
 import Mathlib.Analysis.InnerProductSpace.EuclideanDist
 import Mathlib.MeasureTheory.Measure.Haar.NormedSpace
 import Mathlib.Data.Set.Pointwise.Support

@@ -91,8 +91,8 @@ theorem IsOpen.exists_smooth_support_eq {s : Set E} (hs : IsOpen s) :
       ⟨fun _ => 0, Function.support_zero, contDiff_const, by
         simp only [range_const, singleton_subset_iff, left_mem_Icc, zero_le_one]⟩
   let ι := { f : E → ℝ // f.support ⊆ s ∧ HasCompactSupport f ∧ ContDiff ℝ ⊤ f ∧ range f ⊆ Icc 0 1 }
-  obtain ⟨T, T_count, hT⟩ : ∃ T : Set ι, T.Countable ∧ (⋃ f ∈ T, support (f : E → ℝ)) = s := by
-    have : (⋃ f : ι, (f : E → ℝ).support) = s := by
+  obtain ⟨T, T_count, hT⟩ : ∃ T : Set ι, T.Countable ∧ ⋃ f ∈ T, support (f : E → ℝ) = s := by
+    have : ⋃ f : ι, (f : E → ℝ).support = s := by
       refine' Subset.antisymm (iUnion_subset fun f => f.2.1) _
       intro x hx
       rcases exists_smooth_tsupport_subset (hs.mem_nhds hx) with ⟨f, hf⟩

@@ -570,8 +570,7 @@ instance (priority := 100) {E : Type _} [NormedAddCommGroup E] [NormedSpace ℝ
           _root_.smul_ball A.ne', Real.norm_of_nonneg A.le, smul_zero]
         refine' congr (congr_arg ball (Eq.refl 0)) _
         field_simp [A'.ne']
-        ring
-         }
+        ring }
 
 end ExistsContDiffBumpBase
 

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